Resonant and Near-Resonant Internal Wave Interactions

TL;DR

This paper investigates the dynamics of internal wave spectra, revealing that nonlinear interactions can cause faster evolution than previously thought, challenging the assumption of a near-stationary Garrett and Munk spectrum.

Contribution

It demonstrates that nonlinear transfers can accelerate internal wave spectrum evolution, and shows that including near-resonant interactions improves the kinetic equation's self-consistency.

Findings

Nonlinear transfers can cause evolution faster than one wave period.

Including near-resonant interactions reduces spectrum evolution rates.

The Garrett and Munk spectrum may not be as stationary as previously assumed.

Abstract

We report evaluations of a resonant kinetic equation that suggest the slow time evolution of the Garrett and Munk spectrum is {\em not}, in fact, slow. Instead nonlinear transfers lead to evolution time scales that are smaller than one wave period at high vertical wavenumber. Such values of the transfer rates are inconsistent with conventional wisdom that regards the Garrett and Munk spectrum as an approximate stationary state and puts the self-consistency of a resonant kinetic equation at a serious risk. We explore possible reasons for and resolutions of this paradox. Inclusion of near-resonant interactions decreases the rate at which the spectrum evolves. This leads to improved self-consistency of the kinetic equation.