Turbulent spectrum of 2D internal gravity waves

TL;DR

This paper derives an exact turbulent energy spectrum for 2D internal gravity waves using a novel wave kinetic theory approach, aligning with oceanic observations and revealing self-similar anisotropic turbulence.

Contribution

It introduces a new method in wave kinetic theory to find an exact turbulent spectrum for 2D internal gravity waves, accounting for non-hydrostatic effects and shear modes.

Findings

Spectrum matches oceanic Garrett--Munk spectrum at high frequencies

Unique power law solution with non-zero radial flux identified

Spectrum exhibits self-similarity in scale and frequency

Abstract

We find the turbulent energy spectrum of weakly interacting 2D internal gravity waves using the full, non-hydrostatic dispersion relation. This spectrum is an exact solution of a regularized kinetic equation, from which the zero-frequency shear modes have been excised by a careful limiting process. This is a new method in wave kinetic theory. The turbulent spectrum agrees with the 2D oceanic Garrett--Munk spectrum for frequencies large compared to the Coriolis frequency and vertical scales small compared to the depth of the ocean. We show that this turbulent spectrum is the unique power law solution to the steady kinetic equation with a non-zero radial flux. Our solution provides an interesting insight into a turbulent energy cascade in an anisotropic system -- like isotropic turbulence it is self-similar in scale, but its angular part is peaked along the curve of vanishing frequency and is self-similar in frequency.