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).

**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**.

**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.

**OPERATOR PRODUCT EXPANSION**formalism for turbulence.

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