Wave kinetic equation in a nonstationary and inhomogeneous medium with a weak quadratic nonlinearity

TL;DR

This paper derives a comprehensive wave kinetic equation for incoherent waves in nonstationary, inhomogeneous media with weak quadratic nonlinearity, incorporating effects of medium variability and nonlinear scattering.

Contribution

It provides a systematic derivation of the wave kinetic equation using Weyl phase-space representation for complex media with weak quadratic nonlinearity.

Findings

Captures effects of medium inhomogeneity in space and time

Includes nonlinear wave scattering effects

Framework applicable to weak wave turbulence studies

Abstract

We present a systematic derivation of the wave kinetic equation describing the dynamics of a statistically inhomogeneous incoherent wave field in a medium with a weak quadratic nonlinearity. The medium can be nonstationary and inhomogeneous. Primarily based on the Weyl phase-space representation, our derivation assumes the standard geometrical-optics ordering and the quasinormal approximation for the statistical closure. The resulting wave kinetic equation simultaneously captures the effects of the medium inhomogeneity (both in time and space) and of the nonlinear wave scattering. This general formalism can serve as a stepping stone for future studies of weak wave turbulence interacting with mean fields in nonstationary and inhomogeneous media.