I started in soliton theory and weak turbulence.  For wave turbulence, we discovered the bottleneck effect, which was 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 (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. 

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.

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.  

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