Simultaneous numerical simulation of direct and inverse cascades in wave turbulence

TL;DR

This paper presents the first direct numerical simulation demonstrating simultaneous direct and inverse cascades in wave turbulence, highlighting the impact of long waves background on spectral characteristics, relevant for experimental setups.

Contribution

It introduces the first simulation of concurrent cascades in wave turbulence using Hamiltonian equations, revealing the influence of condensate on spectra.

Findings

Simultaneous formation of direct and inverse cascades observed.

Strong long waves background (condensate) develops during simulations.

Kolmogorov spectra are highly sensitive to the presence of the condensate.

Abstract

Results of direct numerical simulation of isotropic turbulence of surface gravity waves in the framework of Hamiltonian equations are presented. For the first time simultaneous formation of both direct and inverse cascades was observed in the framework of primordial dynamical equations. At the same time, strong long waves background was developed. It was shown, that obtained Kolmogorov spectra are very sensitive to the presence of this condensate. Such situation has to be typical for experimental wave tanks, flumes, and small lakes.