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).
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
Archive author identifier http://arxiv.org/a/falkovich_g_1 Google Scholar Profile
Link to Amazon : gregoryfalkovich .
Popular writings in Hebrew, more plus some art.