Downscale energy fluxes in scale invariant oceanic internal wave turbulence

TL;DR

This paper investigates the energy transfer mechanisms in oceanic internal wave turbulence, identifying key triad interactions and quantifying energy fluxes, which align with ocean mixing parametrizations.

Contribution

It provides an analytical and numerical analysis of scale invariant solutions to the internal wave kinetic equation, highlighting dominant triad interactions and energy flux calculations.

Findings

Triads with extreme scale separation dominate energy transfer.

Quasi-colinear triads in the horizontal plane are significant.

Results agree with established ocean mixing parametrizations.

Abstract

We analyze analytically and numerically the scale invariant stationary solution to the internal wave kinetic equation. Our analysis of the resonant energy transfers shows that the leading order contributions are given (i) by triads with extreme scale separation and (ii) by triads of waves that are quasi-colinear in the horizontal plane. The contributions from other types of triads is found to be subleading. We use the modified scale invariant limit of the Garrett and Munk spectrum of internal waves to calculate the magnitude of the energy flux towards high wave numbers in both the vertical and the horizontal directions. Our results compare favorably with the finescale parametrization of ocean mixing that was proposed in [Polzin et al. (1995)].