A three dimensional wave activity flux applicable to inertio-gravity waves

Abstract

A three dimensional wave activity flux applicable to non-hydrostatic inertio-gravity waves in a time mean flow in a Boussinesq fluid is derived. It is shown that the flux gives the wave-action density flux relative to the local time mean flow, and additive terms in residual circulation are equal to Stokes drift under the WKB limit. The flux is a generalization of three dimensional wave activity fluxes that have been used to analyze quasi-geostrophic wave disturbances. A flux under the log-pressure coordinate system on spherical geometry applicable to global hydrostatic inertio-gravity waves is also derived.