# Research

I started in soliton theory and

**WEAK TURBULENCE**. For wave turbulence, we discovered the**BOTTLENECK EFFECT**, which I generalised 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 the turbulent state, both broken and emerging ones. My colleagues and I have discovered empirically 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 try to use 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.

With my students and collaborators, I applied the theoretical Lagrangian methods developed previously, during my work on 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 interesting 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. Recently we 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. Part of the current work is the development of a method of finding the probabilities of rare fluctuations in turbulence, we found the probability of strong vorticity fluctuations in 2d direct cascade.
We have started to develop the

**OPERATOR PRODUCT EXPANSION**formalism for turbulence.
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 ballistic limit and other phenomena.

Archive author identifier http://arxiv.org/a/falkovich_g_1 Google Scholar Profile

Link to Amazon : gregoryfalkovich .