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.

On the time scales of spectral evolution of nonlinear waves

“…A typical example of this violation has long been known in the Garrett–Munk spectrum of internal gravity waves, where the time-scale separation is not valid in the high-wavenumber/high-frequency portion of the spectrum (e.g. Holloway 1980; McComas & Müller 1981; Lvov, Polzin & Yokoyama 2012; Eden, Pollmann & Olbers 2019; Wu & Pan 2023). In this view, as the spectrum deviates from the stationary state, there exists a critical spectral form (even if the nonlinearity level is relatively low) that drives fast evolution beyond which the WKE fails.…”