| 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. Stochastic classical field theories, such as this one, are equivalent to quantum field theories. This provides a powerful way to systematically study wave turbulence, perturbatively in the coupling. The similarities and even more so, the differences, with conventional quantum field theories are fascinating.
We study renormalization of the quartic interaction, finding sharp departure from widely accepted assumptions in the field. We show that the true dimensionless four-wave coupling is always parametrically different from the naive estimate and that the effective interaction either decays or grows explosively with the extent of the cascade, depending on the sign of the new coupling. The explosive growth possibly signals the appearance of a multi-wave bound state (solitons, shocks, cusps), heuristically similar to confinement in QCD.
Based on work with Michael Smolkin, 2203.08168 and Gregory Falkovich, 2308.00033. Link to the Event Video |