Scale Separated Approaches to the Interaction of Oceanic Internal Waves, part I: Theory

Abstract

We report two parallel derivations for transport equations describing the refraction of high frequency internal waves in a sea of random inertial waves. One derivation casts the fields as amplitude modulated waves in an Eulerian format and ultimately results in a Fokker-Planck (generalized diffusion) equation. The second casts the high frequency waves as a frequency modulated system. An ensemble averaged transport equation is obtained here that is characterized by a dispersion of wave-packets about a mean drift in the spectral domain. In this derivation the Fokker-Planck equation contains an advective term. Both transport equations make unrealistic predictions for energy sourced to internal wave breaking. The amplitude modulated system predicts no mixing, the frequency modulated system over predicts by an order of magnitude.