Inertia-gravity waves and geostrophic turbulence

Abstract

Inertia-gravity waves in the atmosphere and ocean are transported and refracted by geostrophic turbulent currents. Provided that the wave group velocity is much greater than the speed of geostrophic turbulent currents kinetic theory can be used to obtain a comprehensive statistical description of the resulting interaction (Savva et al. J. Fluid Mech. vol. 916 2021 A6). The leading-order process is scattering of wave energy along a surface of constant frequency in wavenumber space. The constant-surface corresponding to the linear dispersion relation of inertia-gravity waves is a cone extending to arbitrarily high wavenumbers. Thus wave scattering by geostrophic turbulence results in a cascade of wave energy to high wavenumbers on the surface of the constant-cone. Solution of the kinetic equations shows establishment of a wave kinetic energy spectrum where is the horizontal wavenumber.