Publications
Most recent papers

Yuri, V. Lvov, Victor S. L'vov , Energy flux and highorder statistics of hydrodynamic turbulence, arXiv:2303.06803
2024

(2024) Applied Physics Letters. 124, 9, 092402. Abstract
The creation of temperature variations in magnetization, and hence in the frequencies of the magnon spectrum in laserheated regions of magnetic films, is an important method for studying Bose\u2013Einstein condensation of magnons, magnon supercurrents, Bogoliubov waves, and similar phenomena. In our study, we demonstrate analytically, numerically, and experimentally that, in addition to the magnetization variations, it is necessary to consider the connected variations of the demagnetizing field. In the case of a heatinduced local minimum of the saturation magnetization, the combination of these two effects results in a local increase in the minimum frequency value of the magnon dispersion at which the Bose\u2013Einstein condensate emerges. As a result, a magnon supercurrent directed away from the hot region is formed.

(2024) Physical Review B. 109, 1, p. 014301 014301. Abstract
We consider flux equilibrium in dissipative nonlinear wave systems subject to external energy pumping. In such systems, the elementary excitations, or quasiparticles, can create a BoseEinstein condensate. We develop a theory on the BoseEinstein condensation of quasiparticles for various regimes of external excitation, ranging from weak and stationary to ultrastrong pumping, enabling us to determine the number of quasiparticles near the bottom of the energy spectrum and their distribution along wave vectors. We identify physical phenomena leading to condensation in each of the regimes. For weak stationary pumping, where the distribution of quasiparticles deviates only slightly from thermodynamic equilibrium, we define a range of pumping parameters where the condensation occurs and estimate the density of the condensate and the fraction of the condensed quasiparticles. As the pumping amplitude increases, a powerful influx of injected quasiparticles is created by the KolmogorovZakharov scattering cascade, leading to their BoseEinstein condensation. With even stronger pumping, kinetic instability may occur, resulting in a direct transfer of injected quasiparticles to the bottom of the spectrum. For the case of ultrastrong parametric pumping, we have developed a stationary nonlinear theory of kinetic instability. The theory agrees qualitatively with experimental data obtained using Brillouin light scattering spectroscopy during parametric pumping of magnons in roomtemperature films of yttriumiron garnet.

(2024) 2024 IEEE International Magnetic Conference  Short Papers, INTERMAG Short Papers 2024  Proceedings. Abstract
Spatial variations in the saturation magnetization of magnetic samples, in which the magnon BoseEinstein condensate is prepared, lead to the appearance of supercurrents and excitation of Bogoliubov waves, which can be exploited for data transfer and processing. Here, we show theoretically and experimentally that demagnetization fields arising in the magnetization landscape strongly influence the dynamics of magnon supercurrents. In our experiment, local laser heating of a tangentially magnetized film of yttrium iron garnet increases the magnetic field in the region of reduced magnetization and, as a result, elevates the bottom of the spinwave spectrum, where BoseEinstein condensate is formed. This causes a magnon supercurrent directed outward from the hot region.
2023

(2023) Journal of Fluid Mechanics. 975, A17. Abstract
We use the DysonWyld diagrammatic technique to analyse the infinite series for the correlation functions of the velocity in hydrodynamic turbulence. We demonstrate the fundamental role played by the triple correlator of the velocity in determining the entire statistics of the hydrodynamic turbulence. All higherorder correlation functions are expressed through the triple correlator. This is shown through the suggested triangular resummation of the infinite diagrammatic series for multipoint correlation functions. The triangular resummation is the next logical step after the DysonWyld line resummation for the Green's function and the double correlator. In particular, it allows us to explain why the inverse cascade of the twodimensional hydrodynamic turbulence is close to Gaussian. Since the triple correlator dictates the flux of energy through the scales, we support the Kolmogorov1941 idea that is one of the main characteristics of hydrodynamic turbulence.

(2023) Phys. Rev. Lett.. 131, 15, 156705. Abstract
Nonlinear interactions are crucial in science and engineering. Here, we investigate wave interactions in a highly nonlinear magnetic system driven by parametric pumping leading to BoseEinstein condensation of spinwave quanta\u2014magnons. Using Brillouin light scattering spectroscopy in yttriumiron garnet films, we found and identified a set of nonlinear processes resulting in offresonant spinwave excitations\u2014virtual magnons. In particular, we discovered a dynamically strong, correlationenhanced fourwave interaction process of the magnon condensate with pairs of parametric magnons having opposite wave vectors and fully correlated phases.

(2023) Nature Physics. 19, 6, p. 898903 Abstract
Turbulence under strong influence of rotation is described as an ensemble of interacting inertial waves across a wide range of length scales. In macroscopic quantum condensates, the quasiclassical turbulent dynamics at large scales is altered at small scales, where the quantization of vorticity is essential. The nature of this transition remains an unanswered question. Here we expand the concept of wavedriven turbulence to rotating quantum fluids where the spectrum of waves extends to microscopic scales as Kelvin waves on quantized vortices. We excite inertial waves at the largest scale by periodic modulation of the angular velocity and observe dissipationindependent transfer of energy to smaller scales and the eventual onset of the elusive Kelvin wave cascade at the lowest temperatures. We further find that energy is pumped to the system through a boundary layer distinct from the classical Ekman layer and support our observations with numerical simulations. Our experiments demonstrate a regime of turbulent motion in quantum fluids where the role of vortex reconnections can be neglected, thus stripping the transition between the classical and the quantum regimes of turbulence down to its constituent components.
2022

(2022) Communications Physics. 5, 1, 196. Abstract
Advances in quantum computing and telecommunications stimulate the search for classical systems allowing partial implementation of a similar functionality under less stringent environmental conditions. Here, we present a classical version of several quantum bit (qubit) functionalities using a twocomponent magnon Bose\u2013Einstein condensate (BEC) formed at opposite wavevectors in a roomtemperature yttriumirongarnet ferrimagnetic film. Employing micromagnetic numerical simulations, we show the use of wavelengthselective parametric pumping to controllably initialize and manipulate the twocomponent BEC. Next, by modeling the interaction of this BEC with a pulse and radiofrequencydriven dynamic magnonic crystal we translate the concept of Rabioscillations into the wavevector domain and demonstrate how to manipulate the magnonBEC system regarding the polar and azimuthal angles in the Bloch sphere representation. We hope that our study provides a significant stimulus on the boundary between qubit functionality and classical systems of interacting BECs, which use a subset of qubitbased algorithms.

(2022) Physical review letters. 128, 22, 224501. Abstract
We report an exact unique constantflux powerlaw analytical solution of the wave kinetic equation for the turbulent energy spectrum, E(k)=C1εacs−−−−√/k, of acoustic waves in 2D with almost linear dispersion law, ωk=csk[1+(ak)2], ak≪1. Here ε is the energy flux over scales, and C1 is the universal constant which was found analytically. Our theory describes, for example, acoustic turbulence in 2D BoseEinstein condensates (BECs). The corresponding 3D counterpart of turbulent acoustic spectrum was found over half a century ago, however, due to the singularity in 2D, no solution has been obtained until now. We show the spectrum E(k) is realizable in direct numerical simulations of forceddissipated GrossPitaevskii equation in the presence of strong condensate.

(2022) Philosophical transactions Mathematical, physical, and engineering sciences. 380, 2219, Abstract
We develop a theory of strong anisotropy of the energy spectra in the thermally driven turbulent counterflow of superfluid 4He. The key ingredients of the theory are the threedimensional differential closure for the vector of the energy flux and the anisotropy of the mutual friction force. We suggest an approximate analytic solution of the resulting energyrate equation, which is fully supported by our numerical solution. The twodimensional energy spectrum is strongly confined in the direction of the counterflow velocity. In agreement with the experiments, the energy spectra in the direction orthogonal to the counterflow exhibit two scaling ranges: a nearclassical nonuniversal cascade dominated range and a universal critical regime at large wavenumbers. The theory predicts the dependence of various details of the spectra and the transition to the universal critical regime on the flow parameters.

(2022) Physical review. E.. 105, 027101. Abstract
In a recent paper [T. Tanogami Phys. Rev. E 103, 023106 ] proposes a scenario for quantum turbulence where the energy spectrum at scales smaller than the intervortex distance is dominated by a quantum stress cascade, in opposition to Kelvin wave cascade predictions. The purpose of the present comment is to highlight some physical issues in the derivation of the quantum stress cascade, in particular to stress that quantization of circulation has been ignored.
2021

(2021) Physical review. B.. 104, 14, A23. Abstract
The alternating current (ac) Josephson effect in a timeindependent spatially inhomogeneous setting is manifested by the occurrence of Josephson oscillations\u2014periodic macroscopic phaseinduced collective motions of the quantum condensate. So far, this phenomenon was observed at cryogenic temperatures in superconductors, in superfluid helium, and in BoseEinstein condensates (BECs) of trapped atoms. Here, we report on the discovery of the ac Josephson effect in a magnon BEC carried by a roomtemperature ferrimagnetic film. The BEC is formed in a parametrically populated magnon gas in the spatial vicinity of a magnetic trench created by a dc electric current. The appearance of the Josephson effect is manifested by oscillations of the magnon BEC density in the trench, caused by a coherent phase shift between this BEC and the BEC in the nearby regions. Our findings advance the physics of roomtemperature macroscopic quantum phenomena and will allow for their application for data processing in magnon spintronics devices.

(2021) Physical Review Fluids. 6, 9, 094601. Abstract[All authors]
We report hotwire measurements performed in two very different, coand counterrotating flows, in normal and superfluid helium at 1.6 K, 2 K, and 2.3 K. As recently reported, the power spectrum of the hotwire signal in superfluid flows exhibits a significant bump at high frequency [Diribarne et al., Phys. Rev. B 103, 144509 (2021)]. We confirm that the bump frequency does not depend significantly on the temperature and further extend the previous analysis of the velocity dependence of the bump, over more than one decade of velocity. The main result is that the bump frequency depends on the turbulence intensity of the flow, and that using the turbulent Reynolds number rather than the velocity as a control parameter collapses results from both coand counterrotating flows. The vortex shedding model previously proposed, in its current form, does not account for this observation. This suggests that the physical origin of the bump is related to the small scale turbulence properties of the flow. We finally propose some qualitative physical mechanism by which the smallest structures of the flow, at intervortex distance, could affect the heat flux of the hotwire.

(2021) Physical Review B. 104, 10, L100410. Abstract
The appearance of spontaneous coherence is a fundamental feature of a BoseEinstein condensate and an essential requirement for possible applications of the condensates for data processing and quantum computing. In the case of a magnon condensate in a magnetic crystal, such computing can be performed even at room temperature. So far, the process of coherence formation in a magnon condensate was inaccessible. We study the evolution of magnon radiation spectra by direct detection of microwave radiation emitted by magnons in a parametrically driven yttrium iron garnet crystal. By using specially shaped bulk samples, we show that the parametrically overpopulated magnon gas evolves to a state, whose coherence is only limited by the natural magnon relaxation into the crystal lattice.

(2021) Physical review. B, Condensed matter and materials physics.. 104, 1, 014420. Abstract
Interaction between quasiparticles of a different nature, such as magnons and phonons in a magnetic medium, leads to the mixing of their properties and the formation of hybrid states in the areas of intersection of individual spectral branches. We recently reported the discovery of a new phenomenon mediated by the magnonphonon interaction: the spontaneous bottleneck accumulation of magnetoelastic bosons under electromagnetic pumping of pure magnons into a ferrimagnetic yttrium iron garnet film. Here, by studying the transport properties of the accumulated magnetoelastic bosons, we reveal that such accumulation occurs in two frequencydistant groups of quasiparticles: quasiphonons and quasimagnons. They propagate with different velocities in different directions relative to the magnetization field. The theoretical model we propose qualitatively describes the double accumulation effect, and the analysis of the twodimensional spectrum of quasiparticles in the hybridization region allows us to determine the wave vectors and frequencies of each of the groups.

(2021) New Journal of Physics. 23, 6, 063005. Abstract[All authors]
Velocity measurements in turbulent superfluid helium between corotating propellers are reported. The parameters are chosen such that the flow is fully turbulent, and its dissipative scales are partly resolved by the velocity sensors. This allows for the first experimental comparison of spectra in quantum versus classical turbulence where dissipative scales are resolved. In some specific conditions, differences are observed, with an excess of energy at small scales in the quantum case compared to the classical one. This difference is consistent with the prediction of a pileup of superfluid kinetic energy at the bottom of the inertial cascade of turbulence due to a specific dissipation mechanism.

(2021) Physical review. B, Condensed matter and materials physics.. 103, 14, 144506. Abstract
We use particle tracking velocimetry to study Eulerian and Lagrangian secondorder statistics of superfluid He4 grid turbulence. The Eulerian energy spectra at scales larger than the mean distance between quantum vortex lines behave classically with close to Kolmogorov1941 scaling and are almost isotropic. The Lagrangian secondorder structure functions and frequency power spectra, measured at scales comparable with the intervortex distance, demonstrate a sharp transition from nearlyclassical behavior to a regime dominated by the motion of quantum vortex lines. Employing the homogeneity of the flow, we verify a set of relations that connect various secondorder statistical objects that stress different aspects of turbulent behavior, allowing a multifaceted analysis. We use the twoway bridge relations between Eulerian energy spectra and secondorder structure functions to reconstruct the energy spectrum from the known velocity secondorder structure function and vice versa. The Lagrangian frequency spectrum reconstructed from the measured Eulerian spectrum using the EulerianLagrangian bridge differs from the measured Lagrangian spectrum in the quasiclassical range which calls for further investigation.
2020

(2020) Physical Review A. 102, 4, 043318. Abstract
We develop the theory of weak wave turbulence in systems described by the SchrödingerHelmholtz equations in two and three dimensions. This model contains as limits both the familiar cubic nonlinear Schrödinger equation, and the SchrödingerNewton equations. The latter, in three dimensions, are a nonrelativistic model of fuzzy dark matter which has a nonlocal gravitational selfpotential, and in two dimensions they describe nonlocal nonlinear optics in the paraxial approximation. We show that in the weakly nonlinear limit the SchrödingerHelmholtz equations have a simultaneous inverse cascade of particles and a forward cascade of energy. The inverse cascade we interpret as a nonequilibrium condensation process, which is a precursor to structure formation at large scales (for example the formation of galactic dark matter haloes or optical solitons). We show that for the SchrödingerNewton equations in two and three dimensions, and in the twodimensional nonlinear Schrödinger equation, the particle and energy fluxes are carried by small deviations from thermodynamic distributions, rather than the KolmogorovZakharov cascades that are familiar in wave turbulence. We develop a differential approximation model to characterize such "warm cascade"states.

(2020) JETP Letters. 111, 10, p. 600601 Abstract
This is a Reply to Sonin\u2019s Comment [arXiv preprint arXiv:2003.09912, 2020] on Eltsov and L\u2019vov [Pis\u2019ma v ZhETF 111, 462 (2020)] in which we provide relation of the energy flux carried by the cascade to the amplitude of the excited Kelvin waves, important for analysis of future experiments.

(2020) JETP Letters. 111, 7, p. 389391 Abstract
Development of experimental techniques to study superfluid dynamics, in particular, application of nanomechanical oscillators to drive vortex lines, enables potential observation of the Kelvinwave cascade on quantized vortices. One of the first questions which then arises in analysis of the experimental results is the relation between the energy flux in the cascade and the amplitude of the Kelvin waves. We provide such relation based on the L'vovNazarenko picture of the cascade. Remarkably, the amplitude of the waves depends on the energy flux extermely weakly, as power one tenth.
2019

(2019) Nature Communications. 10, 1, 2460. Abstract
A macroscopic collective motion of a BoseEinstein condensate (BEC) is commonly associated with phenomena such as superconductivity and superfluidity, often generalised by the term supercurrent. Another type of motion of a quantum condensate is second sounda wave of condensate's parameters. Recently, we reported on the decay of a BEC of magnons caused by a supercurrent outflow of the BEC from the locally heated area of a room temperature magnetic film. Here, we present the observation of a macroscopic BEC transport mechanism related to the excitation of second sound. The condensed magnons, being propelled out of the heated area, form compact humps of BEC density, which propagate many hundreds of micrometers in the form of distinct second soundBogoliubov waves. This discovery advances the physics of quasiparticles and allows for the application of related transport phenomena for lowloss data transfer in magnon spintronics devices.

(2019) Ukrainian Journal of Physics. 64, 10, p. 927932 Abstract
Magnon Bose\u2013Einstein Condensates (BECs) and supercurrents are coherent quantum phenomena, which appear on a macroscopic scale in parametrically populated solid state spin systems. One of the most fascinating and attractive features of these processes is the possibility of magnon condensation and supercurrent excitation even at room temperature. At the same time, valuable information about a magnon BEC state, such as its lifetime, its formation threshold, and coherence, is provided by experiments at various temperatures. Here, we use Brillouin Light Scattering (BLS) spectroscopy for the investigation of the magnon BEC dynamics in a singlecrystal film of yttrium iron garnet in a wide temperature range from 30 K to 380K. By comparing the BLS results with previous microwave measurements, we revealed the direct relation between the damping of the condensed and the parametrically injected magnons. The enhanced supercurrent dynamics was detected at 180 K near the minimum of BEC damping.

(2019) Physical Review B. 100, 13, 134515. Abstract
We report on a combined theoretical and numerical study of counterflow turbulence in superfluid He4 in a wide range of parameters. The energy spectra of the velocity fluctuations of both the normalfluid and superfluid components are strongly anisotropic. The angular dependence of the correlation between velocity fluctuations of the two components plays the key role. A selective energy dissipation intensifies as scales decrease, with the streamwise velocity fluctuations becoming dominant. Most of the flow energy is concentrated in a wavevector plane which is orthogonal to the direction of the counterflow. The phenomenon becomes more prominent at higher temperatures as the coupling between the components depends on the temperature and the direction with respect to the counterflow velocity.

(2019) Physical Review B. 100, 2, 020406. Abstract
We report the experimental realization of a spacetime crystal with tunable periodicity in time and space in a magnon BoseEinstein condensate (BEC), formed in a roomtemperature yttrium iron garnet (YIG) film by a microwave spacehomogeneous magnetic field. The magnon BEC is prepared to have a welldefined frequency and nonzero wave vector. We demonstrate how the crystalline "density" as well as the time and space textures of the resulting crystal may be tuned by varying the experimental parameters: External static magnetic field, temperature, thickness of the YIG film, and power of the microwave field. The proposed spacetime crystals provide an additional dimension for exploring dynamical phases of matter and can serve as a model nonlinear Floquet system, that brings in touch the rich fields of classical nonlinear waves, magnonics, and periodically driven systems.

(2019) Physical Review Letters. 122, 14, 144501. Abstract
Threedimensional anisotropic turbulence in classical fluids tends towards isotropy and homogeneity with decreasing scales, allowingeventuallythe abstract model of homogeneous and isotropic turbulence to be relevant. We show here that the opposite is true for superfluid He4 turbulence in threedimensional counterflow channel geometry. This flow becomes less isotropic upon decreasing scales, becoming eventually quasitwodimensional. The physical reason for this unusual phenomenon is elucidated and supported by theory and simulations.
2018

(2018) Physical Review B. 98, 17, 174509. Abstract
We report a detailed analysis of the energy spectra, second and highorder structure functions of velocity differences in superfluid He4 counterflow turbulence, measured in a wide range of temperatures and heat fluxes. We show that the onedimensional energy spectrum Exz(ky) (averaged over the xz plane, parallel to the channel wall), directly measured as a function of the wallnormal wave vector ky, gives more detailed information on the energy distribution over scales than the corresponding secondorder structure function S2(δy). In particular, we discover two intervals of ky with different apparent exponents: Exz(ky)kymC for kk× and Exz(ky)kymF for kk×. Here k× denotes the wave number that separates scales with relatively strong (for kk×) and relatively weak (for kk×) coupling between the normalfluid and superfluid velocity components. We interpret these k ranges as cascadedominated and mutualfrictiondominated intervals, respectively. The general behavior of the experimental spectra Exz(ky) agrees well with the predicted spectra [L'vov and Pomyalov, Phys. Rev. B 97, 214513 (2018)2469995010.1103/PhysRevB.97.214513]. Analysis of the nthorder structure functions statistics shows that in the energycontaining interval, the statistics of counterflow turbulence is close to Gaussian, similar to the classical hydrodynamic turbulence. In the cascade and mutualfrictiondominated intervals, we found some modest enhancement of intermittency with respect to its level in classical turbulence. However, at small scales, the intermittency becomes much stronger than in the classical turbulence.

(2018) Physical Review Letters. 121, 7, 077203. Abstract
Evolution of an overpopulated gas of magnons to a BoseEinstein condensate and excitation of a magnon supercurrent, propelled by a phase gradient in the condensate wave function, can be observed at room temperature by means of the Brillouin light scattering spectroscopy in an yttrium iron garnet material. We study these phenomena in a wide range of external magnetic fields in order to understand their properties when externally pumped magnons are transferred towards the condensed state via two distinct channels: a multistage KolmogorovZakharov cascade of the weakwave turbulence or a onestep kinetic instability process. Our main result is that opening the kinetic instability channel leads to the formation of a much denser magnon condensate and to a stronger magnon supercurrent compared to the cascade mechanism alone.

(2018) Physical Review B. 97, 21, 214513. Abstract
In the thermally driven superfluid He4 turbulence, the counterflow velocity U_{ns} partially decouples normal and superfluid turbulent velocities. Recently, we suggested [J. Low. Temp. Phys. 187, 497 (2017)] that this decoupling should tremendously increase the turbulent energy dissipation by mutual friction and significantly suppress the energy spectra. Comprehensive measurements of the apparent scaling exponent n_{exp }of the secondorder normalfluid velocity structure function S_{2}(r) ∝ r^{nexp} in the counterflow turbulence [J. Gao et al., Phys. Rev. B 96, 094511 (2017)] confirmed our scenario of gradual dependence of the turbulence statistics on flow parameters. We develop an analytical theory of the counterflow turbulence, accounting for a twofold mechanism of thisphenomenon: (i) a scaledependent competition between the turbulent velocity coupling by mutual friction and the Unsinduced turbulent velocity decoupling and (ii) the turbulent energy dissipation by mutual friction enhanced by the velocity decoupling. The suggested theory predicts the energy spectra for a wide range of flow parameters. The mean exponents of the normalfluid energy spectra m_{10}, found without fitting parameters, qualitatively agree with the observed n_{exp}+ 1 for T 1.85 K.

(2018) Journal Physics D: Applied Physics. 51, 23, 234003 . Abstract[All authors]
We studied the transient behavior of the spin current generated by the longitudinal spin Seebeck effect (LSSE) in a set of platinumcoated yttrium iron garnet (YIG) films of different thicknesses. The LSSE was induced by means of pulsed microwave heating of the Pt layer and the spin currents were measured electrically using the inverse spin Hall effect in the same layer. We demonstrate that the time evolution of the LSSE is determined by the evolution of the thermal gradient triggering the flux of thermal magnons in the vicinity of the YIG/Pt interface. These magnons move ballistically within the YIG film with a constant group velocity, while their number decays exponentially within an effective propagation length. The ballistic flight of the magnons with energies above 20K is a result of their almost linear dispersion law, similar to that of acoustic phonons. By fitting the timedependent LSSE signal for different film thicknesses varying by almost an order of magnitude, we found that the effective propagation length is practically independent of the YIG film thickness. We consider this fact as strong support of a ballistic transport scenario  the ballistic propagation of quasiacoustic magnons in room temperature YIG.

(2018) Physical Review Fluids. 3, 2, 024605. Abstract
The largescale turbulent statistics of mechanically driven superfluid He4 was shown experimentally to follow the classical counterpart. In this paper, we use direct numerical simulations to study the whole range of scales in a range of temperatures T [1.3,2.1] K. The numerics employ selfconsistent and nonlinearly coupled normal and superfluid components. The main results are that (i) the velocity fluctuations of normal and super components are well correlated in the inertial range of scales, but decorrelate at small scales. (ii) The energy transfer by mutual friction between components is particulary efficient in the temperature range between 1.8 and 2 K, leading to enhancement of smallscale intermittency for these temperatures. (iii) At low T and close to Tλ, the scaling properties of the energy spectra and structure functions of the two components are approaching those of classical hydrodynamic turbulence.

(2018) Physical Review B. 97, 1, 014508 . Abstract
Describing superfluid turbulence at intermediate scales between the intervortex distance and the macroscale requires an acceptable equation of motion for the density of quantized vortex lines L. The closure of such an equation for superfluid inhomogeneous flows requires additional inputs besides L and the normal and superfluid velocity fields. In this paper, we offer a minimal closure using one additional anisotropy parameter Il0. Using the example of counterflow superfluid turbulence, we derive two coupled closure equations for the vortex line density and the anisotropy parameter Il0 with an input of the normal and superfluid velocity fields. The various closure assumptions and the predictions of the resulting theory are tested against numerical simulations.
2017

(2017) Journal of Fluid Mechanics. 831, p. 128150 Abstract
A complete Hamiltonian formalism is suggested for inertial waves in rotating incompressible fluids. Resonance threewave interaction processes  decay instability and confluence of two waves  are shown to play a key role in the weakly nonlinear dynamics and statistics of inertial waves in the rapid rotation case. Future applications of the Hamiltonian approach to inertial wave theory are investigated and discussed.

(2017) Journal of Low Temperature Physics. 187, 56, p. 497514 Abstract
Based on our current understanding of statistics of quantum turbulence as well as on results of intensive ongoing analytical, numerical and experimental studies, we overview here the following problems in the largescale, spacehomogeneous, steadystate turbulence of superfluid He4 and He3: (1) energy spectra of normal and superfluid velocity components; (2) crosscorrelation function of normal and superfluid velocities; (3) energy dissipation by mutual friction and viscosity; (4) energy exchange between normal and superfluid components; (5) highorder statistics and intermittency effects. The statistical properties are discussed for turbulence in different types of flows: coflow of He4; turbulent He3 with the laminar normal fluid; pure superflow and counterflow in He4.

(2017) Physical review letters. 118, 23, 237201. Abstract
An ensemble of magnons, quanta of spin waves, can be prepared as a Bose gas of weakly interacting quasiparticles. Furthermore, the thermalization of the overpopulated magnon gas through magnonmagnon scattering processes, which conserve the number of particles, can lead to the formation of a BoseEinstein condensate at the bottom of a spinwave spectrum. However, magnonphonon scattering can significantly modify this scenario and new quasiparticles are formed  magnetoelastic bosons. Our observations of a parametrically populated magnon gas in a singlecrystal film of yttrium iron garnet by means of wavevectorresolved Brillouin light scattering spectroscopy evidence a novel condensation phenomenon: A spontaneous accumulation of hybrid magnetoelastic bosonic quasiparticles at the intersection of the lowest magnon mode and a transversal acoustic wave.

(2017) Journal of Low Temperature Physics. 187, 56, p. 531537 Abstract
We report preliminary results of the complementary experimental and numerical studies on spatiotemporal tangle development and streamwise vortex line density (VLD) distribution in counterflowing ^{4}He. The experiment is set up in a long square channel with VLD and local temperature measured in three streamwise locations. In the steady state, we observe nearly streamwisehomogeneous VLD. Experimental secondsound data as well as numerical data (vortex filament method in a long planar channel starting with seeding vortices localized in multiple locations) show that the initial buildup pattern of VLD displays complex features depending on the position in the channel, but some tangle properties appear uniform along its length.

(2017) Physical Review B. 95, 18, 184510. Abstract
Below the phase transition temperature Tc≃103K He3B has a mixture of normal and superfluid components. Turbulence in this material is carried predominantly by the superfluid component. We explore the statistical properties of this quantum turbulence, stressing the differences from the better known classical counterpart. To this aim we study the timehonored HallVinenBekarevichKhalatnikov coarsegrained equations of superfluid turbulence. We combine pseudospectral direct numerical simulations with analytic considerations based on an integral closure for the energy flux. We avoid the assumption of locality of the energy transfer which was used previously in both analytic and numerical studies of the superfluid He3B turbulence. For T
2016

(2016) Nature Physics. 12, 11, p. 10571062 Abstract
A supercurrent is a macroscopic effect of a phaseinduced collective motion of a quantum condensate. So far, experimentally observed supercurrent phenomena such as superconductivity and superfluidity have been restricted to cryogenic temperatures. Here, we report on the discovery of a supercurrent in a BoseEinstein magnon condensate prepared in a roomtemperature ferrimagnetic film. The magnon condensate is formed in a parametrically pumped magnon gas and is subject to a thermal gradient created by local laser heating of the film. The appearance of the supercurrent, which is driven by a thermally induced phase shift in the condensate wavefunction, is evidenced by analysis of the temporal evolution of the magnon density measured by means of Brillouin light scattering spectroscopy. Our findings offer opportunities for the investigation of roomtemperature macroscopic quantum phenomena and their potential applications at ambient conditions.

(2016) Physical Review B. 94, 17, 174504. Abstract
We report complementary experimental, numerical, and theoretical study of turbulent coflow, counterflow, and pure superflow of superfluid He4 in a channel, resulting in a physically transparent and relatively simple model of decaying quantum turbulence that accounts for interactions of coexisting quantum and classical components of turbulent superfluid He4. We further offer an analytical theory of the energy spectra of steadystate quantum turbulence in the counterflow and pure superflow, based on algebraic approximation for the energy fluxes over scales. The resulting spectra are not of the classic Kolmogorov form, but strongly suppressed by the mutual friction, leading to the energy dissipation at all scales, enhanced by the counterflowinduced decoupling of the normal and superfluid velocity fluctuations.

(2016) Physical Review B. 94, 14, 146502. Abstract
This is a Reply to Nemirovskii's Comment [Phys. Rev. B 94, 146501 (2016)10.1103/PhysRevB.94.146501] on Khomenko et al. [Phys. Rev. B 91, 180504 (2015)PRBMDO1098012110.1103/PhysRevB.91.180504] in which a new form of the production term in Vinen's equation for the evolution of the vortexline density L in the thermal counterflow of superfluid He4 in a channel was suggested. To further substantiate the suggested form which was questioned in the Comment, we present a physical explanation for the improvement of the closure suggested in Khomenko et al. [Phys. Rev. B 91, 180504 (2015)PRBMDO1098012110.1103/PhysRevB.91.180504] in comparison to the form proposed by Vinen. We also discuss the closure for the flux term, which agrees well with the numerical results without any fitting parameters.

(2016) JETP Letters. 103, 10, p. 648652 Abstract
We summarize recent experiments on thermal counterflow turbulence in superfluid He4, emphasizing the observation of turbulence in the normal fluid and its effect on the decay process when the heat flux is turned off. We argue that what is observed as turbulence in the normal fluid is a novel form of coupled turbulence in the superfluid and normal components, with injection of energy on the scales of both the (large) channel width and the (small) spacing between quantized vortices. Although an understanding of this coupled turbulence remains challenging, a theory of its decay is developed which accounts for the experimental observations.

(2016) Physical Review B. 93, 13, 134504. Abstract
In classical turbulence the kinematic viscosity ν is involved in two phenomena. The first is the energy dissipation and the second is the mechanical momentum flux toward the wall. In superfluid turbulence the mechanism of energy dissipation is different, and it is determined by an effective viscosity which was introduced by Vinen and is denoted as ν'. In this paper we show that in superfluid turbulence the transfer of mechanical momentum to the wall is caused by the presence of a quantum vortex tangle, giving rise to another effective "momentum" viscosity that we denote as νm(T). The temperature dependence of the second effective viscosity is markedly different from Vinen's effective viscosity ν'(T). We show that the notion of vortextension force, playing an important role in the theory of quantum turbulence, can be understood as the gradient of the Reynoldsstress tensor, which is, in fact, determined by the second newly defined kinematic viscosity νm(T).

(2016) Physical Review B. 93, 1, 014516 . Abstract
In mechanically driven superfluid turbulence, the mean velocities of the normal and superfluid components are known to coincide: Un=Us. Numerous laboratory, numerical, and analytical studies showed that under these conditions, the mutual friction between the normal and superfluid velocity components also couples their fluctuations: un\u2032(r,t)≈us\u2032(r,t), almost at all scales. We show that this is not the case in thermally driven superfluid turbulence; here the counterflow velocity Uns≡UnUs≠0. We suggest a simple analytic model for the crosscorrelation function un\u2032(r,t)·us\u2032(r\u2032,t) and its dependence on Uns. We demonstrate that un\u2032(r,t) and us\u2032(r,t) are decoupled almost in the entire range of separations rr\u2032 between the energycontaining scale and intervortex distance.
2015

(2015) Physical Review B. 91, 18, 180504. Abstract
The quantization of vortex lines in superfluids requires the introduction of their density L(r,t) in the description of quantum turbulence. The space homogeneous balance equation for L(t), proposed by Vinen on the basis of dimensional and physical considerations, allows a number of competing forms for the production term P. Attempts to choose the correct one on the basis of timedependent homogeneous experiments ended inconclusively. To overcome this difficulty we announce here an approach that employs an inhomogeneous channel flow which is very suitable to distinguish the implications of the various possible forms of the desired equation. We demonstrate that the originally selected form which was extensively used in the literature is in strong contradiction with our data. We therefore present a new form of an inhomogeneous equation for L(r,t) that is in agreement with our data and propose that it should be considered for further studies of superfluid turbulence.

(2015) Physical Review B. 91, 14, 144501. Abstract
We discuss the energy and vorticity spectra of turbulent superfluid ^{4}He in the entire temperature range from T=0 up to the phase transition "λ point," T_{λ}≃2.17K. Contrary to classical developed turbulence in which there are only two typical scales, i.e., the energy injection L and the dissipation scales η, here, the quantization of vorticity introduces two additional scales, the vortex core radius a0 and the mean vortex spacing ℓ. We present these spectra for the super and the normalfluid components in the entire range of scales from L to a_{0} including the crossover scale ℓ where the hydrodynamic eddy cascade is replaced by the cascade of Kelvin waves on individual vortices. At this scale, a bottleneck accumulation of the energy was found earlier at T=0. We show that even very small mutual friction dramatically suppresses the bottleneck effect due to the dissipation of the Kelvin waves. Using our results for the spectra we estimate the Vinen "effective viscosity" ν\u2032 in the entire temperature range and show agreement with numerous experimental observations for ν\u2032(T).
2014

(2014) Physical Review B. 90, 9, 094501. Abstract
We present a comprehensive statistical study of free decay of the quantized vortex tangle in superfluid He4 at low and ultralow temperatures 0≤T≤1.1 K. Using highresolution vortex filament simulations with full BiotSavart vortex dynamics, we show that for ultralow temperatures T≲0.5 K, when the mutual friction parameters α≃α\u2032

(2014) Physical Review B. 90, 2, 024508. Abstract
A nuclear capture reaction of a single neutron by ultracold superfluid He3 results in a rapid overheating followed by the expansion and subsequent cooling of the hot subregion, in a certain analogy with the big bang of the early universe. It was shown in a Grenoble experiment that a significant part of the energy released during the nuclear reaction was not converted into heat even after several seconds. It was thought that the missing energy was stored in a tangle of quantized vortex lines. This explanation, however, contradicts the expected lifetime of a bulk vortex tangle, 105104 s, which is much shorter than the observed time delay of seconds. In this paper we propose a scenario that resolves the contradiction: the vortex tangle, created by the hot spot, emits isolated vortex loops that take with them a significant part of the tangle's energy. These loops quickly reach the container walls. The dilute ensemble of vortex loops attached to the walls can survive for a long time, while the remaining bulk vortex tangle decays quickly.

(2014) Theoretical and Computational Fluid Dynamics. 28, 2, p. 197213 Abstract
We study, numerically and analytically, the relationship between the Eulerian spectrum of kinetic energy, E _{E}(k, t), in isotropic turbulence and the corresponding Lagrangian frequency energy spectrum, E _{L}(ω, t), for which we derive an evolution equation. Our DNS results show that not only E _{L}(ω, t) but also the Lagrangian frequency spectrum of the dissipation rate ε L (ω, t) has its maximum at low frequencies (about the turnover frequency of energycontaining eddies) and decays exponentially at large frequencies ω (about a half of the Kolmogorov microscale frequency) for both stationary and decaying isotropic turbulence. Our main analytical result is the derivation of equations that bridge the Eulerian and Lagrangian spectra and allow the determination of the Lagrangian spectrum, E _{L} (ω) for a given Eulerian spectrum, E _{E} (k), as well as the Lagrangian dissipation, ε L (ω), for a given Eulerian counterpart, ε E (k) = 2 ν k 2 E E (k). These equations were derived from the NavierStokes equations in the sweepingfree coordinate system (intermediate between the Eulerian and Lagrangian frameworks) which eliminates the effect of the kinematic sweeping of the small eddies by the larger eddies. We show that both analytical relationships between E _{L} (ω) and E _{E} (k) and between ε L (ω) and ε E (k) are in very good quantitative agreement with our DNS results and explain how ε L (ω, t) has its maximum at low frequencies and decays exponentially at large frequencies.

(2014) Physics of Fluids. 26, 4, 041703. Abstract
In the vicinity of the superfluid transition in liquid 4He, we explore the relation between two apparently unrelated physical quantitiesthe kinematic viscosity, ν, in the normal state and the quantum of circulation, κ, in the superfluid state. The model developed here leads to the simple relationship ν ≈ κ/6, and links the classical and quantum flow properties of liquid 4He. We critically examine available data relevant to this relation and find that the prediction holds well at the saturated vapor pressure. Additionally,we predict the kinematic viscosity for liquid ^{4}He along the λline at negative pressures

(2014) Proceedings of the National Academy of Sciences of the United States of America. 111, SUPPL. 1, p. 46834690 Abstract
Turbulence in superfluid helium is unusual and presents a challenge to fluid dynamicists because it consists of two coupled, interpenetrating turbulent fluids: the first is inviscid with quantized vorticity, and the second is viscous with continuous vorticity. Despite this double nature, the observed spectra of the superfluid turbulent velocity at sufficiently large length scales are similar to those of ordinary turbulence. We present experimental, numerical, and theoretical results that explain these similarities, and illustrate the limits of our present understanding of superfluid turbulence at smaller scales.

(2014) Physical Review B. 89, 1, 014502. Abstract
The paper presents a comprehensive characterization of welldeveloped vortex tangles in a turbulent counterflow in quantum fluids (with a laminar normal fluid component). We perform and analyze extensive numerical simulations using the vortex filament method, solving the full BiotSavart equations for the vortex dynamics in a wide range of temperatures and counterflow velocities. We start with the analysis of the macroscopic characteristics of the quantum vortex tangle such as vortex line density, its mean anisotropic and curvature parameters, the mean friction force between normal and superfluid components, the drift velocity of the vortex tangle, etc. Next we proceed to the main goal of the paper and move from the traditional macroscopic approach in terms of mean characteristics of the vortex tangle to the microscopic statistical and kinetic levels of description of quantum turbulence. These include objects that are much less studied or even totally neglected such as the vortex reconnection rates, the correlations and probability distribution functions (PDFs) of the vortex loop lengths, of the line curvature, of the mean curvatures of individual loops, the crosscorrelation function between the loop length and its mean curvature, and the autocorrelation function of the vortexline orientations. This detailed statistical information is required for a deeper understanding of quantum turbulence and for the development of its advanced theoretical description. In addition, we identify which of the studied properties are strongly affected by the choice of the reconnection criteria that are traditionally used in the vortex filament method and which of them are practically insensitive to the reconnection procedure. We conclude that the vortex filament method is sufficiently robust and wellsuited for the description of the steadystate vortex tangle in the quantum counterflow.
2013

(2013) Physical review letters. 111, 14, 145302. Abstract
Experimental and simulational studies of the dynamics of vortex reconnections in quantum fluids showed that the distance d between the reconnecting vortices is close to a universal time dependence d=D[κt _{0}t]α with α fluctuating around 1/2 and κ=h/m is the quantum of circulation. Dimensional analysis, based on the assumption that the quantum of circulation κ=h/m is the only relevant parameter in the problem, predicts α=1/2. The theoretical calculation of the dimensionless coefficient D in this formula remained an open problem. In this Letter we present an analytic calculation of D in terms of the given geometry of the reconnecting vortices. We start from the numerically observed generic geometry on the way to vortex reconnection and demonstrate that the dynamics is well described by a selfsimilar analytic solution which provides the wanted information.


(2013) Nature Communications. 4, 1614. Abstract
A superfluid in the absence of a viscous normal component should be the best realization of an ideal inviscid Euler fluid. As expressed by d'Alembert's famous paradox, an ideal fluid does not drag on bodies past which it flows, or in other words it does not exchange momentum with them. In addition, the flow of an ideal fluid does not dissipate kinetic energy. Here we study experimentally whether these properties apply to the flow of superfluid 3 HeB in a rotating cylinder at low temperatures. It is found that ideal behaviour is broken by quantum turbulence, which leads to substantial energy dissipation, as was also observed earlier. Remarkably, the angular momentum exchange between the superfluid and its container approaches nearly ideal behaviour, as the drag almost disappears in the zerotemperature limit. Here the mismatch between energy and angular momentum transfer results in a new physical situation, with severe implications on the flow dynamics.

(2013) Physical review letters. 110, 1, 014502. Abstract
We consider the intermittent behavior of superfluid turbulence in He4. Because of the similarity in the nonlinear structure of the twofluid model of superfluidity and the Euler and NavierStokes equations, one expects the scaling exponents of the structure functions to be the same as in classical turbulence for temperatures close to the superfluid transition T_{λ} and also for T≪T_{λ}. This is not the case when the densities of normal and superfluid components are comparable to each other and mutual friction becomes important. Using shell model simulations, we propose that in this situation there exists a range of scales in which the effective exponents indicate stronger intermittency. We offer a bridge relation between these effective and the classical scaling exponents. Since this effect occurs at accessible temperatures and Reynolds numbers, we propose that experiments should be conducted to further assess the validity and implications of this prediction.
2012

(2012) Physical Review B. 86, 22, 226501. Abstract
We comment on the paper by Sonin with most statements of which we disagree. We use this option to shed light on some important issues of a theory of Kelvinwave turbulence, touched on in Sonin's paper, in particular, on the relation between the Vinen spectrum of strong and the L'vovNazarenko spectrum of weak turbulence of Kelvin waves. We also discuss the role of explicit calculation of the Kelvinwave interaction Hamiltonian and "symmetry arguments" that have to resolve a contradiction between the KozikSvistunov and the L'vovNazarenko spectrum of weak turbulence of Kelvin waves.

(2012) EPL. 99, 4, 46003. Abstract
Kelvin waves propagating on quantum vortices play a crucial role in the phenomenology of energy dissipation of superfluid turbulence. Previous theoretical studies have consistently focused on the zerotemperature limit of the statistical physics of Kelvinwave turbulence. In this letter, we go beyond this athermal limit by introducing a small but finite temperature in the form of nonzero mutual friction dissipative force; A situation regularly encountered in actual experiments of superfluid turbulence. In this case we show that there exists a new typical length scale separating a quasiinertial range of Kelvinwave turbulence from a fardissipation range. The letter culminates with analytical predictions for the energy spectrum of the Kelvinwave turbulence in both of these regimes.

(2012) Physical Review E. 86, 1, 016302. Abstract
We developed a model for the enhancement of the heat flux by spherical and elongated nanoparticles in sheared laminar flows of nanofluids. Besides the heat flux carried by the nanoparticles, the model accounts for the contribution of their rotation to the heat flux inside and outside the particles. The rotation of the nanoparticles has a twofold effect: it induces a fluid advection around the particle and it strongly influences the statistical distribution of particle orientations. These dynamical effects, which were not included in existing thermal models, are responsible for changing the thermal properties of flowing fluids as compared to quiescent fluids. The proposed model is strongly supported by extensive numerical simulations, demonstrating a potential increase of the heat flux far beyond the MaxwellGarnett limit for the spherical nanoparticles. The road ahead, which should lead toward robust predictive models of heat flux enhancement, is discussed.

(2012) Physical review letters. 108, 17, 177002. Abstract
We report the observation of the unusual behavior of induction decay signals in antiferromagnetic monocrystals with SuhlNakamura interactions. The signals show the formation of the BoseEinstein condensation (BEC) of magnons and the existence of spin supercurrent, in complete analogy with the spin superfluidity in the superfluid He3 and the atomic BEC of quantum gases. In the experiments described here, the temperature of the magnon BEC is a thousand times larger than in the superfluid He3. It opens a possibility to apply the spin supercurrent for various magnetic spintronics applications.

(2012) Physical Review B. 85, 10, 104502. Abstract
In superfluid 3HeB, turbulence is carried predominantly by the superfluid component. To explore the statistical properties of this quantum turbulence and its differences from the classical counterpart, we adopt the timehonored approach of shell models. Using this approach, we provide numerical simulations of a Sabra shell model that allows us to uncover the nature of the energy spectrum in the relevant hydrodynamic regimes. These results are in qualitative agreement with analytical expressions for the superfluid turbulent energy spectra that were found using a differential approximation for the energy flux.
2011

(2011) Physical review letters. 107, 13, 135302. Abstract
Steadystate turbulent motion is created in superfluid He3B at low temperatures in the form of a turbulent vortex front, which moves axially along a rotating cylindrical container of He3B and replaces vortexfree flow with vortex lines at constant density. We present the first measurements on the thermal signal from dissipation as a function of time, recorded at 0.2T _{c} during the front motion, which is monitored using NMR techniques. Both the measurements and the numerical calculations of the vortex dynamics show that at low temperatures the density of the propagating vortices falls well below the equilibrium value, i.e., the superfluid rotates at a smaller angular velocity than the container. This is the first evidence for the decoupling of the superfluid from the container reference frame in the zerotemperature limit.

(2011) Physical Review B. 84, 6, 064516. Abstract
We study the statistical and dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids and address the controversy concerning the energy spectrum that is associated with these excitations. Finding the correct energy spectrum is important because Kelvin waves play a major role in the dissipation of energy in superfluid turbulence at nearzero temperatures. In this paper, we show analytically that the solution proposed by enjoys existence, uniqueness, and regularity of the prefactor. Furthermore, we present numerical results of the dynamical equation that describes to leading order the nonlocal regime of the Kelvinwave dynamics. We compare our findings with the analytical results from the proposed local and nonlocal theories for Kelvinwave dynamics and show an agreement with the nonlocal predictions. Accordingly, the spectrum proposed by L'vov and Nazarenko should be used in future theories of quantum turbulence. Finally, for weaker wave forcing we observe an intermittent behavior of the wave spectrum with a fluctuating dissipative scale, which we interpreted as a finitesize effect characteristic of mesoscopic wave turbulence.

(2011) Physical Review B. 84, 5, 054525. Abstract
In a 20483 simulation of quantum turbulence within the GrossPitaevskii equation, it is demonstrated that the largescale motions have a classical Kolmogorov1941 energy spectrum E(k)k ^{}5 ^{/}3, followed by an energy accumulation with E(k) const at k about the reciprocal mean intervortex distance. This behavior was predicted by the L'vovNazarenkoRudenko bottleneck model of gradual eddywave crossover, further developed in the paper.
2010

(2010) Journal of Low Temperature Physics. 161, 56, p. 548554 Abstract
We considered symmetry restriction on the interaction coefficients of Kelvin waves and demonstrated that linear in small wave vector asymptotic, obtained analytically, is not forbidden, as one can expect by naive reasoning. Therefore now we have no reason to doubt in this asymptote, that results in the L'vovNazarenko energy spectrum of Kelvin waves.

(2010) Journal of Low Temperature Physics. 161, 56, p. 606610 Abstract
In the Ref. (Lebedev and L'vov in J. Low Temp. Phys. 161, 2010, doi:10.1007/s1090901002152), this issue, two of us (VVL and VSL) considered symmetry restriction on the interaction coefficients of Kelvin waves and demonstrated that linear in small wave vector asymptotic, obtained analytically, is not forbidden, as Kosik and Svistunov (KS) expect by naive reasoning. Here we discuss this problem in additional details and show that theoretical objections by KS, presented in Ref. (Kozik and Svistunov in J. Low Temp. Phys. 161, 2010, doi:10.1007/s109090100242z), this issue, are irrelevant and their recent numerical simulation, presented in Ref. (Kozik and Svistunov in arXiv:1007.4927v1, 2010)is hardly convincing. There is neither proof of locality nor any refutation of the possibility of linear asymptotic of interaction vertices in the KS texts, Refs. (Kozik and Svistunov in J. Low Temp. Phys. 161, 2010, doi:10.1007/s109090100242z; arXiv:1006.0506v1, 2010). Therefore we can state again that we have no reason to doubt in this asymptote, that results in the L'vovNazarenko energy spectrum of Kelvin waves.

(2010) Physical Review E. 82, 5, 056322. Abstract
Bounding volume results in discreteness of eigenmodes in wave systems. This leads to a depletion or complete loss of wave resonances (threewave, fourwave, etc.), which has a strong effect on wave turbulence (WT) i.e., on the statistical behavior of broadband sets of weakly nonlinear waves. This paper describes three different regimes of WT realizable for different levels of the wave excitations: discrete, mesoscopic and kinetic WT. Discrete WT comprises chaotic dynamics of interacting wave "clusters" consisting of discrete (often finite) number of connected resonant wave triads (or quarters). Kinetic WT refers to the infinitebox theory, described by wellknown wavekinetic equations. Mesoscopic WT is a regime in which either the discrete and the kinetic evolutions alternate or when none of these two types is purely realized. We argue that in mesoscopic systems the wave spectrum experiences a sandpile behavior. Importantly, the mesoscopic regime is realized for a broad range of wave amplitudes which typically spans over several orders on magnitude, and not just for a particular intermediate level.

(2010) Physical review letters. 105, 12, 125301. Abstract
A central question in the dynamics of vortex lines in superfluids is dissipation on approaching the zero temperature limit T→0. From both NMR measurements and vortex filament calculations, we find that vortex flow remains laminar up to large Reynolds numbers Reα∼103 in a cylinder filled with He3B. This is different from viscous fluids and superfluid He4, where the corresponding responses are turbulent. In He3B, laminar vortex flow is possible in the bulk volume even in the presence of sizable perturbations from axial symmetry to below 0.2Tc. The laminar flow displays no excess dissipation beyond mutual friction, which vanishes in the T→0 limit, in contrast with turbulent vortex motion where dissipation has been earlier measured to approach a large Tindependent value at T0.2Tc.

(2010) Low Temperature Physics. 36, 9Aug, p. 785791 Abstract
The physics of smallscale quantum turbulence in superfluids is essentially based on knowledge of the energy spectrum of Kelvin waves, E(k). Here we derive a new type of kinetic equation for Kelvin waves on quantized vortex filaments with random largescale curvature which describes a stepbystep energy cascade over scales resulting from fivewave interactions. This approach replaces the earlier sixwave theory, which has recently been shown to be inconsistent owing to nonlocalization Solving the fourwave kinetic equation, we found a new local spectrum with a universal (curvatureindependent) exponent, E(k) proportional to k(5/3), which must replace the nonlocal spectrum of the sixwave theory, E(k) proportional to k(7/5) in any future theory, e.g., when determining the quantum turbulence decay rate, found by Kosik and Svistunov under an incorrect assumption of locality of energy transfer in sixwave interactions. (c) 2010 American Institute of Physics. [doi:10.1063/1.3499242]

(2010) Physical Review A. 81, 6, 063630. Abstract
We numerically study twodimensional quantum turbulence with a GrossPitaevskii model. With the energy initially accumulated at large scale, quantum turbulence with many quantized vortex points is generated. Due to the lack of enstrophy conservation in this model, direct energy cascade with a KolmogorovObukhov energy spectrum E(k)k^{}5^{/}3 is observed, which is quite different from twodimensional incompressible classical turbulence in the decaying case. A positive value for the energy flux guarantees a direct energy cascade in the inertial range (from large to small scales). After almost all the energy at the large scale cascades to the small scale, the compressible kinetic energy realizes the thermodynamic equilibrium state without quantized vortices.


(2010) Physical Review B. 81, 10, 104526. Abstract
We argue that the physics of interacting Kelvin Waves (KWs) is highly nontrivial and cannot be understood on the basis of pure dimensional reasoning. A consistent theory of KW turbulence in superfluids should be based upon explicit knowledge of their interactions. To achieve this, we present a detailed calculation and comprehensive analysis of the interaction coefficients for KW turbuelence, thereby, resolving previous mistakes stemming from unaccounted contributions. As a first application of this analysis, we derive a local nonlinear (partial differential) equation. This equation is much simpler for analysis and numerical simulations of KWs than the BiotSavart equation, and in contrast to the completely integrable local induction approximation (in which the energy exchange between KWs is absent), describes the nonlinear dynamics of KWs. Second, we show that the previously suggested KozikSvistunov energy spectrum for KWs, which has often been used in the analysis of experimental and numerical data in superfluid turbulence, is irrelevant, because it is based upon an erroneous assumption of the locality of the energy transfer through scales. Moreover, we demonstrate the weak nonlocality of the inverse cascade spectrum with a constant particlenumber flux and find resulting logarithmic corrections to this spectrum.

(2010) JETP Letters. 91, 8, p. 428434 Abstract
We derive a type of kinetic equation for Kelvin waves on quantized vortex filaments with random largescale curvature, that describes stepbystep (local) energy cascade over scales caused by 4wave interactions. Resulting new energy spectrum E_{LN}(k) ∝ k^{5/3} must replace in future theory (e. g., in finding the quantum turbulence decay rate) the previously used spectrum E_{KS}(k) ∝ k^{7/5}, which was recently shown to be inconsistent due to nonlocality of the 6wave energy cascade.
2009

(2009) Physical Review E. 80, 6, 066319. Abstract
Finitedimensional wave turbulence refers to the chaotic dynamics of interacting wave "clusters" consisting of finite number of connected wave triads with exact threewave resonances. We examine this phenomenon using the example of atmospheric planetary (Rossby) waves. It is shown that the dynamics of the clusters is determined by the types of connections between neighboring triads within a cluster; these correspond to substantially different scenarios of energy flux between different triads. All the possible cases of the energy cascade termination are classified. Free and forced chaotic dynamics in the clusters are investigated: due to the huge fluctuations of the energy exchange between resonant triads these two types of evolution have a lot in common. It is confirmed that finitedimensional wave turbulence in finite wave systems is fundamentally different from kinetic wave turbulence in infinite systems; the latter is described by wavekinetic equations that account for interactions with overlapping quasiresonances of finite amplitude waves. The present results are directly applicable to finitedimensional wave turbulence in any wave system in finite domains with threemode interactions as encountered in hydrodynamics, astronomy, plasma physics, chemistry, medicine, etc.

(2009) BoundaryLayer Meteorology. 133, 2, p. 139164 Abstract
We advance our prior energy and fluxbudget (EFB) turbulence closure model for stably stratified atmospheric flow and extend it to account for an additional vertical flux of momentum and additional productions of turbulent kinetic energy (TKE), turbulent potential energy (TPE) and turbulent flux of potential temperature due to largescale internal gravity waves (IGW). For the stationary, homogeneous regime, the first version of the EFB model disregarding largescale IGW yielded universal dependencies of the flux Richardson number, turbulent Prandtl number, energy ratios, and normalised vertical fluxes of momentum and heat on the gradient Richardson number, Ri. Due to the largescale IGW, these dependencies lose their universality. The maximal value of the flux Richardson number (universal constant ≈0.20.25 in the noIGW regime) becomes strongly variable. In the vertically homogeneous stratification, it increases with increasing wave energy and can even exceed 1. For heterogeneous stratification, when internal gravity waves propagate towards stronger stratification, the maximal flux Richardson number decreases with increasing wave energy, reaches zero and then becomes negative. In other words, the vertical flux of potential temperature becomes countergradient. Internal gravity waves also reduce the anisotropy of turbulence: in contrast to the mean wind shear, which generates only horizontal TKE, internal gravity waves generate both horizontal and vertical TKE. Internal gravity waves also increase the share of TPE in the turbulent total energy (TTE = TKE + TPE). A wellknown effect of internal gravity waves is their direct contribution to the vertical transport of momentum. Depending on the direction (downward or upward), internal gravity waves either strengthen or weaken the total vertical flux of momentum. Predictions from the proposed model are consistent with available data from atmospheric and laboratory experiments, direct numerical simulations and largeeddy simulations.

(2009) Physical Review E. 79, 4, 045304(R). Abstract
In light of some recent experiments on quasi twodimensional (2D) turbulent channel flow we provide here a model of the ideal case, for the sake of comparison. The ideal 2D channel flow differs from its threedimensional (3D) counterpart by having a second quadratic conserved variable in addition to the energy and the latter has an inverse rather than a direct cascade. The resulting qualitative differences in profiles of velocity V and energy K as a function of the distance from the wall are highlighted and explained. The most glaring difference is that the 2D channel is much more energetic, with K in wall units increasing logarithmically with the Reynolds number Reτ instead of being Reτ independent in 3D channels.

(2009) Progress in Low Temperature Physics. C ed. p. 45146 Abstract
New techniques, both for generating and detecting turbulence in the helium superfluids ^{3} HeB and ^{4} He, have recently given insight in how turbulence is started, what the dissipation mechanisms are, and how turbulence decays when it appears as a transient state or when externally applied turbulent pumping is switched off. Important simplifications are obtained by using ^{3} HeB as working fluid, where the highly viscous normal component is practically always in a state of laminar flow, or by cooling ^{4} He to low temperatures where the normal fraction becomes vanishingly small. We describe recent studies from the low temperature regime, where mutual friction becomes small or practically vanishes. This allows us to elucidate the mechanisms at work in quantum turbulence on approaching the zero temperature limit.

(2009) Environmental Fluid Mechanics. 9, 3, p. 267295 Abstract
We address the dynamical and statistical description of stably stratified turbulent boundary layers with the important example of the atmospheric boundary layer with a stable temperature stratification in mind. Traditional approaches to this problem, based on the profiles of mean quantities, velocity secondorder correlations, and dimensional estimates of the turbulent thermal flux run into a wellknown difficulty, predicting the suppression of turbulence at a small critical value of the Richardson number, in contradiction with observations. Phenomenological attempts to overcome this problem suffer from various theoretical inconsistencies. Here we present a closure approach taking into full account all the secondorder statistics, which allows us to respect the conservation of total mechanical energy. The analysis culminates in an analytic solution of the profiles of all mean quantities and all secondorder correlations removing the unphysical predictions of previous theories. We propose that the approach taken here is sufficient to describe the lower parts of the atmospheric boundary layer, as long as the Richardson number does not exceed an order of unity. For much higher Richardson numbers the physics may change qualitatively, requiring careful consideration of the potential KelvinHelmoholtz waves and their interaction with the vortical turbulence.
2008

(2008) EPL. 83, 5, 50012. Abstract
The dynamics of nonlinear atmospheric planetary waves is determined by a small number of independent wave clusters consisting of a few connected resonant triads. We classified the different types of connections between neighboring triads that determine the general dynamics of a cluster. Each connection type corresponds to substantially different scenarios of energy flux among the modes. The general approach can be applied directly to various mesoscopic systems with 3mode interactions, encountered in hydrodynamics, astronomy, plasma physics, chemistry, medicine, etc.

(2008) Physical review letters. 101, 9, 094503. Abstract
We ask what determines the (small) angle of turbulent jets. To answer this question we first construct a deterministic vortexstreet model representing the largescale structure in a selfsimilar plane turbulent jet. Without adjustable parameters the model reproduces the mean velocity profiles and the transverse positions of the largescale structures, including their mean sweeping velocities, in a quantitative agreement with experiments. Nevertheless, the exact selfsimilar arrangement of the vortices (or any other deterministic model) necessarily leads to a collapse of the jet angle. The observed (small) angle results from a competition between vortex sweeping tending to strongly collapse the jet and randomness in the vortex structure, with the latter resulting in a weak spreading of the jet.

(2008) Physics of Fluids. 20, 6, 065108. Abstract
We present experimental and theoretical results addressing the Reynolds number (Re) dependence of drag reduction by sufficiently large concentrations of rodlike polymers in turbulent wallbounded flows. It is shown that when Re is small the drag is enhanced. On the other hand, when Re increases, the drag is reduced and eventually, the maximal drag reduction asymptote is attained. The theory is shown to be in agreement with experiments, explaining the universal and rationalizing some of the the nonuniversal aspects of drag reduction by rodlike polymers.

(2008) Physical review letters. 100, 5, 054504. Abstract
In this Letter, we suggest a simple and physically transparent analytical model of pressure driven turbulent wallbounded flows at high but finite Reynolds numbers Re. The model provides an accurate quantitative description of the profiles of the meanvelocity and Reynolds stresses (second order correlations of velocity fluctuations) throughout the entire channel or pipe, for a wide range of Re, using only three Reindependent parameters. The model sheds light on the longstanding controversy between supporters of the centuryold loglaw theory of von Kàrmàn and Prandtl and proposers of a newer theory promoting power laws to describe the intermediate region of the mean velocity profile.

(2008) Journal of Low Temperature Physics. 153, 56, p. 140161 Abstract
We revise the theory of superfluid turbulence near the absolute zero of temperature and suggest a differential approximation model for the energy fluxes in the kspace, ε _{HD}(k) and ε _{KW}(k), carried, respectively, by the collective hydrodynamic (HD) motions of quantized vortex lines and by their individual uncorrelated motions known as Kelvin waves (KW). The model predicts energy spectra of the HD and the KW components of the system, Ε _{HD}(k) and Ε _{KW}(k), which experience a smooth crossover between different regimes of motion over a finite range of scales. For an experimentally relevant range of Δ ≡ ln (l/ a) (l is the mean intervortex separation and a is the vortex core radius) between 10 and 15 the total energy flux ε = ε _{HD}(k) + ε _{KW}(k) and the total energy spectrum Ε(k) = Ε _{HD}(k) + Ε _{KW}(k) are dominated by the HD motions for k HD = const.: Ε(k) ∝ k ^{5/3} for smaller k and tends to equipartition of the HD energy Ε(k) ∝ k ^{2} for larger k. This bottleneck accumulation of the energy spectrum is milder than the one predicted before in (L'vov et al. in Phys. Rev. B 76:024520, 2007) based on a model with sharp HDKW transition. For Δ = 15, it results in a prediction for the effective viscosity ν\u2032 ≃ 0.004κ (κ is the circulation quantum) which is in a reasonable agreement with its experimental value in ^{4}He lowtemperature experiment ≈0.003κ (Walmsley et al. in Phys. Rev. Lett. 99:265302, 2007). For k>2/l, the energy spectrum is dominated by the KW component: almost fluxless KW component close to the thermodynamic equilibrium, Ε ≈ Ε _{KW} ≈ const at smaller k and the KW cascade spectrum Ε(k) → Ε _{KW}(k) ∝ k ^{7/5} at larger k.

(2008) Physica Scripta T. T132, 014009. Abstract
This paper is part of an invited talk given at the international conference 'Turbulent Mixing and Beyond'. We consider nonisothermal fluid flows and revise simplifications of basic hydrodynamic equations for such flows, arriving eventually at a generalization of the OberbeckBoussinesq approximation valid for arbitrary equation of state including both nonideal gases as well as liquids. The proposed approach is based on a suggested general definition of potential temperature. Special attention is paid to the energy conservation principle: the proposed approximation exactly preserves the total mechanical energy by approximate equations of motion. It is emphasized explicitly the importance for any turbulent boundary layer model to respect the conservation laws.

(2008) Physica Scripta T. T132, 014010. Abstract
We present here an extended version of an invited talk we gave at the international conference 'Turbulent Mixing and Beyond'. The dynamical and statistical description of stably stratified turbulent boundary layers with the important example of the stable atmospheric boundary layer in mind is addressed. Traditional approaches to this problem, based on the profiles of mean quantities, velocity secondorder correlations and dimensional estimates of the turbulent thermal flux, run into a wellknown difficulty, predicting the suppression of turbulence at a small critical value of the Richardson number, in contradiction to observations. Phenomenological attempts to overcome this problem suffer from various theoretical inconsistencies. Here, we present an approach taking into full account all the secondorder statistics, which allows us to respect the conservation of total mechanical energy. The analysis culminates in an analytic solution of the profiles of all mean quantities and all secondorder correlations, removing the unphysical predictions of previous theories. We propose that the approach taken here is sufficient to describe the lower parts of the atmospheric boundary layer, as long as the Richardson number does not exceed an order of unity. For much higher Richardson numbers, the physics may change qualitatively, requiring careful consideration of the potential KelvinHelmoholtz waves and their interaction with the vortical turbulence.

(2008) Reviews of Modern Physics. 80, 1, p. 225247 Abstract
The flow of fluids in channels, pipes, or ducts, as in any other wallbounded flow (like water along the hulls of ships or air on airplanes) is hindered by a drag, which increases manyfold when the fluid flow turns from laminar to turbulent. A major technological problem is how to reduce this drag in order to minimize the expense of transporting fluids like oil in pipelines, or to move ships in the ocean. It was discovered that minute concentrations of polymers can reduce the drag in turbulent flows by up to 80%. While experimental knowledge had accumulated over the years, the fundamental theory of drag reduction by polymers remained elusive for a long time, with arguments raging whether this is a "skin" or a "bulk" effect. In this Colloquium the phenomenology of drag reduction by polymers is summarized, stressing both its universal and nonuniversal aspects, and a recent theory is reviewed that provides a quantitative explanation of all the known phenomenology. Both flexible and rodlike polymers are treated, explaining the existence of universal properties like the maximum drag reduction asymptote, as well as nonuniversal crossover phenomena that depend on the Reynolds number, on the nature of the polymer and on its concentration. Finally other agents for drag reduction are discussed with a stress on the important example of bubbles.
2007

(2007) Physical review letters. 99, 26, 265301. Abstract
We present experimental, numerical, and theoretical studies of a vortex front propagating into a region of vortexfree flow of rotating superfluid He3B. We show that the nature of the front changes from laminar through quasiclassical turbulent to quantum turbulent with decreasing temperature. Our experiment provides the first direct measurement of the dissipation rate in turbulent vortex dynamics of He3B and demonstrates that the dissipation becomes mutualfriction independent with decreasing temperature, and it is strongly suppressed when the Kelvinwave cascade on vortex lines is predicted to be involved in the turbulent energy transfer to smaller length scales.

(2007) JETP Letters. 86, 2, p. 102107 Abstract
An analytical model for the timedeveloping turbulent boundary layer (TD TBL) over a flat plate is presented. The model provides explicit formulae for the temporal behavior of the wallshear stress and both the temporal and spatial distributions of the mean streamwise velocity, the turbulence kinetic energy and Reynolds shear stress. The resulting profiles are in good agreement with the DNS results of spatiallydeveloping turbulent boundary layers at momentum thickness Reynolds numbers equal to 1430 and 2900 [57]. Our analytical model is, to the best of our knowledge, the first of its kind for TD TBL.

(2007) Physical Review B. 76, 2, 024520. Abstract
We consider superfluid turbulence near absolute zero of temperature generated by classical means, e.g., towed grid or rotation but not by counterflow. We argue that such turbulence consists of a polarized tangle of mutually interacting vortex filaments with quantized vorticity. For this system, we predict and describe a bottleneck accumulation of the energy spectrum at the classicalquantum crossover scale. Demanding the same energy flux through scales, the value of the energy at the crossover scale should exceed the Kolmogorov41 (K41) spectrum by a large factor ln10/3 (ℓ/a0) (ℓ is the mean intervortex distance and a0 is the vortex core radius) for the classical and quantum spectra to be matched in value. One of the important consequences of the bottleneck is that it causes the mean vortex line density to be considerably higher than that based on K41 alone, and this should be taken into account in (re)interpretation of new (and old) experiments as well as in further theoretical studies.

(2007) Physical review letters. 98, 19, 198501. Abstract
We suggest a way of rationalizing intraseasonal oscillations of Earth's atmospheric flow as four meteorologically relevant triads of interacting planetary waves, isolated from the system of all of the rest of the planetary waves. Our model is independent of the topography (mountains, etc.) and gives a natural explanation of intraseasonal oscillations in both the Northern and the Southern Hemispheres. Spherical planetary waves are an example of a wave mesoscopic system obeying discrete resonances that also appears in other areas of physics.

(2007) Environmental Fluid Mechanics. 7, 2, p. 173193 Abstract
A mechanism of formation of smallscale inhomogeneities in spatial distributions of aerosols and droplets associated with clustering instability in the atmospheric turbulent flow is discussed. The particle clustering is a consequence of a spontaneous breakdown of their homogeneous space distribution due to the clustering instability, and is caused by a combined effect of the particle inertia and a finite correlation time of the turbulent velocity field. In this paper a theoretical approach proposed in Elperin et al. (2002) Phys Rev E 66:036302 is further developed and applied to investigate the mechanisms of formation of smallscale aerosol inhomogeneities in the atmospheric turbulent flow. The theory of the particle clustering instability is extended to the case when the particle Stokes time is larger than the Kolmogorov time scale, but is much smaller than the correlation time at the integral scale of turbulence. We determined the criterion of the clustering instability for the Stokes number larger than 1. We discussed applications of the analyzed effects to the dynamics of aerosols and droplets in the atmospheric turbulent flow.
2006

(2006) JETP Letters. 84, 6, p. 289293 Abstract
In this Letter, we discuss the parametric instability of the texture of homogeneous (in time) spin precession and explain how the spatial inhomogeneity of the texture may change the threshold of the instability in comparison with the idealized spatial homogeneous case considered in our JETP Letter 83, 530 (2006). This discussion is inspired by the critical comment of I.A. Fomin (JETP Lett., this issue) related to the above questions. In addition, we considered here the results of direct numerical solution of the full LeggettTakagi equation of motion for magnetization in ^{3}HeB and experimental data for the magnetic field dependence of the catastrophic relaxation that provide solid support for the theory of this phenomenon presented in our 2006 JETP Letter.

(2006) Journal of Low Temperature Physics. 145, 14, p. 125142 Abstract
We suggest a "minimal model" for the 3D turbulent energy spectra in superfluids, based on their twofluid description. We start from the NavierStokes equation for the normal fluid and from the coarsegrained hydrodynamic equation for the superfluid component (obtained from the Euler equation for the superfluid velocity after averaging over the vortex lines) and introduce a mutual friction coupling term, proportional to the counterflow velocity, the average superfluid vorticity and to the temperature dependent parameter q=α/(1+ α\u2032), where α and α\u2032 denote the dimensionless parameters characterizing the mutual friction between quantized vortices and the normal component of the liquid. We then derive the energy balance equations, taking into account the crossvelocity correlations. We obtain all asymptotical solutions for normal and superfluid energy spectra for limiting cases of small/big normal to superfluid density ratio and coupling. We discuss the applicability of our model to superfluid He II and to ^{3}HeB.

(2006) JETP Letters. 84, 2, p. 6267 Abstract
Turbulent boundary layers exhibit a universal structure that nevertheless is rather complex and is composed of a viscous sublayer, a buffer zone, and a turbulent loglaw region. In this letter, we present a simple analytic model of turbulent boundary layers that culminates in explicit formulas for the profiles of the mean velocity, the kinetic energy, and the Reynolds stress as a function of the distance from the wall. The resulting profiles are in close quantitative agreement with measurements over the entire structure of the boundary layer without any need of refitting in the different zones.

(2006) JETP Letters. 83, 12, p. 530535 Abstract
The quantitative analysis of the "catastrophic relaxation" of the coherent spin precession in ^{3}HeB is presented. This phenomenon has been observed below a temperature of about 0.5 T_{c} as an abrupt shortening of the induction signal decay. It is explained in terms of the decay instability of the homogeneous transverse NMR mode into spin waves of the longitudinal NMR. Recently, the cross interaction amplitude between the two modes has been calculated by Sourovtsev and Fomin [9] for the socalled BrinkmanSmith configuration, i.e., for the orientation of the orbital momentum of Cooper pairs along the magnetic field, L ∥ H. In their treatment, the interaction is caused by the anisotropy of the speed of the spin waves. We found that, in the more general case of the nonparallel orientation of L corresponding to the typical conditions of the experiment, the spinorbital interaction provides the additional interaction between the modes. By analyzing the experimental data, we are able to distinguish which contribution is dominating in different regimes.

(2006) JETP Letters. 83, 12, p. 541545 Abstract
We present a phenomenological model for 2D turbulence in which the energy spectrum obeys a nonlinear fourthorder differential equation. This equation respects the scaling properties of the original NavierStokes equations, and it has both the 5/3 inversecascade and the 3 directcascade spectra. In addition, our model has RaleighJeans thermodynamic distributions as exact steady state solutions. We use the model to derive a relation between the directcascade and the inversecascade Kolmogorov constants, which is in good qualitative agreement with the laboratory and numerical experiments. We discuss a steady state solution where both the enstrophy and the energy cascades are present simultaneously, and we discuss it in the context of the NastromGage spectrum observed in atmospheric turbulence. We also consider the effect of the bottom friction on the cascade solutions and show that it leads to an additional decrease and finitewavenumber cutoffs of the respective cascade spectra, which agrees with the existing experimental and numerical results.

(2006) Journal of Fluid Mechanics. 551, p. 185195 Abstract
We employ the full FENEP model of the hydrodynamics of a dilute polymer solution to derive a theoretical approach to drag reduction in wallbounded turbulence. We recapture the results of a recent simplified theory which derived the universal maximum drag reduction (MDR) asymptote, and complement that theory with a discussion of the crossover from the MDR to the Newtonian plug when the drag reduction saturates. The FENEP model gives rise to a rather complex theory due to the interaction of the velocity field with the polymeric conformation tensor, making analytic estimates quite taxing. To overcome this we develop the theory in a computerassisted manner, checking at each point the analytic estimates by direct numerical simulations (DNS) of viscoelastic turbulence in a channel.

(2006) Physical Review E. 73, 3, 036308. Abstract
Drag reduction by bubbles in stationary turbulent flows is sensitive to the compressibility of the bubbles. Without this dynamical effect the bubbles only renormalize the fluid density and viscosity, an effect that by itself can only lead to a small percentage of drag reduction. We show in this paper that the dynamics of bubbles and their effect on the compressibility of the mixture can lead to a much higher drag reduction.

(2006) Physical Review E. 73, 1, 016303. Abstract
We construct a simple analytic model for wallbounded turbulence, containing only four adjustable parameters. Two of these parameters are responsible for the viscous dissipation of the components of the Reynolds stress tensor. The other two parameters control the nonlinear relaxation of these objects. The model offers an analytic description of the profiles of the mean velocity and the correlation functions of velocity fluctuations in the entire boundary region, from the viscous sublayer, through the buffer layer, and further into the loglaw turbulent region. In particular, the model predicts a very simple distribution of the turbulent kinetic energy in the loglaw region between the velocity components: the streamwise component contains a half of the total energy whereas the wallnormal and crossstream components contain a quarter each. In addition, the model predicts a very simple relation between the von Kármán slope κ and the turbulent velocity in the loglaw region v+ (in wall units): v+ =6κ. These predictions are in excellent agreement with direct numerical simulation data and with recent laboratory experiments.
2005

(2005) Europhysics Letters. 72, 6, p. 943949 Abstract
A celebrated universal aspect of wallbounded turbulent flows is the von Kármán loglawofthewall, describing how the mean velocity in the streamwise direction depends on the distance from the wall. Although the loglaw is known for more than 75 years, the von Kármán constant governing the slope of the loglaw was not determined theoretically. In this letter we show that the von Kármán constant can be estimated from homogeneous turbulent data, i. e, without information from wallbounded flows.

(2005) Physical review letters. 95, 19, 194502. Abstract
Drag reduction by polymers in wall turbulence is bounded from above by a universal maximal drag reduction (MDR) velocity profile that is a log law, estimated experimentally by Virk as V+(y+) 11.7log y+17. Here V+(y) and y+ are the mean streamwise velocity and the distance from the wall in "wall" units. In this Letter we propose that this MDR profile is an edge solution of the NavierStokes equations (with an effective viscosity profile) beyond which no turbulent solutions exist. This insight rationalizes the universality of the MDR and provides a maximum principle which allows an ab initio calculation of the parameters in this law without any viscoelastic experimental input.

(2005) Environmental Fluid Mechanics. 5, 4, p. 373386 Abstract
We discuss a simple analytical model of the turbulent boundary layer (TBL) over flat plane. The model offers an analytical description of the profiles of mean velocity and turbulent activity in the entire boundary region, from the viscous sublayer, through the buffer layer further into the loglaw turbulent region. In contrast to various existing interpolation formulas the model allows one to generalize the description of simple TBL of a Newtonian fluid for more complicated flows of turbulent suspensions laden with heavy particles, bubbles, longchain polymers, to include the gravity acceleration, etc.

(2005) Physical Review E. 72, 1, 016305. Abstract
We address the "additive equivalence" discovered by Virk and coworkers: drag reduction affected by flexible and rigid rodlike polymers added to turbulent wallbounded flows is limited from above by a very similar maximum drag reduction (MDR) asymptote. Considering the equations of motion of rodlike polymers in wallbounded turbulent ensembles, we show that although the microscopic mechanism of attaining the MDR is very different, the macroscopic theory is isomorphic, rationalizing the interesting experimental observations.

(2005) Physical review letters. 94, 17, 174502. Abstract
Drag reduction by microbubbles is a promising engineering method for improving ship performance. A fundamental theory of the phenomenon is lacking, however, making actual design quite haphazard. We offer here a theory of drag reduction by microbubbles in the limit of very small bubbles, when the effect of the bubbles is mainly to normalize the density and the viscosity of the carrier fluid. The theory culminates with a prediction of the degree of drag reduction given the concentration profile of the bubbles. Comparisons with experiments are discussed and the road ahead is sketched.

(2005) Physical Review E. 71, 1, 016305. Abstract
The interaction of polymers with turbulent shear flows is examined. We focus on the structure of the elastic stress tensor, which is proportional to the polymer conformation tensor. We examine this object in turbulent flows of increasing complexity. First is isotropic turbulence, then anisotropic (but homogenous) shear turbulence, and finally wall bounded turbulence. The main result of this paper is that for all these flows the polymer stress tensor attains a universal structure in the limit of large Deborah number De≫ 1. We present analytic results for the suppression of the coilstretch transition at large Deborah numbers. Above the transition the turbulent velocity fluctuations are strongly correlated with the polymer's elongation: there appear highquality "hydroelastic" waves in which turbulent kinetic energy turns into polymer potential energy and vice versa. These waves determine the trace of the elastic stress tensor but practically do not modify its universal structure. We demonstrate that the influence of the polymers on the balance of energy and momentum can be accurately described by an effective polymer viscosity that is proportional to the crossstream component of the elastic stress tensor. This component is smaller than the streamwise component by a factor proportional to De ^{2}. Finally we tie our results to wall bounded turbulence and clarify some puzzling facts observed in the problem of drag reduction by polymers.
2004

(2004) Europhysics Letters. 68, 6, p. 825831 Abstract
Drag reduction by polymers in turbulent wallbounded flows exhibits universal and nonuniversal aspects. The universal maximal moanvelocity profile was explained in a recent theory. The saturation of this profile and the crossover back to the Newtonian plug are nonuniversal, depending on Reynolds number Re, concentration of polymer cp and the degree of polymerization N _{p}. We explain the mechanism of saturation stemming from the finiteness of extensibility of the polymers, predict its dependence on c _{p} and N in the limit of small c_{p} and large R_{e}, and present the excellent comparison of our predictions to experiments on drag reduction by DNA.

(2004) Physical Review E. 70, 5 2, p. 05530110553014 055301(R). Abstract
The drag reduction by polymers in turbulent flows was analyzed. The drag reduction, in a recent theory, was found to be consistent with the effective viscocity growing linearly with the distance from the wall. the reduction in the Reynolds stress overwhelmed the increase in the viscous drag by the selfconsistent solution. By using the direct numerical simulations it was shown that a linear viscosity profile reduced the drag in agreement with the theory and in close correspondence with direct simulations of the FENEP model at the same flow conditions.

(2004) Physical review letters. 92, 24, p. 24450312445034 244503. Abstract
The mechanism of drag reduction by polymers in turbulent wallbounded flows was investigated. A new logarithmic law for the mean velocity was derived with a slope that fit existing data. The phenomenonology of the maximum drag reduction asymptote which is the maximum drag reduction attained by polymers was developed on the basis of the equations of fluid mechanics. It was observed that the mechanism of drag reduction is the suppression of the Reynolds stress in the elastic sublayer.

(2004) JETP Letters. 80, 7, p. 479483 Abstract
Turbulence spectra in superfluids are modified by the nonlinear energy dissipation caused by the mutual friction between quantized vortices and the normal component of the liquid. We have found a new state of fully developed turbulence, which occurs in some range of two Reynolds parameters characterizing the superfluid flow. This state displays both the KolmogorovObukhov 5/3scaling law E_{k} ∞k^{5/3} and a new "3scaling law" E_{k} ∞ k^{3}, each in a wellseparated range of k.
2003

(2003) Chemical Physics Letters. 381, 56, p. 650653 Abstract
A model is given that shows that the electronic properties of close packed organized organic layers, adsorbed on conductive substrate, may be very different from the properties of the single adsorbed molecule. The difference arises from a cooperative effect that results in electron transfer between the substrate and the layer. It is induced when molecules having dipole moment and low polarizability are organized so that their dipole moment is perpendicular to the surface. The thermodynamics of the problem is described. The model provides a possible rationalization to recent observed new experimental properties of adsorbed organized organic layers.

(2003) Physical Review E. 68, 4 2, p. 4630814630826 046308. Abstract
A multizone shell (MSZ) model for wallbounded flows, accounting for the space inhomogenity in a piecewise approximation in which the crosssectional area of the flow was subdivided into zones, was discussed. The MSZ model includes a set of complex variables describing the amplitudes of the nearwall coherent structure. The evolution of the mean velocity profile with increasing Reynolds number from the laminar profile toward the universal logarithmic profile near the flatplane boundary layer was also elaborated.

(2003) Physical Review E. 67, 6 2, p. 066310/1066310/9 066310. Abstract
The forced structure functions F_{p}(k_{n}) for two types of initial conditions was analyzed using the Sabra shell model of turbulence. Decay 1 that was considered four times, which differed in order of magnitudes. Decay 2 that was considered three different times t=10^{2}T, 10^{3}T, and 10^{4}T. In all these cases it was found that the scaling exponents ζ_{p} and the dimensionless amplitudes C_{p} for the three even orders p=2, 4, and 6.

(2003) Physical Review E. 67, 5 2, p. 056312/1056312/11 056312. Abstract
A systematic study of drag reduction was performed on the basis of DNS of the FENEP model. Simulations of Newtonian and viscoelastic flows in channel configuration at the same friction Reynolds number were investigated. First, the list of empirical modes that represent the velocity field in an optimal way in an energy decreasing order was found. The important discovery was that this list contains the very same modes for the Newtonian and viscoelastic flows.

(2003) Physical Review E. 67, 4 2, p. 4631414631421 046314. Abstract
The effect of particle inertia on turbulence in a suspension was investigated. The energy suppression due to the fluidparticle friction and the energy enhancement during the cascade process due to decrease of the effective density of the smallscale motions were described analytically. Numerical simulations presented the qualitative picture of the isotropic homogeneous turbulence of dilute suspensions.

(2003) Physical Review E. 67, 2, 026312. Abstract
In anisotropic turbulence, the correlation functions are decomposed in the irreducible representations of the SO(3) symmetry group (with different "angular momenta" l). For different values of l, the secondorder correlation function is characterized by different scaling exponents zeta(2)(l). In this paper, we compute these scaling exponents in a closure approximation. By linearizing the closure equations in small anisotropy we set up a linear operator and find its zero modes in the inertial interval of scales. Thus the scaling exponents in each l sector follow from solvability condition, and are not determined by dimensional analysis. The main result of our calculation is that the scaling exponents zeta(2)(l) form a strictly increasing spectrum at least until l=6, guaranteeing that the effects of anisotropy decay as power laws when the scale of observation diminishes. The results of our calculations are compared to available experiments and simulations.

(2003) Physical Review E. 67, 2 2, p. 2631012631011 026310. Abstract
The stabilization of hydrodynamic flows was studied by small viscosity variations. The primary and secondary instability of simple channel flows was addressed. It was reiterated that the large effect was not due to a modified dissipation but due to reduced energy intake from the mean flow to the fluctuations.
2002

(2002) FractalsComplex Geometry Patterns And Scaling In Nature And Society. 10, 3, p. 291296 Abstract
We introduce a model of hydrodynamic turbulence with a tunable parameter ε, which represents the ratio between deterministic and random components in the coupling between N identical copies of the turbulent field. To compute the anomalous scaling exponents ζ_{n} (of the nth order structure functions) for chosen values of ε, we consider a systematic closure procedure for the hierarchy of equations for the norder correlation functions, in the limit N → ∞. The parameter ε regularizes the closure procedure, in the sense that discarded terms are of higher order in ε compared to those retained. It turns out that after the terms of O(1), the first nonzero terms are O(ε^{4}). Within this εcontrolled procedure, we have a finite and closed set of scaleinvariant equations for the 2nd and 3rd order statistical objects of the theory. This set of equations retains all terms of O(1) and O(ε^{4}) and neglects terms of O(ε^{6}). On this basis, we expect anomalous corrections δζ_{n} in the scaling exponents ζ_{n} to increase with ε_{n}. This expectation is confirmed by extensive numerical simulations using up to 25 copies and 28 shells for various values of ε_{n}. The simulations demonstrate that in the limit N → ∞, the scaling is normal for ε cr with ε_{cr} ≈ 0.6. We observed the birth of anomalous scaling at ε = ε_{cr} with δζ_{n} ∝ ε^{4}  ε_{cr}^{4} according to our expectation.

(2002) Physical Review E. 66, 3, Abstract
A theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution is suggested. The reason for the clustering instability is a combined effect of the particles inertia and a finite correlation time of the velocity field. The crucial parameter for the clustering instability is the size of the particles. The critical size is estimated for a strong clustering (with a finite fraction of particles in clusters) associated with the growth of the mean absolute value of the particles number density and for a weak clustering associated with the growth of the second and higher moments. A new concept of compressibility of the turbulent diffusion tensor caused by a finite correlation time of an incompressible velocity field is introduced. In this model of the velocity field, the field of Lagrangian trajectories is not divergence free. A mechanism of saturation of the clustering instability associated with the particles collisions in the clusters is suggested. Applications of the analyzed effects to the dynamics of droplets in the turbulent atmosphere are discussed. An estimated nonlinear level of the saturation of the droplets number density in clouds exceeds by the orders of magnitude their mean number density. The critical size of cloud droplets required for cluster formation is more than [formula presented].

(2002) Physical Review Letters. 89, 6, p. 064501/1064501/4 064501. Abstract
The statistics of twodimensional turbulence exhibit a riddle: the scaling exponents in the regime of inverse energy cascade agree with the K41 theory of turbulence far from equilibrium, but the probability distribution functions are close to Gaussianlike in equilibrium. The skewness Sequivalent toS(3)(R)/S2(3/2)(R) was measured as S(exp)approximate to0.03. This contradiction is lifted by understanding that twodimensional turbulence is not far from a situation with equipartition of enstrophy, which exists as true thermodynamic equilibrium with K41 exponents in space dimension of d=4/3. We evaluate the skewness S(d) for 4/3 less than or equal todless than or equal to2, showing that S(d)=0 at d=4/3, and that it remains as small as Sexp in two dimensions.

(2002) Physics Today. 55, 4, p. 91 Abstract
Victor Iosifovich Belinicher, a prominent Russian theoretical physicist, was among the passengers on the airplane traveling from Tel Aviv, Israel, to Novosibirsk, Russia, that was accidentally hit by a Ukrainian antiaircraft missile fired during military exercises on 4 October 2001. This senseless tragedy ended the life of a highly respected member of the scientific community, a colleague, a friend, and a teacher.Born on 7 November 1945 in Sverdlovsk, Russia, Belinicher was one of the first students who graduated from the newly established Novosibirsk University in the Akademgorodok Scientific Center in Novosibirsk. In 1971, he received his PhD in physics and mathematics, under the supervision of Dmitrii Shirkov, for work on the Lagrangian formalism for particles of arbitrary spin. He earned his DSc degree in 1982 on the theory of the photogalvanic effect.In 1973, Belinicher joined the Institute of Automation and Electrometry of the Russian Academy of Sciences (RAS) as a research scientist. He particularly enjoyed the atmosphere of intense scientific interaction and intellectual challenge at Akademgorodok. He studied a variety of problems in condensed matter physics, semiconductor physics, and the physics of nonlinear phenomena. One of his most important contributions was a comprehensive theory of the photogalvanic effect in crystals that lack inversion symmetry. The systematic microscopic theory worked out by Belinicher and his colleagues addressed the most important mechanisms producing the effect, ultimately connecting the effect’s origin to the absence of a detailed balance condition in media that lack a center of symmetry. A review article by Belinicher and Boris I. Sturman published in 1980 in Soviet Physics Uspekhi on the photogalvanic effect remains one of the most cited works in the field.While at the institute, Belinicher began a longlasting collaboration with one of us (L’vov). In 1984, they developed a new diagrammatic technique—which generalized the Keldysh formalism to the case of spin operators—for nonequilibrium processes in magnetism. In subsequent work in 1987, they formulated the scaleinvariant theory of hydrodynamic turbulence. An earlier approach, advanced in the 1960s by Henry Wyld, suffered from divergences in each order of perturbation theory, and known regularizations were limited to the first order. Belinicher and L’vov found a transformation, now named after them, which removes divergences from all orders. This notable work created a basis for further intensive studies of hydrodynamic turbulence by means of modern methods of theoretical physics.Belinicher joined the RAS’s Institute of Semiconductor Physics in 1988 as a leading research scientist. His interests turned toward the newly discovered highT c superconductors and to the general problem of strong electronic correlations associated with those materials. Belinicher worked intensely to develop a model that would describe the essential electronic properties of highT c materials. The contributions he made, together with his graduate students and colleagues, to the understanding of the physics of the Hubbard model, spin liquids, and spin–polaron mechanisms of superconductivity significantly influenced progress in those areas. In recent years, he devoted much of his time to the derivation of a consistent field theory of the twodimensional antiferromagnet and to yet another strongly correlated problem—Coulomb blockade in a system of quantum dots. Undoubtedly, Belinicher’s contributions to physics will continue to serve as a basis for new findings, and his work will become part of textbooks for future generations of physicists.Belinicher also lectured and mentored many students at Novosibirsk University, where he was appointed as a professor of physics in 1995. He taught both undergraduate and advanced theoretical courses.In the 1990s, Belinicher was a visiting professor at several institutions in Europe and Israel, particularly at the University of Coimbra in Portugal, and the Weizmann Institute of Science in Rehovot, Israel, where he contributed invaluably to many studies. His outgoing, cooperative character together with an extraordinary dedication to physics brought him many friends and professional colleagues from all around the world.Belinicher was an intense and persistent man who believed deeply in maintaining the quality of his research. For him, science was the absolute priority in his life. He approached nonscientific problems with the same energetic attitude that he applied to his research, whether they involved an issue in turbulent Russian politics or a development of the local computer network. He taught students to treasure the time they devoted to research.Belinicher was open and optimistic, and generously shared his energy and vigor. He was a bright, talented theorist who pursued the deepest and most complicated problems in physics. He was full of plans for the future when the terrible accident ended his life. His family, friends, and colleagues have suffered a great loss

(2002) Physical Review E. 65, 2, Abstract
A variation principle is suggested to find selfsimilar solitary solutions (referred to as solitons) of shell model of turbulence. For the Sabra shell model the shape of the solitons is approximated by rational trial functions with relative accuracy of [formula presented] It is found how the soliton shape, propagation time [formula presented] (from a shell n to shells with [formula presented] and the dynamical exponent [formula presented] (which governs the time rescaling of the solitons in different shells) depend on parameters of the model. For a finite interval of z the author discovered quasisolitons which approximate with high accuracy corresponding selfsimilar equations for an interval of times from [formula presented] to some time in the vicinity of the peak maximum or even after it. The conjecture is that the trajectories in the vicinity of the quasisolitons (with continuous spectra of [formula presented] provide an essential contribution to the multiscaling statistics of highorder correlation functions, referred to in the paper as an asymptotic multiscaling. This contribution may be even more important than that of the trajectories in the vicinity of the exact soliton with a fixed value [formula presented] Moreover there are no solitons in some regions of the parameters where quasisolitons provide a dominant contribution to the asymptotic multiscaling.

Strong and weak clustering of inertial particles in turbulent flows(2002) arXiv. nlin/02020. Abstract
We suggested a theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution. The reason of the {\em clustering instability} is a combined effect of the particle inertia and finite correlation time of the velocity field. The crucial parameter for the instability is a size of the particles. The critical size is estimated for a {\em strong clustering} (with a finite fraction of particles in clusters) associated with the growth of the mean absolute value of the particles number density and for a {\em weak clustering} associated with the growth of the second and higher moments. A nonlinear mechanism for a saturation of the clustering instability (particles collisions in the clusters) is suggested. Applications of the analyzed effects to the dynamics of aerosols and droplets in the turbulent atmosphere are discussed. The critical size of atmospheric aerosols and droplets in clustering is of the order of (20−30)μm, and a lower estimate of the number of particles in a cluster is about hundreds.

(2002) Physical review letters. 89, 7, 074501 . Abstract
We consider shell models that display an inverse energy cascade similar to twodimensional turbulence (together with a direct cascade of an enstrophylike invariant). Previous attempts to construct such models ended negatively, stating that shell models give rise to a \u201cquasiequilibrium\u201d situation with equipartition of the energy among the shells. We show analytically that the quasiequilibrium state predicts its own disappearance upon changing the model parameters in favor of the establishment of an inverse cascade regime with Kolmogorov scaling. The latter regime is found where predicted, offering a useful model to study inverse cascades.

Onefluid description of turbulently flowing suspension(2002) arXiv. Abstract
We suggested a onefluid model of a turbulent dilute suspension which accounts for the "twoway'' fluidparticle interactions by kdependent effective density of suspension and additional damping term in the NavierStokes equation. We presented analytical description of the particle modification of turbulence including scale invariant suppression of a small k part of turbulent spectrum (independent of the particle response time) and possible enhancement of large k region [up to the factor (1+ϕ)2/3]. Our results are in agreement with qualitative picture of isotropic homogeneous turbulence of dilute suspensions previously observed in laboratory and numerical experiments.
2001

(2001) Physical review letters. 87, 17, 174501. Abstract
Motivated by turbulent drag reduction by minute concentrations of polymers we study the effects of minor viscosity contrasts on the stability of hydrodynamic flows. The key player is a localized region where fluctuations are produced by interactions with the mean flow (the \u201ccritical layer\u201d). We show that a layer of weakly spacedependent viscosity placed near the critical layer has a very large stabilizing effect on hydrodynamic fluctuations, retarding significantly the onset of turbulence. The effect is not due to a modified dissipation (as is assumed in theories of drag reduction) but is due to reduced energy intake from the mean flow to the fluctuations. Similar physics may act in turbulent drag reduction.

(2001) Physical Review E. 63, 5 II, p. 5611815611810 056118. Abstract
The detailed dynamic scaling properties of the natural phenomena and prediction of the probability of their occurrence was discussed. The dynamical scaling form is characterized by static and dynamic exponents whose values were determined by analyzing the isolated events in short time horizons. The probability density functions were used to demonstrate the existence of scaling properties of extreme events.
2000

(2000) Physica A. 288, 14, p. 280307 Abstract
We present a short review of the work conducted by our group on the subject of anomalous scaling in anisotropic turbulence. The basic idea that unifies all the applications discussed here is that the equations of motion for correlation functions are always linear and invariant to rotations, and therefore the solutions foliate into sectors of the symmetry group of all rotations (SO(3)). We have considered models of passive scalar and passive vector advections by a rapidly changing turbulent velocity field (Kraichnantype models) for which we find a discrete spectrum of universal anomalous exponents, with a different exponent characterizing the scaling behavior in every sector. Generically the correlation functions and structure functions appear as sums over all these contributions, with nonuniversal amplitudes which are determined by the anisotropic boundary conditions. In addition we considered NavierStokes turbulence by analyzing simulations and experiments, and reached some interesting conclusions regarding the scaling exponents in the anisotropic sectors. The theory presented here clarifies questions like the restoration of local isotropy upon decreasing scales. We explain when the local isotropy is fully restored and when the lingering effects of the anisotropic forcing appear for arbitrarily small scales.

(2000) Europhysics Letters. 50, 4, p. 473479 Abstract
The major difficulty in developing theories for anomalous scaling in hydrodynamic turbulence is the lack of a small parameter. In this letter we introduce a shell model of turbulence that exhibits anomalous scaling with a tunable parameter ∈, 0 ≤ ∈ ≤ 1, representing the ratio between deterministic and random components in the coupling between N identical copies of the turbulent field. Our numerical experiments give strong evidence that in the limit N → ∞ anomalous scaling sets in proportional to ∈^{4}. This result shows consistency with the nonperturbative closure proposed by the authors in Phys. Fluids, 12 (2000) 803. In this procedure closed equations of motion for the loworder correlation and response functions are obtained, keeping terms proportional to ∈^{0} and ∈^{4}, discarding terms of orders ∈^{6} and higher. Moreover we give strong evidences that the birth of anomalous scaling appears at a finite critical ∈, being ∈_{c} ≈ 0.6.

(2000) Physics of Fluids. 12, 4, p. 803821 Abstract
We present a model of hydrodynamic turbulence for which the program of computing the scaling exponents from first principles can be developed in a controlled fashion. The model consists of N suitably coupled copies of the "Sabra" shell model of turbulence. The couplings are chosen to include two components: random and deterministic, with a relative importance that is characterized by a parameter called ∈. It is demonstrated, using numerical simulations of up to 25 copies and 28 shells that in the N→∞ limit but for 0

(2000) Physical Review E. 61, 1, p. 407421 Abstract
The statistical objects characterizing turbulence in real turbulent flows differ from those of the ideal homogeneous isotropic model. They contain contributions from various two and threedimensional aspects, and from the superposition of inhomogeneous and anisotropic contributions. We employ the recently introduced decomposition of statistical tensor objects into irreducible representations of the SO(3) symmetry group (characterized by j and m indices, where [Formula Presented] to disentangle some of these contributions, separating the universal and the asymptotic from the specific aspects of the flow. The different j contributions transform differently under rotations, and so form a complete basis in which to represent the tensor objects under study. The experimental data are recorded with hotwire probes placed at various heights in the atmospheric surface layer. Time series data from single probes and from pairs of probes are analyzed to compute the amplitudes and exponents of different contributions to the second order statistical objects characterized by [Formula Presented] 1, and 2. The analysis shows the need to make a careful distinction between longlived quasitwodimensional turbulent motions (close to the ground) and relatively shortlived threedimensional motions. We demonstrate that the leading scaling exponents in the three leading sectors [Formula Presented] 1, and 2) appear to be different but universal, independent of the positions of the probe, the tensorial component considered, and the large scale properties. The measured values of the scaling exponent are [Formula Presented] [Formula Presented] and [Formula Presented] We present theoretical arguments for the values of these exponents using the Clebsch representation of the Euler equations; neglecting anomalous corrections, the values obtained are 2/3, 1, and 4/3, respectively. Some enigmas and questions for the future are sketched.

(2000) Physical Review E. 61, 3, p. 25862594 Abstract
We found universal anizopropic spectra of acoustic turbulence with the linear dispersion law [Formula Presented] within the framework of generalized kinetic equation which takes into account the finite time of threewave interactions. This anisotropic spectra can assume both scaleinvariant and nonscaleinvariant form. The implications for the evolution of the acoustic turbulence with nonisotropic pumping are discussed. The main result of the article is that the spectra of acoustic turbulence tend to become more isotropic.

(2000) Physical Review E. 62, 6, p. 80378057 Abstract
The main difficulty of statistical theories of fluid turbulence is the lack of an obvious small parameter. In this paper we show that the formerly established fusion rules can be employed to develop a theory in which Kolmogorov\u2019s statistics of 1941 (K41) acts as the zero order, or background statistics, and the anomalous corrections to the K41 scaling exponents [Formula Presented] of the [Formula Presented]order structure functions can be computed analytically. The crux of the method consists of renormalizing a fourpoint interaction amplitude on the basis of the fusion rules. This amplitude includes a small dimensionless parameter, which is shown to be of the order of the anomaly of [Formula Presented] [Formula Presented] Higherorder interaction amplitudes are shown to be even smaller. The corrections to K41 to [Formula Presented] result from standard logarithmically divergent ladder diagrams in which the fourpoint interaction acts as a \u201crung.\u201d The theory allows a calculation of the anomalous exponents [Formula Presented] in powers of the small parameter [Formula Presented] The n dependence of the scaling exponents [Formula Presented] stems from pure combinatorics of the ladder diagrams. In this paper we calculate the exponents [Formula Presented] up to [Formula Presented] Previously derived bridge relations allow a calculation of the anomalous exponents of correlations of the dissipation field and of dynamical correlations in terms of the same parameter [Formula Presented] The actual evaluation of the small parameter [Formula Presented] from first principles requires additional developments that are outside the scope of this paper.

(2000) Physical Review E. 62, 4, p. 49044919 Abstract
Kraichnan\u2019s model of passive scalar advection in which the driving (Gaussian) velocity field has fast temporal decorrelation is studied as a case model for understanding the anomalous scaling behavior in the anisotropic sectors of turbulent fields. We show here that the solutions of the Kraichnan equation for the norder correlation functions foliate into sectors that are classified by the irreducible representations of the [Formula Presented] symmetry group. We find a discrete spectrum of universal anomalous exponents, with a different exponent characterizing the scaling behavior in every sector. Generically the correlation functions and structure functions appear as sums over all these contributions, with nonuniversal amplitudes that are determined by the anisotropic boundary conditions. The isotropic sector is always characterized by the smallest exponent, and therefore for sufficiently small scales local isotropy is always restored. The calculation of the anomalous exponents is done in two complementary ways. In the first they are obtained from the analysis of the correlation functions of gradient fields. The theory of these functions involves the control of logarithmic divergences that translate into anomalous scaling with the ratio of the inner and the outer scales appearing in the final result. In the second method we compute the exponents from the zero modes of the Kraichnan equation for the correlation functions of the scalar field itself. In this case the renormalization scale is the outer scale. The two approaches lead to the same scaling exponents for the same statistical objects, illuminating the relative role of the outer and inner scales as renormalization scales. In addition we derive exact fusion rules, which govern the small scale asymptotics of the correlation functions in all the sectors of the symmetry group and in all dimensions.
1999

(1999) Physical Review E. 60, 4 A, p. 41754184 Abstract
The Taylor hypothesis, which allows surrogating spatial measurements requiring many experimental probes by time series from one or two probes, is examined on the basis of a simple analytic model of turbulent statistics. The main points are as follows: (i) The Taylor hypothesis introduces systematic errors in the evaluation of scaling exponents. (ii) When the mean wind V̄_{0} is not infinitely larger than the rootmeansquare longitudinal turbulent fluctuations v_{T}, the effective Taylor advection velocity V_{ad} should take the latter into account. (iii) When two or more probes are employed the application of the Taylor hypothesis and the optimal choice of the effective advecting wind V_{ad} need extra care. We present practical considerations for minimizing the errors incurred in experiments using one or two probes. (iv) Analysis of the Taylor hypothesis when different probes experience different mean winds is offered.

(1999) Europhysics Letters. 46, 5, p. 609612 Abstract
We show that the Sabra shell model of turbulence, which was introduced recently, displays a Hamiltonian structure for given values of the parameters. The requirement of scale independence of the flux of this Hamiltonian allows us to compute exactly a oneparameter family of anomalous scaling exponents associated with 4thorder correlation functions.

(1999) Physical Review E. 60, 6, p. 66566662 Abstract
It was shown recently that the anomalous scaling of simultaneous correlation functions in turbulence is intimately related to the breaking of temporal scale invariance, which is equivalent to the appearance of infinitely many times scales in the time dependence of timecorrelation functions. In this paper we derive a continued fraction representation of turbulent time correlation functions which is exact and in which the multiplicity of time scales is explicit. We demonstrate that this form yields precisely the same scaling laws for time derivatives and time integrals as the “multifractal” representation that was used before. Truncating the continued fraction representation yields the “best” estimates of time correlation functions if the given information is limited to the scaling exponents of the simultaneous correlation functions up to a certain, finite order. It is worth noting that the derivation of a continued fraction representation obtained here for a time evolution operator which is not Hermitian or antiHermitian may be of independent interest.

(1999) Physical Review E. 59, 6, p. 67536765 Abstract
The theory of fully developed turbulence is usually considered in an idealized homogeneous and isotropic state. Real turbulent flows exhibit the effects of anisotropic forcing. The analysis of correlation functions and structure functions in isotropic and anisotropic situations is facilitated and made rational when performed in terms of the irreducible representations of the relevant symmetry group which is the group of all rotations SO(3). In this paper we first consider the needed general theory, and explain why we expect different (universal) scaling exponents in the different sectors of the symmetry group. We exemplify the theory context of isotropic turbulence (for third order tensorial structure functions) and in weakly anisotropic turbulence (for the second order structure function). The utility of the resulting expressions for the analysis of experimental data is demonstrated in the context of high Reynolds number measurements of turbulence in the atmosphere.
1998


(1998) Journal of Statistical Physics. 93, 34, p. 797832 Abstract
We develop a consistent closure procedure for the calculation of the scaling exponents ζ_{n} of the nthorder correlation functions in fully developed hydrodynamic turbulence, starting from first principles. The closure procedure is constructed to respect the fundamental rescaling symmetry of the Euler equation. The starting point of the procedure is an infinite hierarchy of coupled equations that are obeyed identically with respect to scaling for any set of scaling exponents ζ_{n}. This hierarchy was discussed in detail in a recent publication by V. S. L'vov and I. Procaccia. The scaling exponents in this set of equations cannot be found from power counting. In this paper we present in detail the lowest nontrivial closure of this infinite set of equations, and prove that this closure leads to the determination of the scaling exponents from solvability conditions. The equations under consideration after this closure are nonlinear integrodifferential equations, reflecting the nonlinearity of the original NavierStokes equations. Nevertheless they have a very special structure such that the determination of the scaling exponents requires a procedure that is very similar to the solution of linear homogeneous equations, in which amplitudes are determined by fitting to the boundary conditions in the space of scales. The renormalization scale that is necessary for any anomalous scaling appears at this point. The Hölder inequalities on the scaling exponents select the renormalization scale as the outer scale of turbulence L. We demonstrate that the solvability condition of our equations leads to nonKolmogorov values of the scaling exponents ζ_{n}. Finally, we show that this solutions is a first approximation in a systematic series of improving approximations for the calculation of the anomalous exponents in turbulence.

(1998) Physica A. 257, 4Jan, p. 165196 Abstract
We propose a scheme for the calculation from the NavierStokes equations of the scaling exponents in of the nth order correlation functions in fully developed hydrodynamic turbulence. The scheme is nonperturbative and constructed to respect the fundamental rescaling symmetry of the Euler equation. It constitutes an infinite hierarchy of coupled equations that are obeyed identically with respect to scaling for any set of scaling exponents zeta(n). As a consequence the scaling exponents are determined by solvability conditions and not from power counting. It is argued that in order to achieve such a formulation one must recognize that the manypoint spacetime correlation functions are not scale invariant in their time arguments, The assumption of full scale invariance leads unavoidably to Kolmogorov exponents. It is argued that the determination of all the scaling exponents in requires equations for infinitely many renormalized objects. One can however proceed in controlled successive approximations by successive truncations of the infinite hierarchy of equations. Clues as to how to truncate without reintroducing power counting can be obtained from renormalized perturbation theory. To this aim we show that the fully resummed perturbation theory is equivalent in its contents to the exact hierarchy of equations obeyed by the nth order correlation functions and Green's function. In light of this important result we can safely use finite resummations to construct successive closures of the infinite hierarchy of equations. This paper presents the conceptual and technical details of the scheme. The analysis of the highorder closure procedures which do not destroy the rescaling symmetry and the actual calculations for truncated models will be presented in a forthcoming paper in collaboration with V. Belinicher. (C) 1998 Elsevier Science B.V. All rights reserved.

(1998) Europhysics Letters. 43, 3, p. 277283 Abstract
A recent theoretical development in the understanding of the smallscale structure of NavierStokes turbulence has been the proposition that the scales η_{n}(R) that separate inertial from viscous behavior of manypoint correlation functions depend on the order n and on the typical separations R of points in the correlation. This is of fundamental significance in itself but it also has implications for the scaling behaviour of various correlation functions. This dependence has never been observed directly in laboratory experiments. In order to observe it, turbulence data which both display a welldeveloped scaling range with clean scaling behaviour and are wellresolved in the small scales to well within the viscous range is required. The data of the experiments performed in the laboratory of P. Tabeling of NavierStokes turbulence in a helium cell with counterrotating disks approach these criteria, and provide supporting evidence for the existence of the predicted scaling of the viscous scale.

(1998) Physica A. 254, 12, p. 215230 Abstract
In this short paper we describe the essential ideas behind a new consistent closure procedure for the calculation of the scaling exponents ζ_{n} of the nth order correlation functions in fully developed hydrodynamic turbulence, starting from first principles. The closure procedure is constructed to respect the fundamental rescaling symmetry of the Euler equation. The starting point of the procedure is an infinite hierarchy of coupled equations that are obeyed identically with respect to scaling for any set of scaling exponents ζ_{n}. This hierarchy was discussed in detail in a recent publication [V.S. L'vov and I. Procaccia, Physica A (1998), in press, chaodyn/9707015]. The scaling exponents in this set of equations cannot be found from power counting. In this short paper we discuss in detail low order nontrivial closures of this infinite set of equations, and prove that these closures lead to the determination of the scaling exponents from solvability conditions. The equations under consideration after this closure are nonlinear integrodifferential equations, reflecting the nonlinearity of the original NavierStokes equations. Nevertheless, they have a very special structure such that the determination of the scaling exponents requires a procedure that is very similar to the solution of linear homogeneous equations, in which amplitudes are determined by fitting to the boundary conditions in the space of scales. The renormalization scale that is necessary for any anomalous scaling appears at this point. The Hölder inequalities on the scaling exponents select the renormalization scale as the outer scale of turbulence L.

(1998) Physical review letters. 81, 4, p. 802805 Abstract
In a series of recent works it was proposed that shell models of turbulence exhibit inertial range scaling exponents that depend on the nature of the dissipative mechanism. If true, and if one could imply a similar phenomenon to NavierStokes turbulence, this finding would cast strong doubts on the universality of scaling in turbulence. In this Letter we propose that these \u201cnonuniversalities\u201d are just corrections to scaling that disappear when the Reynolds number goes to infinity.

(1998) Physical Review E. 58, 2, p. 18111822 Abstract
We introduce a shell model of turbulence that exhibits improved properties in comparison to the standard (and very popular) Gledzer, Ohkitani, and Yamada (GOY) model. The nonlinear coupling is chosen to minimize correlations between different shells. In particular, the secondorder correlation function is diagonal in the shell index and the thirdorder correlation exists only between three consecutive shells. Spurious oscillations in the scaling regime, which are an annoying feature of the GOY model, are eliminated by our choice of nonlinear coupling. We demonstrate that the model exhibits multiscaling similar to the GOY model. The scaling exponents are shown to be independent of the viscous mechanism as is expected for NavierStokes turbulence and other shell models. These properties of the model make it optimal for further attempts to achieve understanding of multiscaling in nonlinear dynamics.

(1998) Physical review letters. 81, 24, p. 53305333 Abstract
We analyze turbulent velocity signals in the atmospheric surface layer, obtained by pairs of probes separated by inertialrange distances parallel to the ground and (nominally) orthogonal to the mean wind. The Taylor microscale Reynolds number ranges up to 20 000. Choosing a suitable coordinate system with respect to the mean wind, we derive theoretical forms for second order structure functions and fit them to experimental data. The effect of flow anisotropy is small for the longitudinal component but significant for the transverse component. The data provide an estimate for a universal exponent from among a hierarchy that governs the decay of flow anisotropy with the scale size.
1997

(1997) Physical review letters. 79, 21, p. 41664169 Abstract
We present results from direct numerical simulations of the Kraichnan model for passive scalar advection by a rapidly varying random scaling velocity field for intermediate values of the velocity scaling exponent. These results are compared with the scaling exponents predicted for this model by Kraichnan. Further, we test the recently proposed fusion rules which govern the scaling properties of multipoint correlations, and present results on the linearity of the conditional statistics of the Laplacian operator on the scalar field.

(1997) Physical review letters. 79, 11, p. 20502052 Abstract
The phenomenology of the scaling behavior of higher order structure functions of velocity differences across a scale R in turbulence should be built around the irreducible representations of the rotation symmetry group. Every irreducible representation is associated with a scalar function of R which may exhibit different scaling exponents. The common practice of using moments of longitudinal and transverse fluctuations mixes different scalar functions and therefore may mix different scaling exponents. It is shown explicitly how to extract pure scaling exponents for correlation functions of arbitrary orders.

(1997) Physical Review E. 56, 1, p. 390405 Abstract
We develop expressions for the nonlinear wave damping and frequency correction of a field of random, spatially homogeneous, acoustic waves. The implications for the nature of the equilibrium spectral energy distribution are discussed.

Hydrodynamic turbulence: a 19th century problem with a challenge for the 21st century(1997) Turbulence Modeling And Vortex Dynamics. 491, p. 116 Abstract
The theoretical calculation of the scaling exponents that characterize the statistics of fully developed turbulence is one of the major open problems of statistical physics. We review the subject, explain some of the recent developments, and point out the road ahead.

Nonperturbative zero modes in the Kraichnan model for turbulent advection(1997) Physical Review E. 55, 4, p. R3836R3839 Abstract
The anomalous scaling behavior of the nth order correlation functions [formula presented] of the Kraichnan model of turbulent passive scalar advection is believed to be dominated by the homogeneous solutions (zero modes) of the Kraichnan equation B[formula presented][formula presented]=0. Previous analysis found zero modes in perturbation theory with respect to a small parameter. We present a computerassisted analysis of the simplest nontrivial case of n=3: we demonstrate nonperturbatively the existence of anomalous scaling, and compare the results with the perturbative predictions.

(1997) Physical Review E. 55, 6, p. 70307035 Abstract
On the basis of the NavierStokes equations, we develop the high Reynolds number statistical theory of differenttime, manypoint spatial correlation functions of velocity differences. We find that their time dependence is not scale invariant: norder correlation functions exhibit infinitely many distinct decorrelation times that are characterized by anomalous dynamical scaling exponents. We derive exact scaling relations that bridge all these dynamical exponents to the static anomalous exponents [Formula Presented] of the standard structure functions. We propose a representation of the time dependence using the Legendretransform formalism of multifractals that automatically reproduces all the newly found bridge relationships.

(1997) Physical Review E. 56, 1 SUPPL. A, p. 406416 Abstract
The anomalous scaling behavior of the nthorder correlation functions F_{n} of the Kraichnan model of turbulent passive scalar advection is believed to be dominated by the homogeneous solutions (zero modes) of the Kraichnan equation B_{n}F_{n} = 0. In this paper we present an extensive analysis of the simplest (nontrivial) case of n = 3 in the isotropic sector. The main parameter of the model, denoted as ζ_{h}, characterizes the eddy diffusivity and can take values in the interval 0≤ζ_{h}≤2. After choosing appropriate variables we can present nonperturbative numerical calculations of the zero modes in a projective two dimensional circle. In this presentation it is also very easy to perform perturbative calculations of the scaling exponent ζ_{3} of the zero modes in the limit ζ_{h}→0, and we display quantitative agreement with the nonperturbative calculations in this limit. Another interesting limit is ζ_{h}→2. This second limit is singular, and calls for a study of a boundary layer using techniques of singular perturbation theory. Our analysis of this limit shows that the scaling exponent ζ_{3} vanishes as √ζ_{2}/Inζ_{2}, where ζ_{2} is the scaling exponent of the secondorder correlation function. In this limit as well, perturbative calculations are consistent with the nonperturbative calculations.

(1997) Physical review letters. 79, 17, p. 31743177 Abstract
We present the first experimental tests of the recently derived fusion rules for NavierStokes turbulence. The fusion rules address the asymptotic properties of manypoint correlation functions as some of the coordinates coalesce, and form an important ingredient of the nonperturbative statistical theory of turbulence. Here we test the fusion rules when the spatial separations lie within the inertial range, and find good agreement between experiment and theory. For inertialrange separations and for velocity increments which are not too large, a simple linear relation appears to exist for the Laplacian of the velocity fluctuation conditioned on velocity increments.

Exact Result for the 3rd Order Correlations of Velocity in Turbulence with Helicity(1997) arXiv. 9705016. Abstract
All statistical models of turbulence take into account Kolmogorov's exact result known as the "4/5 law" which stems from energy conservation. This law states that the energy flux expressed as a spatial derivative of the 3rd order velocity correlator equals the rate of energy dissipation. We have found an additional exact result which stems from the conservation of helicity in turbulence without inversion symmetry. It equates the flux of helicity expressed as a second spatial derivative of the 3rd order velocity correlator with the rate of helicity dissipation. This exact result must be incorporated to all statistical theories of turbulence with helicity. After submitting this paper for publication we learned that the main result was independently found by Otto Chkhetiani in JETP Lett . 63, 808 (1996).
1996

(1996) Physics of Fluids. 8, 10, p. 25652567 Abstract
Correlation functions of nonscalar fields in isotropic hydrodynamic turbulence are characterized by a set of universal exponents. These exponents also characterize the rate of decay of the effects of anisotropic forcing in developed turbulence. These exponents are important for the general theory of turbulence, and for modeling anisotropic flows. We propose methods for measuring these exponents by designing new laboratory experiments.


(1996) Physical review letters. 76, 21, p. 39633966 Abstract
It is shown that the description of anomalous scaling in turbulent systems requires the simultaneous use of two normalization scales. This phenomenon stems from the existence of two independent (infinite) sets of anomalous scaling exponents that appear in leading order, one set due to infrared anomalies and the other due to ultraviolet anomalies. To expose this clearly we introduce here a set of local fields whose correlation functions depend simultaneously on the two sets of exponents. Thus the Kolmogorov picture of \u201cinertial range\u201d scaling is shown to fail because of anomalies that are sensitive to the two ends of this range.

(1996) Physical Review E. 53, 4, p. 34683490 Abstract
Elements of the analytic structure of anomalous scaling and intermittency in fully developed hydrodynamic turbulence are described. We focus here on the structure functions of velocity differences that satisfy inertial range scaling laws Sn(R)similar to R(zeta n), and the correlation of energy dissipation Kepsilon epsilon(R)similar to R(mu). The goal is to understand from first principles what is the mechanism that is responsible for changing the exponents zeta(n) and mu from their classical Kolmogorov values. In paper II of this series [V. S. L'vov and I. Procaccia, Phys. Rev. E 52, 3858 (1995)] it was shown that the existence of an ultraviolet scale (the dissipation scale eta) is associated with a spectrum of anomalous exponents that characterize the ultraviolet divergences of correlations of gradient fields. The leading scaling exponent in this family was denoted Delta. The exact resummation of ladder diagrams resulted in a ''bridging relation,'' which determined Delta in terms of zeta(2): Delta = 2zeta(2). In this paper we continue our analysis and show that nonperturbative effects may introduce multiscaling (i.e., zeta(n) not linear in n) with the renormalization scale being the infrared outer scale of turbulence L. It is shown that deviations from the classical Kolmogorov 1941 theory scaling of Sn(R) (zeta(n) not equal n/3) must appear if the correlation of dissipation is mixing (i.e., mu>0). We suggest possible scenarios for multiscaling, and discuss the implication of these scenarios on the values of the scaling exponents zeta(n) and their ''bridge'' with mu.

(1996) Physical review letters. 76, 11, p. 18281831 Abstract
In turbulent flows the nth order structure functions S_{n}(R) scale like R^{ζ}_{n} when R is in the \u201cinertial range\u201d. Extended SelfSimilarity refers to the substantial increase in the range of power law behaviour of S_{n}(R) when they are plotted as a function of S_{2}(R) or S_{3}(R) In this Letter we demonstrate this phenomenon analytically in the context of the \u201cmultiscaling\u201d turbulent advection of a passive scalar. This model gives rise to a series of differential equations for the structure functions S_{n}(R) which can be solved and shown to exhibit extended self similarity. The phenomenon is understood by comparing the equations for S_{n} to those for S_{n}(S_{2}).

(1996) Physical Review E. 54, 6, p. 62686284 Abstract
In this paper we address nonperturbative aspects of the analytic theory of hydrodynamic turbulence. Of paramount importance for this theory are the "fusion rules" that describe the asymptotic properties of [Formula Presented]point correlation functions when some of the coordinates tend toward one other. We first derive here, on the basis of two fundamental assumptions, a set of fusion rules for correlations of velocity differences when all the separations are in the inertial interval. Using this set of fusion rules we consider the standard hierarchy of equations relating the [Formula Presented]order correlations (originating from the viscous term in the NavierStokes equations) to [Formula Presented] order (originating from the nonlinear term) and demonstrate that for fully unfused correlations the viscous term is negligible. Consequently the hierarchic chain of equations is decoupled in the sense that the correlations of [Formula Presented] order satisfy a homogeneous equation that may exhibit anomalous scaling solutions. Using the same hierarchy of equations when some separations go to zero we derive, on the basis of the NavierStokes equations, a second set of fusion rules for correlations with differences in the viscous range. The latter includes gradient fields. We demonstrate that every [Formula Presented]order correlation function of velocity differences [Formula Presented] exhibits its own crossover length [Formula Presented] to dissipative behavior as a function of, say, [Formula Presented]. This length depends on [Formula Presented] and on the remaining separations [Formula Presented] When all these separations are of the same order [Formula Presented] this length scales as [Formula Presented] with [Formula Presented], with [Formula Presented] being the scaling exponent of the [Formula Presented]order structure function. We derive a class of exact scaling relations bridging the exponents of correlations of gradient fields to the exponents [Formula Presented] of the [Formula Presented]order structure functions. One of these relations is the well known "bridge relation" for the scaling exponent of dissipation fluctuations [Formula Presented].

(1996) Physica Scripta. 67, p. 131135 Abstract
In this short note we present a brief overview of our recent progress in understanding the universal statistics of fully developed turbulence, with a stress on anomalous scaling.

(1996) Physical Review E. 54, 6, p. 63646371 Abstract
We consider turbulent advection of a scalar field [Formula Presented], passive or active, and focus on the statistics of gradient fields conditioned on scalar differences [Formula Presented] across a scale [Formula Presented]. In particular we focus on two conditional averages [Formula Presented] and [Formula Presented]. We find exact relations between these averages, and with the help of the fusion rules we propose a general representation for these objects in terms of the probability density function [Formula Presented] of [Formula Presented]. These results offer a way to analyze experimental data that is presented in this paper. The main question that we ask is whether the conditional average [Formula Presented] is linear in [Formula Presented]. We show that there exists a dimensionless parameter which governs the deviation from linearity. The data analysis indicates that this parameter is very small for passive scalar advection, and is generally a decreasing function of the Rayleigh number for the convection data.

Exact resummations in the theory of hydrodynamic turbulence. III. Scenarios for anomalous scaling and intermittency(1996) Physical Review E  Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 53, 4, p. 34683490 Abstract
The lectures presented by one of us (IP) at the Les Houches summer school dealt with the scaling properties of high Reynolds number turbulence in fluid flows. The results presented are available in the literature and there is no real need to reproduce them here. Quite on the contrary, some of the basic tools of the field and theoretical techniques are not available in a pedagogical format, and it seems worthwhile to present them here for the benefit of the interested student. We begin with a detailed exposition of the naive perturbation theory for the ensemble averages of hydrodynamic observables (the mean velocity, the response functions and the correlation functions). The effective expansion parameter in such a theory is the Reynolds number (Re); one needs therefore to perform infinite resummations to change the effective expansion parameter. We present in detail the DysonWyld line resummation which allows one to dress the propagators, and to change the effective expansion parameter from Re to O(1). Next we develop the ``dressed vertex" representation of the diagrammatic series. Lastly we discuss in full detail the pathintegral formulation of the statistical theory of turbulence, and show that it is equivalent order by order to the DysonWyld theory. On the basis of the material presented here one can proceed smoothly to read the recent developments in this field.

Fusion rules and conditional statistics in turbulent advection(1996) Physical Review E. 54, 5, p. R4520R4523 Abstract
Fusion rules in turbulence address the asymptotic properties of manypoint correlation functions when some of the coordinates are very close to each other. Here we put to the experimental test some nontrivial consequences of the fusion rules for scalar correlations in turbulence. To this aim we examine passive turbulent advection as well as convective turbulence. Adding one assumption to the fusion rules, one obtains a prediction for universal conditional statistics of gradient fields. We examine the conditional average of the scalar dissipation field [Formula Presented] for [Formula Presented] in the inertial range and find that it is linear in [Formula Presented] with a fully determined proportionality constant. The implications of these findings for the general scaling theory of scalar turbulence are discussed.


Anomalous Scaling in Turbulence: a Field Theoretic Approach(1996) Nonlinear Dynamics, Chaotic and Complex Systems. Abstract

(1996) Physical review letters. 76, 16, p. 28982901 Abstract
Fusion rules in turbulence specify the analytic structure of manypoint correlation functisons of the turbulent field when a group of coordinates coalesce. We show that the existence of universal flux equilibrium in fully developed turbulent systems combined with a direct cascade induces universal fusion rules. In certain examples these fusion rules suffice to compute the multiscaling exponents exactly, and in other examples they give rise to an infinite number of scaling relations that constrain enormously the structure of the allowed theory.

(1996) Physical review letters. 77, 17, p. 35413544 Abstract
It is shown that the idea that scaling behavior in turbulence is limited by one outer length L and one inner length η is untenable. Every nth order correlation function of velocity differences F_{n}\(R_{1}, R_{2}.,\) exhibits its own crossover length η_{n} to dissipative behavior as a function of R_{1}. This depends on n and on the remaining separations R_{2}, R_{3}., One result is that when separations are of the same order R, this scales as η_{n}\(R\)∼η\(R/L\)^{xn} with x_{n} = \(ζ_{m} ζ_{n+1} + ζ_{3} ζ_{2}\)/\(2  ζ_{2}), ζ_{n} the scaling exponent of the nth order structure function. We derive an infinite set of scaling relations that bridge the exponents of correlations of gradient fields to the exponents ζ_{n}, including the \u201cbridge relation\u201d for the scaling exponent of dissipation fluctuations μ = 2ζ_{6}.

(1996) Physical Review E. 53, 4, p. 35183535 Abstract
Kraichnan\u2019s model of passive scalar advection in which the driving velocity field has fast temporal decorrelation is studied as a case model for understanding the appearance of anomalous scaling in turbulent systems. We demonstrate how the techniques of renormalized perturbation theory lead (after exact resummations) to equations for the statistical quantities that also reveal nonperturbative effects. It is shown that ultraviolet divergences in the diagrammatic expansion translate into anomalous scaling with the inner length acting as the renormalization scale. In this paper, we compute analytically the infinite set of anomalous exponents that stem from the ultraviolet divergences. Notwithstanding these computations, nonperturbative effects furnish a possibility of anomalous scaling based on the outer renormalization scale. The mechanism for this intricate behavior is examined and explained in detail. We show that in the language of L\u2019vov, Procaccia, and Fairhall [Phys. Rev. E 50, 4684, (4684)], the problem is "critical," i.e., the anomalous exponent of the scalar primary field [Formula Presented]. This is precisely the condition that allows for anomalous scaling in the structure functions as well, and we prove that this anomaly must be based on the outer renormalization scale. Finally, we derive the scaling laws that were proposed by Kraichnan for this problem and show that his scaling exponents are consistent with our theory.
1995

(1995) Chaos Solitons & Fractals. 5, 10, p. 18551869 Abstract
Threedimensional turbulence of incompressible fluid is described by using Clebsch canonical variables. This reveals the families of new local integrals of motion so that there are additional cascade spectra besides the energy cascade. A weakly anisotropic spectrum of developed turbulence is shown to be as universal as isotropic Kolmogorov spectrum. The correlation functions of threedimensional incompressible turbulence approach their isotropic values in the inertial interval so that the share taken by the anisotropic parts of velocity correlators decrease with the wavenumber as k^{ 2 3}, which satisfactorily fits the experimental data. The complementarity of the turbulence description in Clebsch and velocity variables is demonstrated.

(1995) EPL. 29, 9, p. 681686 Abstract
We show that the Kolmogorov1941 picture of fully developed hydrodynamic turbulence (with the scaling of the structure functions S_{n}(R) α R^{n/3}) necessarily leads to an anomalous scaling for correlation functions which include the rate of energy dissipation e(t, r), these correlation functions being described by an independent index. The mechanism for anomalous scaling, suggested on the basis of the NavierStokes equation, is the multistep interaction of eddies from the inertial interval with eddies at the viscous scale via a set of eddies of intermediate scales.

(1995) EPL. 29, 4, p. 291296 Abstract
We discuss the theoretical implications of the experimental results for the cross correlations between velocity differences and dissipative fields which are reported in the companion (preceding) letter (Europhys. Lett., 28 (1994) 635). The first implication is that 3d hydrodynamic turbulence has no conformal symmetry. Secondly, the experiment confirms the nonconformal scaling behaviour of such correlations as predicted by the analytical theory of the present authors. The results of the measurements lend support to the subcritical scenario that was suggested recently as an explanation of the nonKolmogorov scaling of the structure functions in large but finite Reynolds number turbulence.

(1995) Physical Review E. 52, 4, p. 38403857 Abstract
This paper is the first in a series of papers that aim at understanding the scaling behavior of hydrodynamic turbulence. We present in this paper a perturbative theory for the structure functions and the response functions of the hydrodynamic velocity field in real space and time. Starting from the NavierStokes equations (at high Reynolds number Re) we show that the standard perturbative expansions that suffer from infrared divergences can be exactly resummed using the BelinicherL'vov transformation. After this exact (partial) resummation it is proven that the resulting perturbation theory is free of divergences, both in large and in small spatial separations. The hydrodynamic response and the correlations have contributions that arise from mediated interactions which take place at some spacetime coordinates. It is shown that the main contribution arises when these coordinates lie within a shell of a ''ball of locality'' that is defined and discussed. We argue that the real spacetime formalism that is developed here offers a clear and intuitive understanding of every diagram in the theory, and of every element in the diagrams. One major consequence of this theory is that none of the familiar perturbative mechanisms may ruin the classical 1941 Kolmogorov (K41) scaling solution for the structure functions. Accordingly, corrections to the K41 solutions should be sought in nonperturbative effects. These effects are the subjects of paper II (the following paper) and a future paper in this series that will propose a mechanism for anomalous scaling in turbulence, which in particular allows a multiscaling of the structure functions.

(1995) Physical Review E. 52, 4, p. 38583875 Abstract
In paper I of this series on fluid turbulence we showed that exact resummations of the perturbative theory of the structure functions of velocity differences result in a finite (order by order) theory. These findings exclude any known perturbative mechanism for anomalous scaling of the velocity structure functions. In this paper we continue to build the theory of turbulence and commence the analysis of nonperturbative effects that form the analytic basis of anomalous scaling. Starting from the NavierStokes equations (at high Reynolds number Re) we discuss the simplest examples of the appearance of anomalous exponents in fluid mechanics. These examples are the nonlinear (fourpoint) Green's function and related quantities. We show that the renormalized perturbation theory for these functions contains ''ladder'' diagrams with (convergent) logarithmic terms that sum up to anomalous exponents. Using a sum rule that is derived here we calculate the leading anomalous exponent and show that it is critical. This result opens up the possibility of multiscaling of the structure functions with the outer scale of turbulence as the renormalization length. This possibility will be discussed in detail in a concluding paper of this series.

(1995) Physical review letters. 74, 14, p. 26902693 Abstract
A physical interpretation of a recent NavierStokes based theory for scaling in developed hydrodynamic turbulence is presented. It is proposed that corrections to the normal Kolmogorov scaling behavior of the nth order velocity structure functions are finite Reynolds number effects which disappear when the inertial interval exceeds 56 decades. These corrections originate from the correlation between the velocity differences and energy dissipation which are characterized by an anomalous (subcritical) exponent. The values of the experimentally observed scaling indices for the nth order structure functions for n between 4 and 14 are in agreement with our findings.
1994

SCALING OF CORRELATIONFUNCTIONS OF VELOCITYGRADIENTS IN HYDRODYNAMIC TURBULENCE(1994) JETP Letters. 59, 8, p. 577583 Abstract
As is demonstrated in Refs. 2 and 3 in the limit of infinitely large Reynolds numbers, the correlation functions of the velocity predicted by Kolmogorov's 1941 theory (K41) are actually solutions of diagrammatic equations. Here we demonstrate that correlation functions of the velocity derivatives, del(alpha)upsilon(beta), should possess scaling exponents which have no relation to the K41 dimensional estimates. This phenomenon is referred to as anomalous scaling. This result is proved in diagrammatic terms: We have extracted a series of logarithmically diverging diagrams, whose summation leads to the renarmalization of the normal K41 dimensions. For a description of the scaling of various functions of del(alpha)upsilon(beta), an infinite set of primary fields O(n) with independent scaling exponents DELTA(n) can be introduced. Symmetry reasons enable us to predict relations between the scaling of different correlation functions. We also formulate restrictions imposed on the structure of the correlation functions due to the incompressibility condition. We also propose some tests which make it possible to check experimentally the conformal symmetry of the turbulent correlation functions. Further, we demonstrate that the anomalous scaling behavior should reveal itself in the asymptotic behavior of the correlation functions of the velocity differences. We propose a method to obtain the anomalous exponents from the experiment.

(1994) Physical Review E. 49, 2, p. R959R962 Abstract
An exact relation between the Green's function and the dressed thirdorder vertex Γ was found for the KardarParisiZhang (KPZ) model of surface roughening in (1+d) dimensions. This relation, of the Wardidentity type, follows from a hidden symmetry of the problem, which generalizes in some sense the Galilean invariance of the KPZ equation. This relation allows one to conclude that in the region of strong coupling, ΓΓ0∼0.1Γ0, where Γ0 is the bare value of the vertex Γ. The identity is generalized for higherorder vertices, enabling us to predict some relations between observable correlation functions.

(1994) Physical review letters. 72, 2, p. 307 Abstract
A Comment on the Letter by C. Jayaprakash, F. Hayot, and R. Pandit, Phys. Rev. Lett. 71, 12 (1993).

(1994) Physical Review E. 49, 5, p. 40444051 Abstract
In the inertial interval of turbulence one asserts that the velocity structure functions Sn(r) scale like rnnζ. Recent experiments indicate that Sn(r) has a more general universal form [rf(r/η)]nnζ, where η is the Kolmogorov viscous scale. This form seems to be obeyed on a range of scales that is larger than power law scaling. It is shown here that this extended universality stems from the structure of the NavierStokes equations and from the property of the locality of interactions. The approach discussed here allows us to estimate the range of validity of the universal form. In addition, we examine the possibility that the observed deviations from the classical values of ζn=1/3 are due to the finite values of the Reynolds numbers and the anisotropy of the excitation of turbulence.

Anomalous Scaling and Fusion Rules in Hydrodynamic Turbulence(1994) arXiv. chaodyn/9. Abstract
It is shown that statistical properties of developed hydrodynamic turbulence are characterized by an infinite set of independent anomalous exponents which describes the scaling behavior of hydrodynamic fields constructed from the second and larger powers of the velocity derivatives. A physical mechanism responsible for anomalous scaling, ``telescopic multistep eddy interaction", is discovered and investigated. The essence of this mechanism is the existence of a very large number (R/η)Δj≫1 of channels of interaction of large eddies of scale R in the inertial interval with eddies of viscous scale η via a set of eddies of all intermediate scales between R and η. The description of this mechanism based on the NS equation in the quasi Lagrangian representation is presented. In the diagrammatic expansion of the correlation function of the energy dissipation field Kεε(R), we have found an infinite series of logarithmically diverging diagrams. Their summation leads to a renormalization of the normal Kolmogorov41 dimensions. For a description of the scaling of various hydrodynamic fields an infinite set of primary fields On with independent scaling exponents Δn was introduced. We have proposed a symmetry classification of the fields On enabling one to predict relations between scaling the behavior of different correlation functions.

Anomalous scaling in fluid mechanics: The case of the passive scalar: The case of the passive scalar(1994) Physical Review E. 50, 6, p. 46844704 Abstract
A mechanism for anomalous scaling in turbulent advection of passive scalars is identified as being similar to a recently discovered mechanism in NavierStokes dynamics [V. V. Lebedev and V. S. Lvov, JETP Lett. 59, 577 (1994)]. This mechanism is demonstrated in the context of a passive scalar field that is driven by a rapidly varying velocity field. The mechanism is not perturbative, and its demonstration within renormalized perturbation theory calls for a resummation of infinite sets of diagrams. For the example studied here we make use of a small parameter, the ratio of the typical time scales of the passive scalar vs that of the velocity field, to classify the diagrams of renormalized perturbation theory such that the relevant ones can be resummed exactly. The main observation here, as in the NavierStokes counterpart, is that the dissipative terms lead to logarithmic divergences in the diagrammatic expansion, and these are resummed to an anomalous exponent. The anomalous exponent can be measured directly in the scaling behavior of the dissipation twopoint correlation function, and it also affects the scaling laws of the structure functions. It is shown that when the structure functions exhibit anomalous scaling, the dissipation correlation function does not decay on length scales that are in the scaling range. The implication of our findings is that the concept of an inertial range in which the dissipative terms can be ignored is untenable. The consequences of this mechanism for other cases of possible anomalous scaling in turbulence are discussed.

(1994) Physical review letters. 73, 3, p. 432435 Abstract
We study analytically and numerically the corrections to scaling in turbulence which arise due to finite size effects as anisotropic forcing or boundary conditions at large scales. We find that the deviations δζm from the classical Kolmogorov scaling ζm=m/3 of the velocity moments u(k)mkζm decrease like δζm(Re)=cmRe3/10. If, on the contrary, anomalous scaling in the inertial subrange can experimentally be verified in the large Re limit, this will support the suggestion that small scale structures should be responsible, originating form viscous effects either in the bulk (vortex tubes or sheets) or from the boundary layers (plumes or swirls), as both are underestimated in our reduced wave vector set approximation of the NavierStokes dynamics.
1993

QUASIEQUILIBRIUM SOLUTION OF THE 1+D KPZ MODEL(1993) JETP Letters. 58, 4, p. 310315 Abstract
The properties of the correlation functions of solutions of the 1 + d KPZ equation in the region of the strong interaction of fluctuations are considered. It is proved that analytical continuation of the solution realized at d = 1 for the dimensions 1

(1993) Physics ReportsReview Section Of Physics Letters. 229, 3, p. 81144 Abstract
A review of magnon properties of yttriumiron garnet (YIG), a classical object for experimental studies in magnetism, is presented. Both experimental and theoretical results concerned with thermodynamics and kinetics of YIG are described. The main purposes of the review are to introduce a new method of approximate calculation of the magnon spectra in magnets with large unit cell and to obtain by means of this method some basic properties of YIG. In particular, it is shown that the problem of calculating the frequencies of all the 20 magnon branches over the entire Brillouin zone contains two small parameters. First, because of the large number of magnetic atoms in the unit cell the distance between the nearest interacting magnetic atoms is small in comparison with the lattice constant and, accordingly, with the wavelength of a spin wave. An effective longwavelength character thus arises in the problem. Second, there are a large number of wavevector directions along which many elements of the Hamiltonian matrix vanish by symmetry in the basis which diagonalizes this matrix for k = 0. These matrix elements thus have an additional, angular smallness for arbitrary directions of k. These matrix elements can be taken into account using perturbation theory. As a result, the large elements of the Hamiltonian matrix are few in number, and they can be eliminated by several twodimensional rotations. Approximate expressions, differing from the computer calculations by {lessthan or approximate} 10%, are thus obtained for the frequencies. Neutron scattering data are used to find the values of the exchange integrals in YIG and to obtain the magnon spectra. It is shown that in the energy range T {lessthan or approximate} 260 K only magnons of the lower branch are excited; the spectrum of these "ferromagnons" is quadratic in the wave vector only up to 40 K and becomes linear in the region ω_{k} {greaterthan or approximate} 40 K. For temperatures up to 400 K the temperature dependence of the magnetization is calculated in the spinwave approximation and good agreement with experimental data is found. A brief review of experimental data on magnon relaxation in YIG is presented. The magnonmagnon interactions which cause the magnon relaxation are described. The amplitude of the fourmagnon exchange interaction is determined, and the temperature correction to the frequency is evaluated. This temperature correction is positive, in contrast to the case of simple cubic ferromagnet with nearestneighbour interaction. The exchange relaxation rate is calculated for normal and umklapp processes. It is shown that the magnetic dipole interaction is important only for the ferromagnons; the amplitude of this interaction and the corresponding relaxation rate are determined. Threemagnon scattering processes are allowed only for wave vectors larger than a certain k_{/}; at k = k_{/} there is a discontinuity in the wavevector dependence of the damping. A calculation is given for the nonvanishing contribution to the relaxation at k = 0 on account of scattering processes involving optical magnons; this contribution is due to the local uniaxial anisotropy. The relative role of each of the investigated relaxation mechanisms is discussed, and the correspondence of the present results with the experimental data is examined.

(1993) EPL. 22, 6, p. 419423 Abstract
Properties of correlation functions of solutions of KPZ and KS equations (that describe roughening) in the region of stfong interaction of fluctuations are considered. We prove analytically a possibility of existence of a scaling solution in this region despite the «asymptoticfreedom» situation occurring near the marginal dimension d = 2 (corresponding to growth of an interface in a real threedimensional space). The proof is based on the locality of the interaction of fluctuations in /space which can be demonstrated by passing to socalled quasiLagrangian variables. The inequalities restricting possible values of scaling indices are found.

(1993) Nonlinearity. 6, 1, p. 2547 002. Abstract
Under the assumption that the KardarParisiZhang model (KPZ) possesses scale invariant solutions, there exists an exact calculation of the dynamic scaling exponent z=3/2. The authors prove that both KPZ and the related KuramotoSivashinsky model indeed possess scale invariant solutions in 1+1 dimensions which are in fact the same for both models. The proof entails an examination of the higher order diagrams in the perturbation theory in terms of the dressed Green function and the correlator. Although each higher order diagram contains logarithmic divergences, endangering the existence of the scale invariant solution, the authors show that these divergences cancel in each order. The proof uses a fluctuationdissipation theorem (FDT), which is an exact result for KPZ in 1+1 dimensions.

(1993) Physical Review E. 48, 2, p. R669R672 Abstract
Laws of decay of simultaneous manypoint correlation of turbulentvelocity differences are derived in the asymptotic region where either one space point of a group of points is far away from another group of points. An asymptotic decomposition rule of (n+m)point correlators in terms of (n+1), (m+1), and twopoint correlators is presented. These results may be directly applied or easily extended to the turbulence of cold electron plasma, convective turbulence, some problems of surface roughening at crystal growth, etc.

(1993) Physical Review E. 47, 3, p. 17941802 Abstract
Exact relations of two types in the statistical theory of fully developed homogeneous isotropic turbulence in an incompressible fluid were found. The relations of the first type connect twopoint and threepoint objects of the theory which are correlation functions and susceptibilities. The second type of relations are the "frequency sum rules" which express some frequency integrals from "fully dressed" manypoint objects (like vertices) via corresponding bare values. Our approach is based on the NavierStokes equation in quasiLagrangian variables and on the generating functional technique for correlation functions and susceptibilities. The derivation of these relations uses no perturbation expansions and no additional assumptions. This means that the relations are exact in the framework of the statistical theory of turbulence. We showed that "a manypoint scaling" gives birth to the "global scaling." Here "manypoint scaling" is the assumption that twopoint, threepoint, etc. objects of the theory of turbulence are uniform functions in the inertial interval and may be characterized by some scaling exponents. Under this assumption the only global scaleinvariant model of fully developed turbulence suggested by Kolmogorov [Dokl. Akad. Nauk SSR 32, 19 (1941)] is consistent with the exact relations deduced.

(1993) Physical Review E. 47, 6, p. 41614168 Abstract
The scaling ranges of temperature and velocity fluctuations in thermally driven turbulence are studied by analyzing the various contributions to the equations of motion. The crossover wave number kB between BolgianoObukhov and KolmogorovObukhov scaling is estimated in terms of the forcings. By evaluating the thermal and buoyant stirrings and dissipations of RayleighBénard convection experiments we find kB much larger than L1, the energycontaining scale, but smaller than (10η)1, the viscous scale. For computer simulation of randomly thermal driven turbulence we find kB of the order of L1. This might explain why the BolgianoObukhov scaling was observed in laboratory experiments whereas KolmogorovObukhov scaling was found in computer simulation of thermally driven turbulence.
1992

(1992) PHYSICA D. 57, 12, p. 8595 Abstract
The stationary spectrum of hydrodynamic convective turbulence is shown to be defined by influxes of two independent motion integrals: entropy and mechanical energy. A careful analysis of the conservation laws is performed. It is shown that in the inertial range of scales kinetic energy converts into potential energy due to presence of temperature fluctuations independently of the type of longscale stratification (stable or unstable one). Under a purely entropic excitation (for example, by horizontal temperature gradient) the spectrum with constant entropy flux, F_{vv} ∼ k^{ 21 5}, fills the whole of the inertial interval and crossover to the KolmogorovObukhov spectrum with constant energy flux, F_{vv} ∼ k^{ 11 3}, is absent. An estimate for crossover scale is obtained for a mixed method of excitation with both nonzero energy pumping and nonzero entropy extraction caused by an environment. A simple but consistent differential model is suggested for the description of the fluxes of energy and entropy in kspace. Twoflux universal spectraof the velocity and temperature fluctuations are obtained.

(1992) Physical review letters. 69, 24, p. 35433546 Abstract
It is shown that the scale invariant solutions of the KS and KPZ models of surface roughening are identical for dimensions d2 in the strong coupling limit. For d>2, these models posses two different scaling solutions, one with dindependent scaling exponents y=z=2, and the other with ddependent nontrivial exponents. The first of these solutions is realizable in one of these models, but not the other. These conclusions are valid to all orders in renormalized perturbation theory.

(1992) Physical Review A. 46, 6, p. 32203224 Abstract
The longwavelength properties of the KuramotoSivashinsky equation are studied in 2+1 dimensions using numerical and analytic techniques. It is shown that this equation is not in the universality class of the KardarParisiZhang model. Its roughening exponents are (up to logarithmic corrections) like those of the freefield theory, with dimension 2 being the marginal dimension for roughening. Assuming that the solution has logarithmic corrections, we derive a scaling relation for the exponents of the logarithmic terms. This solution is consistent order by order with the DysonWyld diagrams. We explain why previous renormalizationgroup treatments failed.

(1992) Physical Review A. 46, 8, p. 47624772 Abstract
The problem of interaction locality in k space is studied in a diagrammatic perturbation approach for the NavierStokes equation in quasiLagrangian variables. Analyzing the whole diagram series we have found an exact relation between the asymptotic behavior of the triplecorrelation function of velocities that governs the energy transfer over scales and the doublecorrelation function giving the energy distribution. Namely, at rR, we obtain S3(r,R,Rr)S2(R)(r/R) [S3(r)/S2(r)]R2ζ1r22ζ, where ζ2 is the static exponent of doublevelocity moment. This relation between two different physical quantities (in principle, measurable independently) is accessible to an experimental check. Also, this relation allows us to describe an energy exchange between distant scales in k space: For any steady spectrum carrying constant energy flux, the interactions of the given keddies with large (k1k) and small eddies (k2k) are shown to decrease by the same law with the distance in k space, such as (k1/k)22ζ and (k/k2)22ζ. It means a balance of interactions for such a spectrum. Considering, in particular, the multifractal picture of developed turbulence, we analyze the range of exponents h of the velocity field [δv(r)rh] which provides the locality of interaction in the k space. It is shown that the condition of infrared locality of interaction (with larger k1eddies) could give only the upper restriction for the exponent. The upper limit thus found (hmax=1) coincides with the boundary exponent of singularity of energy dissipation. As far as an interaction locality in the ultraviolet limit (k2k) is concerned, we prove that any reasonable dimension function D(h) provides locality whatever small h is considered.
1991

(1991) Physics ReportsReview Section Of Physics Letters. 207, 1, p. 147 Abstract
The statistical theory of fully developed homogeneous turbulence of an incompressible fluid presented here is based on the Hamiltonian equations for an ideal fluid in the Clebsch variables using the Wyld diagram technique. This theory is formulated in terms of the local Green function G(r, k, ω) and the local pair correlation function N(r, k, ω) describing the statistical properties of keddies in the vicinity of point r. One of the major difficulties arising from the masking effect of the sweeping interaction is effectively solved by transforming to a moving reference system associated with the fluid velocity in some reference pointr_{0}. This change of coordinates eliminates the sweeping of keddies in a region of scale 1 k surrounding the reference point r_{0}. The convergence of all the integrals in the diagrams of arbitrary order of perturbation theory both in the IR and UV regions, is proved. This gives a diagrammatic proof of the KolmogorovObukhov hypothesis that the dynamic interaction of eddies is local. In the inertial interval, the scale invariant solution of the DysonWyld diagram equations has been obtained, which is consistent with the known RichardsonKolmogorovObukhov concept of fully developed uniform turbulence. This new theory provides techniques for calculating the statistical characteristics of turbulence. For the purpose of illustration the asymptotic form of the simultaneous manypoint velocity correlation functions when one of the wave vectors or the sum of a group of wave vectors tends to zero, is calculated.

(1991) Physical Review Letters. 67, 6, p. 687690 Abstract
It is shown that the frequencytemperature spectrum recently observed by Wu et al. in developed convective turbulence, F(TT)(omega) isproportionaltoomega1/4, follows from the condition that the entropy flux in k space is constant. just as the KolmogorovObukhov spectrum of barotropic turbulence, F(VV)(k) congruentto (epsilon/rho)2/3k11/3, follows from the condition that kineticenergy fluxepsilon(k) = epsilon. On the contrary, for convective turbulenceepsilon(k) changes as k4/5 because of conversion of kinetic energy into a potential energy, which leads to a stronger k dependence of the double velocity moment [F(VV)(k) infinity k21/5] than that for barotropic turbulence.
1990

ON THE SCALEINVARIANT THEORY OF DEVELOPED HYDRODYNAMIC TURBULENCE KOLMOGOROV TYPE(1990) NONLINEAR EVOLUTION OF SPATIOTEMPORAL STRUCTURES IN DISSIPATIVE CONTINUOUS SYSTEMS. 225, p. 553562 Abstract
Keywords: Mechanics; Physics, Applied
1989

UNIVERSAL DOUBLEFLOW SPECTRA OF WEAK SOUND TURBULENCE(1989) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 96, 6, p. 20332037 Abstract

INTERCENTER CARRIER TRANSITIONS IN PARTIALLY DISORDERED SILICON  CALCULATION(1989) Fizika Tverdogo Tela. 31, 11, p. 197205 Abstract

INTERCENTER CARRIER TRANSITIONS IN PARTIALLY DISORDERED SILICON  EXPERIMENT AND DISCUSSION OF RESULTS(1989) Fizika Tverdogo Tela. 31, 11, p. 206213 Abstract

REARRANGEMENT OF THE SPINWAVE DISTRIBUTION IN CONDITIONS OF PARAMAGNETICRESONANCE IN FERRITES(1989) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 96, 1, p. 314329 Abstract
1987

PARALLEL PUMPING OF SPINWAVES UNDER CONDITIONS OF MAGNETICFIELD DRIFT(1987) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 93, 4, p. 12691280 Abstract

COMPOSITE ELECTROCHEMICAL COATINGS FOR MOLYBDENUM(1987) Protection of Metals. 23, 5, p. 653654 Abstract

SCALEINVARIANT THEORY OF DEVELOPED HYDRODYNAMIC TURBULENCE(1987) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 93, 2, p. 533551 Abstract
1986
1984

NONEQUILIBRIUM ELECTRON POLARIZATION AND THE MASER EFFECT ON SPINDEPENDENT RECOMBINATION VIA EXCHANGECOUPLED PAIRS(1984) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 87, 1, p. 234240 Abstract

SPIN DIAGRAM TECHNIQUE FOR NONEQUILIBRIUM PROCESSES IN THE THEORY OF MAGNETISM(1984) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 86, 3, p. 967980 Abstract

INTERACTION AND RELAXATION OF MAGNONS IN THE 20SUBLATTICE FERRIMAGNET IRONYTTRIUM GARNET(1984) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 86, 5, p. 19461960 Abstract

(1984) in ``Nonlinear and Turbulent Processes in Physics", ed. by R.Z. Sagdeev, Gordon and Brich. Publ. NY 1984, p. pp. 14551464

Computational techniques in the life of a physical laboratory. Optoelectronic Instrumentation and Data Processing (Avtometriya)(1984) Electron Press, NY. p. N4, pp.5056

CAMAC class, Optoelectronics Instrumentation and Data Processing (Avtometria)(1984) Electron Press, NY. p. N4, 5962

Highcapacity realtime system for processing hydrophysical data. Optoelectronics Instrumentation and Data Processing (Avtometria)(1984) Electron Press, NY. p. N5, pp.312

(1984) in "LaminarTurbulent Transition IUTAM Symposium Novosibirsk 1984", ed. by V.V. Kozlov, SpringerVerlag. p. 653658
1983

SPINWAVE SPECTRA AND THERMODYNAMICS OF THE IRONYTTRIUM GARNET, A 20SUBLATTICE FERROMAGNET(1983) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 84, 3, p. 10431058 Abstract
1982

INVESTIGATION OF SPINDEPENDENT RECOMBINATION IN SEMICONDUCTORS(1982) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 83, 4, p. 15571566 Abstract

INTERACTION BETWEEN PARAMETRICALLY EXCITED SPINWAVES AND THERMAL SPINWAVES(1982) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 82, 5, p. 15621577 Abstract

LaserDoppler velocimeter techniques and its amplifications, Opptoelectronics Instrumentation and Data Processing (Autometria)(1982) Electron Press, NY. p. N3, 415

LaserDoppler velocimeter techniques and its amplifications, Opptoelectronics Instrumentation and Data Processing (Autometria)(1982) Electron Press, NY. p. N3, 415

Beginning CAMACpracticum(1982) Novosibirsk University.
1981

(1981) Soviet Physics JETPUSSR. 53, 2, p. 299300 Abstract
Weak turbulence of waves with a weakly damped dispersion law is discussed. In the stationary case, small anisotropic additions to an isotropic spectrum of the Kolmogorov type are found. It is shown that a small anisotropic source located in a region of small k leads to an essentially anisotropic spectrum in a region of large k. Strongly anisotropic stationary spectra are found. [Russian original  Zh. Eksp. Teor. Fiz. 80, 592596 (February 1981)]

(1981) PHYSICA D. 2, 1, p. 3851 Abstract
Laminarturbulent transition in circular Couette flow is discussed. Phenomenological equations are proposed describing the breakdown of azimuthal waves coherency. The correspondence is established between the flow turbulization and the stochastic attractor in the phase space of these equations. Evolution of attractor structure is investigated experimentally in terms of motion in some effective phase space. It is shown that during the transition to turbulence the increase in number of degrees of freedom is combined with the stochastic behaviour of rapid motion envelopes.

STATISTICAL DESCRIPTION OF A CHAIN OF INTERACTING TAYLOR VORTEXES IN THE DIRECT INTERACTION APPROXIMATION(1981) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 80, 5, p. 19691980 Abstract

(1981) PHYSICA D. 2, 1, p. 203217 Abstract
New results in the theory of the developed hydrodynamic turbulence spectra are reviewed. Within the limits of the hypothesis of interaction locality it is shown that the series of equations for the moments has a scaleinvariant solution with the Kolmogorov index values. With the help of the Wyld diagram technique the equations in the Direct Interaction Approximation are formulated which accurately take into account the transfer effect and have the precise solution in the form of the Kolmogorov spectrum. In the framework of these equations the corrections to the Kolmogorov spectrum due to gyrotropy and compressibility are found.

(1981) PHYSICA D. 2, 1, p. 224243 Abstract
The interaction of sound with hydrodynamic turbulence has been studied in detail. The sound absorption decrement, the correlation time and length and the frequency diffusion coefficient for the acoustic wave packet are calculated. The spectral composition of the sound radiated by a unit, turbulent volume and the spectral energy density of sound in equilibrium with the turbulence are studied. The region of applicability of the kinetic equation for sound with a linear dispersion low is found.

SECONDARY TURBULENCE OF PARAMETRICALLY EXCITED SPINWAVES(1981) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 81, 2, p. 757767 Abstract

KINETIC INSTABILITY OF A STRONGLY NONEQUILIBRIUM SPINWAVE SYSTEM AND TUNABLE RADIATION FROM FERRITE(1981) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 81, 3, p. 10221036 Abstract

NONLINEAR THEORY OF THE KINETIC EXCITATION OF WAVES(1981) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 81, 4, p. 14061422 Abstract

BIFURCATION AND CHAOS IN A TAYLOR VORTEX SYSTEM  A NATURAL AND NUMERICAL EXPERIMENT(1981) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 80, 3, p. 10991121 Abstract
1980


TRANSITION TO TURBULENCE IN SIMPLE HYDRODYNAMICAL FLOW(1980) Vestnik Akademii Nauk SSSR. 10, p. 2535 Abstract

Turbulent transition in a circular Couette flow, in "LaminarTurbulent Transition"(1980) ed. R. Eppler and H. Fasel, SpringerVerlag 1980.

Stepbystep transition to turbulence in a Couette flow in ``nonlinear waves"(1980) ed. by GaponovGrekhov, Nauka Publ. Moscow, 1980. p. pp. 5777

Experimental technique and results of studies of laminarturbulent transition in a simple hydrodynamic flow. Optoelectronic Instrumentation and Data Processing (Avtometria)(1980) Electron Press, NY. p. N4, 11114
1979


STRONGLY ANISOTROPIC DISTRIBUTIONS OF PARAMETRICALLY EXCITED WAVES IN ISOTROPIC MEDIA(1979) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 76, 6, p. 22662278 Abstract
1978

SOUND AND HYDRODYNAMIC TURBULENCE IN A COMPRESSIBLE LIQUID(1978) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 74, 4, p. 14451457 Abstract

SPECTRAL DENSITY OF PARAMETRICALLY EXCITED WAVES(1978) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 75, 3, p. 11141131 Abstract

COLLECTIVE OSCILLATIONS AND INSTABILITY OF SINGLE FREQUENCY STATE OF PARAMETRICALLY EXCITED WAVES(1978) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 75, 5, p. 16311645 Abstract

SCATTERING AND INTERACTION OF SOUND WITH SOUND IN A TURBULENT MEDIUM(1978) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 75, 5, p. 16691682 Abstract
1977

(1977) Physics Letters A. 64, 2, p. 157158 Abstract
In the Direct Interaction Approximation [1] equations have been formulated, which completely take into account the transfer effect and have a precise solution in the form of the Kolmogorov spectrum.

EXCITATION OF SPINWAVES BY UNIFORM PRECESSION OF MAGNETIZATION AT 2MAGNON SCATTERING(1977) Fizika Tverdogo Tela. 19, 10, p. 31313133 Abstract

EFFECT OF MODULATION INSTABILITY ON RELAXATION OF A RELATIVISTIC ELECTRONBEAM IN A PLASMA(1977) JETP Letters. 25, 1, p. 810 Abstract

SPINDEPENDENT CARRIER RECOMBINATION ON A SILICON SURFACE(1977) SOVIET PHYSICS SEMICONDUCTORSUSSR. 11, 6, p. 661664 Abstract

SPATIALLY INHOMOGENEOUS SINGULAR SPECTRA OF WEAK TURBULENCE(1977) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 72, 1, p. 127140 Abstract

HIGH AMPLITUDE COLLECTIVE OSCILLATIONS AND DOUBLE PARAMETRIC RESONANCE OF MAGNONS(1977) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 72, 1, p. 272284 Abstract

Investigation of wave turbulence. In: ``Fundamental Studies in Physics and Mathematics"(1977) (Nauka Publ., Novosibirsk, 1977). p. pp. 194198

1976

NICKEL SELFDIFFUSION IN NICKELIRON ALLOYS(1976) FIZIKA METALLOV I METALLOVEDENIE. 41, 4, p. 775781 Abstract
1975

NONLINEARTHEORY OF PARAMETRICEXCITATION OF WAVES(1975) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 69, 6, p. 20792092 Abstract

DAMPING OF MONOCHROMATIC WAVES IN A NONLINEAR MEDIUM(1975) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 68, 1, p. 308316 Abstract

(1975) Quan. Electronics 18 N10. p. 14841097
1974

NONLINEARTHEORY OF PARAMETRICEXCITATION OF SPINWAVES IN ANTIFERROMAGNETS(1974) JETP Letters. 19, 11, p. 351352 Abstract

TURBULENCE OF SPINWAVES BEYOND THRESHOLD OF THEIR PARAMETRICEXCITATION(1974) Uspekhi Fizicheskikh Nauk. 114, 4, p. 609654 Abstract

NONLINEARTHEORY OF PARAMETRICEXCITATION OF SPINWAVES IN ANTIFERROMAGNETIC SUBSTANCES(1974) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 67, 5, p. 19321948 Abstract
1973

STRONG TURBULENCY AND SELFFOCUSING OF PARAMETRICALLY EXCITED SPINWAVES(1973) Fizika Tverdogo Tela. 15, 3, p. 793800 Abstract

NONLINEARTHEORY OF PARAMETRIC INSTABILITY OF WAVES IN A PLASMA(1973) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 64, 2, p. 515525 Abstract

THEORY OF MAGNETIZATION SELFOSCILLATIONS ON PARAMETRIC EXCITATION OF SPINWAVES(1973) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 64, 3, p. 10741086 Abstract
1972

INSTABILITY OF MONOCHROMATIC STANDING SPINWAVES WITH PARALLEL PUMPING(1972) SOVIET PHYSICS SOLID STATE,USSR. 13, 12, p. 29492954 Abstract

PARAMETRIC EXCITATION OF SPINWAVES IN FERROMAGNETS WITH MAGNETIC INHOMOGENEITIES(1972) Fizika Tverdogo Tela. 14, 10, p. 2913& Abstract

RESONANCE PHENOMENA IN PARAMETRIC SPINWAVE SYSTEM(1972) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 63, 1, p. 182& Abstract

NEW MECHANISM FOR LIMITING SPINWAVE AMPLITUDES UNDER PARALLEL PUMPING  REPLY(1972) SOVIET PHYSICS SOLID STATE,USSR. 13, 9, p. 2321& Abstract

PARALLEL SPINWAVE PUMPING IN YTTRIUM GARNET SINGLECRYSTALS(1972) Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki. 62, 5, p. 1782& Abstract

NONSTATIONARY BEHAVIOR OF PARAMETRICALLY EXCITED SPINWAVE SYSTEM(1972) Fizika Tverdogo Tela. 14, 3, p. 832& Abstract
1971

PROOF OF STAGEBYSTAGE EXCITATION OF PARAMETRIC SPIN WAVES(1971) JETP LETTERSUSSR. 14, 5, p. 206& Abstract

ONSET OF TUBULENCE DURING PARAMETRIC EXCITATION OF WAVES(1971) Soviet Physics JETPUSSR. 33, 6, p. 1113& Abstract

STATIONARY NONLINEAR THEORY OF PARAMETRIC EXCITATION OF WAVES(1971) Soviet Physics JETPUSSR. 32, 4, p. 656& Abstract

Nonlinear theory of ferromagnetic resonance(1971) Fiz Tverd Tela. 13, 2, p. 52332. Abstract
The aim of the present paper is to construct a consistent nonlinear theory of ferromagnetic resonance which takes into account both the spin wave uniform precession and spin wave spin wave interaction. See also English translation in Sov PhysSolid State v 13 n 2 Aug 1971 p 41825
1970
1968

NUCLEAR MAGNETIC RESONANCE STUDY OF EXCHANGE INTERACTIONS IN RBNIF3(1968) SOVIET PHYSICS SOLID STATE,USSR. 10, 5, p. 1040& Abstract

DIFFRACTION OF LIGHT BY FERROMAGNETIC DOMAINS(1968) SOVIET PHYSICS SOLID STATE,USSR. 10, 6, p. 1287& Abstract

TWOMAGNON COMBINATION SCATTERING OF LIGHT IN MAGNETICALLY ORDERED DIELECTRICS(1968) SOVIET PHYSICS SOLID STATE,USSR. 9, 10, p. 2328& Abstract

PIEZOMAGNETORESISTANCE OF NTYPE GE FOR A MIXED SCATTERING MECHANISM(1968) SOVIET PHYSICS SOLID STATE,USSR. 9, 11, p. 2628& Abstract

RAMAN SCATTERING OF LIGHT AND FARADAY EFFECT IN MAGNETICALLY ORDERED DIELECTRICS(1968) Soviet Physics JETPUSSR. 26, 1, p. 113& Abstract

LIGHT SCATTERING NEAR A 2NDORDER PHASE TRANSITION IN A DIELECTRIC MAGNET(1968) SOVIET PHYSICS SOLID STATE,USSR. 10, 2, p. 354& Abstract
1967


OPTICAL ACTIVITY OF DEFORMED CRYSTALS(1967) SOVIET PHYSICS SOLID STATE,USSR. 9, 4, p. 1000& Abstract
1966

THERMOMAGNETIC EFFECTS IN DEFORMED NTYPE GE(1966) SOVIET PHYSICS SOLID STATE,USSR. 8, 5, p. 1285& Abstract


GALVANOMAGNETIC AND THERMOMAGNETIC EFFECTS IN STRAINED NGE(1966) SOVIET PHYSICS SOLID STATE,USSR. 8, 5, p. 1081& Abstract

ELASTOGALVANOMAGNETIC EFFECTS IN NTYPE GE(1966) SOVIET PHYSICS SOLID STATE,USSR. 8, 5, p. 1091& Abstract