On the mathematical fluid dynamics of atmospheric gravity (buoyancy) waves

Abstract

AbstractStarting from the general, governing equations for a viscous, compressible fluid written in rotating, spherical coordinates, with an associated prescription for its thermodynamics, we construct a general amplitude perturbation of the background state of the atmosphere. The background state, with a purely zonal flow (wind) is suitably non-dimensionalised and the thin-shell parameter introduced; this is the sole basis upon which we construct the asymptotic solution of this problem. A corresponding, but different, non-dimensionalisation is performed on the system representing the perturbation. This approach shows how the Boussinesq approximation arises, but it also shows that rotation (Coriolis) terms cannot be ignored. Furthermore, any consistent solution requires that changes in pressure, density and temperature, due to the passage of the wave, are all the same (asymptotic) size. Comparison is made with existing theories, and we comment on the new aspects that have been uncovered in this investigation. Finally, we indicate where these ideas might be taken in the future.