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

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