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