Work

Inhomogeneity-induced wavenumber diffusion

Year: 2025

Type: article

Abstract: Inertia–gravity waves are scattered by background flows as a result of Doppler shift by a non-uniform velocity. In the Wentzel–Kramers–Brillouin regime, the scattering process reduces to a diffusion in spectral space. Other inhomogeneities that 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 a 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.

Source: Journal of Fluid Mechanics

DOI: 10.1017/jfm.2025.23

Authors: Michael R. Cox, Hossein A. Kafiabad, Jacques Vanneste

Institutions: Maxwell Institute for Mathematical Sciences, University of Edinburgh, Durham University

Language: English

Topic: Oceanographic and Atmospheric Processes

Subfield: Oceanography

Field: Earth and Planetary Sciences

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: Universität Hamburg, Engineering and Physical Sciences Research Council, Natural Environment Research Council