Direct numerical experiment on measuring of dispersion relation for gravity waves in the presence of condensate

TL;DR

This paper reports a numerical experiment measuring the dispersion relation of gravity waves in the presence of a condensate, revealing its significant influence on the inverse cascade spectrum.

Contribution

The study provides the first direct measurement of the dispersion relation affected by condensate, highlighting its impact on wave turbulence dynamics.

Findings

Condensate significantly influences the inverse cascade spectrum.

The dispersion relation is altered in the presence of condensate.

Inverse cascade mechanisms are affected by condensate presence.

Abstract

During previous numerical experiments on isotropic turbulence of surface gravity waves we observed formation of the long wave background (condensate). It was shown (Korotkevich, Phys. Rev. Lett. vol. 101 (7), 074504 (2008)), that presence of the condensate changes a spectrum of direct cascade, corresponding to the flux of energy to the small scales from pumping region (large scales). Recent experiments show that the inverse cascade spectrum is also affected by the condensate. In this case mechanism proposed as a cause for the change of direct cascade spectrum cannot work. But inverse cascade is directly influenced by the linear dispersion relation for waves, as a result direct measurement of the dispersion relation in the presence of condensate is necessary. We performed the measurement of this dispersion relation from the direct numerical experiment. The results demonstrate that in the region of inverse cascade influence of the condensate cannot be neglected.