Numerical study on fast spectral evolution due to double resonance and applicability of generalized kinetic equation

TL;DR

This paper numerically investigates the rapid spectral evolution caused by double resonance in a two-layer fluid system and assesses the effectiveness of the generalized kinetic equation in modeling this phenomenon.

Contribution

It demonstrates through numerical analysis that the generalized kinetic equation can qualitatively capture spectral features but overestimates growth, highlighting its limitations.

Findings

GKE reproduces sharp spectral peaks due to double resonance.

GKE overestimates the growth rate of spectral peaks.

GKE fails to accurately predict the temporal evolution near double resonance.

Abstract

It is known that for a two-layer fluid system, the kinetic equation governing the evolution of the spectrum of the wave field given by the standard wave turbulence theory (WTT) breaks down due to the existence of a "double resonance", and the spectrum can evolve on a time scale much faster than that predicted by the standard WTT. In this study, using a simplified model for a two-layer fluid system, the applicability of the generalized kinetic equation (GKE) for such a situation is examined numerically. It is shown that the GKE can reproduce the appearance of a sharp peak in the surface wave spectrum due to double resonance, but it overestimates the growth of the peak, consequently failing to quantitatively describe the temporal evolution of the spectrum correctly, particularly near the double resonance point.