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

Abstract

We study the spectral energy transfer due to wave–triad interactions in the Garrett–Munk spectrum of internal gravity waves 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 evaluate directly the downscale energy flux available for ocean mixing, whose value is in close agreement with the finescale parameterization. We further decompose the energy transfer into contributions from different mechanisms, including local interactions and three types of non-local interactions, namely parametric subharmonic instability, elastic scattering (ES) and induced diffusion (ID). Through analysis on the role of each mechanism, we resolve two long-standing paradoxes regarding the mechanism for forward cascade in frequency and zero ID flux for the 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.