Diffusion of inertia-gravity waves by geostrophic turbulence

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The scattering of inertia-gravity waves by large-scale geostrophic turbulence in a rapidly rotating, strongly stratified fluid leads to the diffusion of wave energy on the constant-frequency cone in wavenumber space. We derive the corresponding diffusion equation and relate its diffusivity to the wave characteristics and the energy spectrum of the turbulent flow. We check the predictions of this equation against numerical simulations of the three-dimensional Boussinesq equations in initial-value and forced scenarios with
horizontally isotropic wave and flow fields. In the forced case, wavenumber diffusion results in a k−2 wave energy spectrum consistent with as-yet unexplained features of observed atmospheric and oceanic spectra.
Original languageEnglish
Pages (from-to)R71-R713
Number of pages13
JournalJournal of Fluid Mechanics
Early online date30 Apr 2019
Publication statusPublished - 25 Jun 2019


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