Analysis Seminar

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A drunkard’s view of dual cascades in wave turbulence

Speaker: Oliver Buhler, New York University

Location: Warren Weaver Hall 1302

Date: Thursday, October 12, 2023, 11 a.m.

Synopsis:

Spectral cascades in 3d and 2d hydrodynamic turbulence are reasonably well understood and served as a role model for subsequent studies of analogous cascades in wave turbulence.  In particular, the workings of the famous dual cascade in 2d turbulence became the paradigm for wave turbulence systems based on four-wave resonances (e.g. surface waves, or the nonlinear Schrödinger equation with cubic nonlinearity).  However, it can be argued that the familiarity of dual cascades masks profound differences between the 2d hydrodynamic case and its wave turbulence counterpart, and that these differences can strongly affect detailed turbulence measurements in numerical models or experiments.  In this elementary talk, I will introduce the various cascade pictures at a simple level and then illustrate the peculiarities of the wave turbulence dual cascade based on recent high-resolution simulations.  I will also present a new semi-empiric toy model of dual cascades in wave turbulence that is surprisingly accurate in explaining the peculiar results of the numerical simulations.