On long waves with cross-wind in an atmosphere

Abstract

Asymptotic equations of long waves in a compressible medium of infinite height with arbitrary density and wind profiles, including cross-wind, are systematically derived to provide the mathematical description of certain pressure-front phenomena observed in the atmosphere. It is assumed that the final state of the wave is a plane wave moving with nearly constant velocity, even though its velocity field has a component transverse to the direction of propagation. The coefficients of the asymptotic long-wave equations are found to depend on the equilibrium profiles of the density and of the velocity component in the direction of propagation of the wave, but not on the profile of the transverse velocity. Any horizontal direction of propagation is found to be possible, even for waves of permanent type.