Near-inertial wave scattering by random flows

TL;DR

This paper develops a theoretical framework and numerical validation for how turbulent random flows scatter and isotropize oceanic near-inertial waves, affecting their propagation and dispersion over tens of days.

Contribution

It introduces a transport equation for wave-energy transfer due to flow scattering and demonstrates its predictions with numerical simulations, highlighting the impact on near-inertial wave dynamics.

Findings

Wave scattering causes energy redistribution among waves of the same frequency.

Scattering leads to isotropization of the wave field in isotropic flows.

Time scales for scattering and isotropization are on the order of tens of days.

Abstract

The impact of a turbulent flow on wind-driven oceanic near-inertial waves is examined using a linearised shallow-water model of the mixed layer. Modelling the flow as a homogeneous and stationary random process with spatial scales comparable to the wavelengths, we derive a transport (or kinetic) equation governing wave-energy transfers in both physical and spectral spaces. This equation describes the scattering of the waves by the flow which results in a redistribution of energy between waves with the same frequency (or, equivalently, with the same wavenumber) and, for isotropic flows, in the isotropisation of the wave field. The time scales for the scattering and isotropisation are obtained explicitly and found to be of the order of tens of days for typical oceanic parameters. The predictions inferred from the transport equation are confirmed by a series of numerical simulations. Two situations in which near-inertial waves are strongly influenced by flow scattering are investigated through dedicated nonlinear shallow-water simulations. In the first, a wavepacket propagating equatorwards as a result from the $\beta$-effect is shown to be slowed down and dispersed both zonally and meridionally by scattering. In the second, waves generated by moving cyclones are shown to be strongly disturbed by scattering, leading again to an increased dispersion.