Inertia-gravity-wave diffusion by geostrophic turbulence: the impact of flow time dependence. (10th March 2023)

• Record Type: Journal Article
• Authors: Cox, Michael R.; Kafiabad, Hossein A.; Vanneste, Jacques
• Is Part Of: Journal of fluid mechanics. Volume 958(2023)
• Publication Date: 2023-03-10
• Subjects: waves in rotating fluids -- internal waves -- geostrophic turbulence; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2023.83
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: 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.