Inhomogeneity-induced wavenumber diffusion

TL;DR

This paper extends the spectral diffusion model for inertia-gravity waves to include effects of inhomogeneities like density and buoyancy variations, revealing their significant roles alongside Doppler shift in wave scattering.

Contribution

It generalizes the spectral diffusion equation to incorporate inhomogeneities beyond background flow, applying it to rotating shallow water and Boussinesq systems.

Findings

Height and buoyancy inhomogeneities significantly contribute to spectral diffusion.

Regimes exist where all inhomogeneity effects are equally important.

Exact solutions and ray tracing validate the extended diffusion model.

Abstract

Inertia-gravity waves are scattered by background flows as a result of Doppler shift by a non-uniform velocity. In the WKB regime, the scattering process reduces to a diffusion in spectral space. Other inhomogeneities the waves encounter, such as density variations, also cause scattering and spectral diffusion. We generalise the spectral diffusion equation to account for these inhomogeneities. We apply the result to the rotating shallow water system, for which height inhomogeneities arise from velocity inhomogeneities through geostrophy, and to the Boussinesq system for which buoyancy inhomogeneities arise similarly. We compare the contributions that height and buoyancy variations make to the spectral diffusion with the contribution of the Doppler shift. In both systems, we find regimes where all contributions are significant. We support our findings with exact solutions of the diffusion equation and with ray tracing simulations in the shallow water case.