Inertia-gravity-wave diffusion by geostrophic turbulence: the impact of flow time dependence

Cox, Michael R.; Kafiabad, Hossein A.; Vanneste, Jacques

Abstract

The scattering of three-dimensional inertia-gravity waves by a turbulent geostrophic flow leads to the redistribution of their action through what is approximately a diffusion process in wavevector space. The corresponding diffusivity tensor was obtained by Kafiabad et al. (J. Fluid Mech., vol. 869, 2019, R7) under the assumption of a time-independent geostrophic flow. We relax this assumption to examine how the weak diffusion of wave action across constant-frequency cones that results from the slow time dependence of the geostrophic flow affects the distribution of wave energy. We find that the stationary wave-energy spectrum that arises from a single-frequency wave forcing is localised within a thin boundary layer around the constant-frequency cone, with a thickness controlled by the acceleration spectrum of the geostrophic flow. We obtain an explicit analytic formula for the wave-energy spectrum which shows good agreement with the results of a high-resolution simulation of the Boussinesq equations.

Citation

Cox, M. R., Kafiabad, H. A., & Vanneste, J. (2023). Inertia-gravity-wave diffusion by geostrophic turbulence: the impact of flow time dependence. Journal of Fluid Mechanics, 958, Article A21. https://doi.org/10.1017/jfm.2023.83

• Journal Article Type: Article
• Online Publication Date: Mar 3, 2023
• Publication Date: 2023
• Deposit Date: Mar 12, 2023
• Publicly Available Date: Apr 24, 2023
• Journal: Journal of Fluid Mechanics
• Print ISSN: 0022-1120
• Electronic ISSN: 1469-7645
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 958
• Article Number: A21
• DOI: https://doi.org/10.1017/jfm.2023.83
• Public URL: https://durham-repository.worktribe.com/output/1178545
• Related Public URLs: https://arxiv.org/abs/2207.09386