Density representation of Long's equation

International audienceLong's equation describes two dimensional stratified atmospheric flow over terrain. Its solutions using regular first order perturbations and linear approximation were investigated analytically and numerically by many authors. Special attention was paid to the properties of the gravity waves that have been predicted to be generated as a result. In this paper we derive a new representation of this equation in terms of the atmospheric density. This new equation is used then to study the steady state that results from some ideal upstream density profiles and the generation of gravity waves. Furthermore we compare the new formulation with the stream function formulation of Long equation and develop new criteria for the stability of the flow