# Magneto-Fluid Dynamics Seminar

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

**Speaker:**
Daniel Ruiz, Sandia National Laboratory

**Location:**
Warren Weaver Hall 905

**Date:**
Tuesday, February 20, 2018, 11 a.m.

**Synopsis:**

In this talk, I present a systematic derivation of a 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, the derivation makes use of the well-known ordering assumptions of geometrical optics and of a statistical closure based on the quasinormal approximation. The resulting wave kinetic equation describes the wave dynamics in the ray phase space. It captures linear effects, such as refraction, linear damping, and external sources, as well as nonlinear wave scattering. This general formalism could potentially serve as a stepping stone for future studies of weak wave turbulence interacting with mean fields in nonstationary and inhomogeneous media. In particular, I demonstrate how the general formalism can be applied to the study of interacting drift-wave turbulence and zonal flows in plasmas.