A Closure for Internal Wave–Mean Flow Interaction. Part I: Energy Conversion

Abstract

AbstractWhen internal (inertia-)gravity waves propagate in a vertically sheared geostrophic (eddying or mean) flow, they exchange energy with the flow. A novel concept parameterizing internal wave–mean flow interaction in ocean circulation models is demonstrated, based on the description of the entire wave field by the wave-energy density in physical and wavenumber space and its prognostic computation by the radiative transfer equation. The concept enables a simplification of the radiative transfer equation with a small number of reasonable assumptions and a derivation of simple but consistent parameterizations in terms of spectrally integrated energy compartments that are used as prognostic model variables. The effect of the waves on the mean flow in this paradigm is in accordance with the nonacceleration theorem: only in the presence of dissipation do waves globally exchange energy with the mean flow in the time mean. The exchange can have either direction. These basic features of wave–mean flow interaction are theoretically derived in a Wentzel–Kramers–Brillouin (WKB) approximation of the wave dynamics and confirmed in a suite of numerical experiments with unidirectional shear flow.