Wave turbulence beyond weak nonlinearity

Speaker: Vladimir Rosenhaus

Abstract: Wave turbulence is a ubiquitous phenomenon, having been studied and
observed for half a century. An example are waves on the surface of the ocean, driven by
wind. For small waves, the wave turbulence is weak; it can be studied perturbatively.
Until recently, all results have been exclusively at leading order in the nonlinearity. We go
beyond this, deriving terms in the wave kinetic equation, order by order in the
nonlinearity parameter. We give simple and compact expressions. We argue that naive
estimates on the range of validity of the Kolmogorov-Zakharov state are in general
incorrect. We address the behavior of multimode correlators in a turbulent state: how
does the scattering of two waves change depending on if it they are in a calm tank of
water versus a turbulent one? In other words, how does wave turbulence renormalize
interactions. We find that the perturbative expansion is nontrivial: in general naive
perturbation theory yields divergences; we discuss analogies with similar issues in
quantum field theories, such as the renormalization of the electron charge.