A One-Dimensional Model for Investigating Scale-separated Approaches to the Interaction of Oceanic Internal Waves

TL;DR

This study compares numerical and theoretical models of internal wave interactions in the ocean, revealing that traditional scale-separated assumptions overestimate energy transfer and suggesting a shift towards models emphasizing local interactions.

Contribution

It introduces a nuanced approach to modeling internal wave interactions, challenging the traditional scale-separated paradigm with evidence supporting local interaction dominance.

Findings

Numerical results align with wave turbulence theory at low amplitudes.

Energy transport is overestimated by traditional models at oceanic amplitudes.

Local interactions are more significant than previously thought in internal wave dynamics.

Abstract

High-frequency wave propagation in near-inertial wave shear has been considered fundamental in setting the spectral character of the oceanic internal wave continuum and for transporting energy to wave-breaking. We compare idealized ray tracing numerical results with metrics derived using a wave turbulence derivation for the kinetic equation and a path integral to study such scale-separated interactions. At small inertial wave amplitudes, all three provide consistent descriptions for the mean drift of wavepackets in the spectral domain and dispersion about that mean drift. Extrapolating our results to the background internal wavefield over-predicts downscale energy transports by an order of magnitude. At oceanic amplitudes, however, the numerics support diminished transport and dispersion that coincide with the mean drift time scale becoming similar to the lagged correlation time scale. Despite this decrease, numerical estimates of downscale energy transfer are still significantly larger than oceanic derived metrics. Our results support replacing the long standing interpretive paradigm of extreme scale-separated interactions with a more nuanced slate of 'local' interactions in the kinetic equation.