Speaker
Description
The theory of wave turbulence -- developed over the past five decades -- is a consistent framework for describing cascades in a broad class of weakly interacting systems including: waves in the ocean, plasma waves, spin waves, acoustic waves, and many others. The Kolmogorov-Zakharov scaling for the distribution of mode occupation numbers is a solution of the weakly interacting kinetic equations, which been verified numerically and/or experimentally in a number of contexts. If the flux pumped into the system is large, or even if the flux is small and one is far along the cascade (at a wavenumber that differs significantly from the pumping scale) -- as is often the case in physical realizations -- the standard weak wave turbulence theory is insufficient.
We describe how this problem of find strong wave turbulence scaling can be mapped onto a problem of renormalization group flows in far-from-equilibrium states. Two contexts are solvable. The first is large N: We study turbulent cascade in a large N nonlinear Schrodinger equation. We find two forms of universality in the strong turbulence spectrum: in focusing media it is independent of the flux magnitude (the widely used critical balance solution), while in defocusing media it is independent of the bare coupling constant, with the largest scale appearing instead. These results are confirmed by direct numerical simulation. The second is the epsilon expansion. We conclude with a discussion of how FRG may be a useful tool for solving the problem of strong wave turbulence scaling in a general nonlinear system.