Nonlocal gravity wave turbulence in presence of condensate

TL;DR

This paper develops a theory for weak gravity wave turbulence on deep water, emphasizing nonlocal interactions with a strong low-frequency condensate, explaining recent numerical observations.

Contribution

It introduces a linear spectral diffusion model capturing nonlocal interactions with a condensate, providing a new theoretical framework for gravity wave turbulence.

Findings

Derived a scaling solution for the spectral diffusion equation.

Proposed the condensate as a key factor in wave spectrum formation.

Offered an explanation for recent numerical results on gravity wave spectra.

Abstract

We develop a theory of turbulence of weak random gravity waves on surface of deep water in which the main nonlinear process at high-frequency part of the spectrum is a nonlocal interaction with a strong low-frequency component. The latter component, which we call ``condensate", may appear in the system due to, e.g., the finite size effects which lead to an energy stagnation at waves whose wavelength is comparable to the size of the retaining flume. Our theory assumes the form of a linear spectral diffusion equation. We find a scaling solution of this equation and propose it as a possible explanation of recent numerical results for the gravity wave spectrum.