Inertia-gravity-wave scattering by three-dimensional geostrophic turbulence

In rotating stratified flows including in the atmosphere and ocean, inertia-gravity waves (IGWs) often coexist with geostrophically balanced turbulent flows. Advection refraction by such lead to wave scattering, redistributing IGW energy position–wavenumber phase space. We give a detailed description of this process deriving kinetic equation governing evolution phase-space density. The derivation relies on smallness Rossby number characterising geostrophic flow, which is treated as random field known statistics, makes no assumption spatial scale separation, neglects wave–wave interactions. It extends previous work restricted near-inertial waves, barotropic or much shorter than flow scales. describes transfers that are IGWs same frequency, result time separation between flow. formulate constant-frequency surface – double cone wavenumber space using polar spherical coordinates, we examine form two scattering cross-sections involved, quantify with, respectively, opposite directions vertical propagation. captures both horizontal isotropisation cascade across scales from scattering. focus our attention latter assess predictions against direct simulations three-dimensional Boussinesq equations, finding good agreement.