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Diffusion of inertia-gravity waves by geostrophic turbulence

Published online by Cambridge University Press:  30 April 2019

Hossein A. Kafiabad Open the ORCID record for Hossein A. Kafiabad [Opens in a new window] ,
Miles A. C. Savva  and
Jacques Vanneste Open the ORCID record for Jacques Vanneste [Opens in a new window]
Hossein A. Kafiabad
Affiliation:
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3FD, UK
Miles A. C. Savva
Affiliation:
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3FD, UK
Jacques Vanneste*
Affiliation:
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3FD, UK
*
†Email address for correspondence: j.vanneste@ed.ac.uk
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Abstract

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.

JFM classification

Geophysical and Geological Flows: Geostrophic turbulence Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Waves in rotating fluids
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 869 , 25 June 2019 , R7
Copyright
© 2019 Cambridge University Press 

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