Numerical verification of random phase-and-amplitude formalism of weak turbulence

TL;DR

This paper evaluates the accuracy of the Random Phase and Amplitude Formalism (RPA) in weak turbulence by comparing its predictions with direct numerical simulations, confirming RPA's validity across various statistical measures.

Contribution

It provides the first numerical verification of RPA's predictions for a three-wave Hamiltonian system, demonstrating its reliability without assuming Gaussianity.

Findings

RPA predictions align well with DNS results

RPA accurately describes fluctuation growth of wave mode amplitudes

Validation supports RPA's use in weak turbulence analysis

Abstract

The Random Phase and Amplitude Formalism (RPA) has significantly extended the scope of weak turbulence studies. Because RPA does not assume any proximity to the Gaussianity in the wavenumber space, it can predict, for example, how the fluctuation of the complex amplitude of each wave mode grows through nonlinear interactions with other modes, and how it approaches the Gaussianity. Thus, RPA has a great potential capability, but its validity has been assessed neither numerically nor experimentally. We compare the theoretical predictions given by RPA with the results of direct numerical simulation (DNS) for a three-wave Hamiltonian system, thereby assess the validity of RPA. The predictions of RPA agree quite well with the results of DNS in all the aspects of statistical characteristics of mode amplitudes studied here.