Momentum and Energy Exchanges due to Orographically Scattered Gravity Waves

Abstract

The scattering of two-dimensional, hydrostatic, Boussinesq, internal gravity waves by orographic features is considered, with special attention paid to energy and momentum fluxes. A general integral equation for the streamfunction is derived from which a special Fourier representation is shown to hold in a well-defined region of the atmosphere. This leads to simple expressions for the energy and momentum fluxes and to a useful form for the energy conservation law. Scattering efficiency functions are defined. When the topography satisfies certain conditions, analytic approximations can be used to determine the scattering; it is found that the reflected momentum flux is larger than the incident flux. The manner in which viscosity affects this result is discussed. In the special case that the maximum topographic slope is less than that of the incident wave fronts, a simple integral equation is derived and used to calculate numerically the scattering from several different orographies. In every case, the flux anomaly mentioned above persists. The numerical results show that there is very little interference between nearby orographic features, and suggest that the vertical scale of the topography must be of the order of one-quarter of the incident vertical wavelength to significantly scatter. On the basis of these results, it is possible that topographic scattering may significantly affect the tidal momentum flux in the Venusian atmosphere.