Energy cascade in the Garrett-Munk spectrum of internal gravity waves

TL;DR

This study numerically evaluates the energy transfer mechanisms in the Garrett-Munk spectrum of internal gravity waves, clarifying the roles of local and nonlocal interactions in ocean mixing.

Contribution

It provides a detailed numerical analysis of wave-triad interactions, decomposing energy transfer mechanisms and resolving long-standing paradoxes in the field.

Findings

Numerical evaluation aligns with empirical ocean mixing flux estimates.

Identifies the significance of elastic scattering and local interactions in energy transfer.

Resolves paradoxes regarding forward cascade mechanisms and zero induced diffusion flux.

Abstract

We study the spectral energy transfer due to wave-triad interactions in the Garrett-Munk spectrum of internal gravity waves (IGWs) based on a numerical evaluation of the collision integral in the wave kinetic equation. Our numerical evaluation builds on the reduction of the collision integral on the resonant manifold for a horizontally isotropic spectrum. We directly evaluate the downscale energy flux available for ocean mixing, whose value is in close agreement with the empirical finescale parameterization. We further decompose the energy transfer into contributions from different mechanisms, including local interactions and three types of nonlocal interactions, namely parametric subharmonic instability (PSI), elastic scattering (ES) and induced diffusion (ID). Through analysis on the role of each type of interaction, we resolve two long-standing paradoxes regarding the mechanism for forward cascade in frequency and zero ID flux for GM76 spectrum. In addition, our analysis estimates the contribution of each mechanism to the energy transfer in each spectral direction, and reveals new understanding of the importance of local interactions and ES in the energy transfer.