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Near-inertial-wave scattering by random flows

Eric Danioux and Jacques Vanneste*

  • School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom

  • *Corresponding author: J.Vanneste@ed.ac.uk
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Phys. Rev. Fluids 1, 033701 – Published 14 July, 2016

DOI: https://doi.org/10.1103/PhysRevFluids.1.033701

Abstract

The impact of a turbulent flow on wind-driven oceanic near-inertial waves is examined using a linearized shallow-water model of the mixed layer. Modeling 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 wave number) and, for isotropic flows, in the isotropization of the wave field. The time scales for the scattering and isotropization 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 wave packet propagating equatorward as a result from the β 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.

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Phys. Rev. Fluids 1, 033701– Published 14 July, 2016
  • Received 22 January 2016

©2016 American Physical Society

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