Diffusion of inertia-gravity waves by geostrophic turbulence

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.

References in corpus (2)

• Scattering of internal tides by barotropic quasigeostrophic flows
• Near-inertial wave scattering by random flows

Cited by in corpus (8)

• Inertia-gravity-wave scattering by geostrophic turbulence
• Transition from geostrophic flows to inertia-gravity waves in the spectrum of a differentially heated rotating annulus experiment
• Energy cascade in the Garrett-Munk spectrum of internal gravity waves
• Inertia-gravity-wave diffusion by geostrophic turbulence: the impact of flow time dependence
• Resonant and near-resonant internal wave triads for non-uniform stratifications. Part 2: Vertically bounded domain with mild-slope bathymetry
• Dynamical large deviations for an inhomogeneous wave kinetic theory: linear wave scattering by a random medium
• Laboratory observation of internal gravity wave turbulence in a three-dimensional, large-scale facility
• Inhomogeneity-induced wavenumber diffusion