Research overview

I started in soliton theory and WEAK TURBULENCE.  For wave turbulence, we discovered the BOTTLENECK EFFECT, which I generalized for incompressible turbulence later. We then worked on a direct vorticity cascade in 2d turbulence and the related problem of a passive scalar in a spatially smooth flow. Work on a passive scalar in a non-smooth flow resulted in the discovery of zero modes (statistical integrals of motion) as a mechanism for an ANOMALOUS SCALING in turbulence. Those results and related work are described in this review and that report.  Since then, I have been interested in symmetries of turbulent state, both broken and emerging ones. My colleagues and I have discovered empirical traces of CONFORMAL INVARIANCE in the family of inverse cascades and are presently attempting to build an analytic theory of that and related subjects (without much success so far).

I continue to work on fundamental problems of turbulence theory, and collaborate with experimentalists on the coexistence of turbulence and coherent condensate both in fluid and optical turbulence. In collaboration with experimentalists, we discovered how large vortex and small-scale turbulence conspire to provide for an inverse energy cascade in thick fluid layers, which has potential implications for geophysical, astrophysical, and industrial applications.
In statistical physics, we suggested a fluid-mechanical view of fluctuation relations far from equilibrium. Conversely, I try to find a way to derive such relations for fluid particles using Lagrangian formalism. We have found empirically how the degree of non-equilibrium (breakdown of detailed balance) is encoded in the motion of a single fluid particle and suggested a simple (flight-crash) model to explain the scaling of irreversibility degree with the Reynolds number of energy cascades in both 2 and 3 dimensions.
We applied the Lagrangian methods developed previously for a passive scalar to inertial particles with a view to cloud formation and rain phenomena.  We predicted and explored the SLING EFFECT in collisions of water droplets in clouds. We discovered experimentally and described theoretically another set of inertial particles, small floaters; the effect of capillarity on these is in violation of Archemedes' law. For those floaters, we were able to measure the multi-fractality of the floater concentration and to find the caustics that appear due to the sling effect. It was discovered, to much of our surprise, that the sign of thermo- and turbophoresis for very inertial particles is actually opposite to what was assumed since Maxwell: very inertial particles do not concentrate in the minimum of temperature or turbulence intensity but fly through and escape --- localization-delocalization phase transition.
We adapted to turbulence and other problems the saddle-point INSTANTON method of treating a path integral. Application to finding the probabilities of rare fluctuations in turbulence is difficult, we found the probability of strong vorticity fluctuations in 2d direct cascade.  
Lame attempt at operator product expansion formalism for turbulence.
The possibility of strongly interacting electron systems allowed us to introduce the new field of viscous electronics, which is the subject of active theoretical and experimental research. In particular, we predicted negative nonlocal resistance, current vortices, conductivity exceeding the ballistic limit, and other phenomena. We described and observed fluidity onset in an electron system.

Now we attempt to apply the tools of INFORMATION THEORY to turbulence.

Archive author identifier     Google Scholar Profile

Link to Amazon : gregoryfalkovich .

Popular writings in Hebrew, more plus some art.

ResearcherID : K-1561-2012     ORCID ORCID logo