Scattering and diffusion of inertia-gravity waves

Abstract

Inertia-gravity waves (IGWs) propagate under the restoring forces of buoyancy and the Coriolis effect. They are present in the ocean and the atmosphere and play a key role in the energetics of both. As IGWs propagate, they encounter inhomogeneities such as background flows, bottom topography and other waves. If these inhomogeneities are weak and either slowly evolving or stationary, the IGWs are scattered and their energy spreads through wavenumber space whilst preserving frequency.

The scattering of IGWs by weak, slowly evolving background flows can be modelled as a spectral diffusion process providing the IGWs propagate in the WKB regime, that is, they have much shorter spatial scales than the background flow. Previous studies consider Doppler shift to be the sole mechanism causing IGW diffusion. If the flow evolves so slowly it can be considered stationary, it can be shown that energy diffuses along cones of constant frequency in wavenumber space.

In this thesis, we relax the assumption of time-independent background flow and find that a slowly time-dependent flow induces energy diffusion across the constant frequency cones. We solve the corresponding diffusion equation and find energy decays rapidly away from the cone within a thin boundary layer.

We consider mechanisms for wave diffusion other than Doppler shift. We generalise the diffusion equation to account for any weak, slowly evolving inhomogeneities interacting with waves in the WKB regime. We evaluate the general diffusivity and find exact solutions for two examples of these inhomogeneities: fluctuations in the IGW buoyancy frequency due to the thermal wind balance and, for a rotating shallow water system, fluctuations in the layer height due to geostrophic balance. For the latter, we support our findings with ray tracing simulations.