Wave drag by three-dimensional mountain lee-waves in nonplanar shear flow

Abstract

The effect of both cross-wind and vertical shear of the basic flow are considered in a linear, hydrostatic model of stationary, mountain lee-waves in a stably stratified airstream. Analytical solutions are first determined for a constant lapse rate basic-state. A solution corresponding to a cross-wind variation, represented by the hyperbolic secant profile, is compared with a constant flow over the same isolated hill. In the former case, wave-energy is trapped by the background shear. This effect is responsible for a greater wave-drag on the airstream than the drag produced in the constant wind case. However, these values of the wave-drag are always less than the drag exerted by two-dimensional waves over a ridge. A two-layer model is then considered, in order to examine the effect of a stable stratosphere over a less stable troposphere. The results show that the drag is sensitive to the phase difference between the transmitted and reflected waves in the lower layer. This sensitivity is more pronounced when cross-stream shear of the basic flow is taken into account. Finally, the relationship between the present model dynamics and the mechanism suggested for the dynamics of wave-induced downslope winds, presented by Klemp & Lilly, is pointed out. DOI: 10.1111/j.2153-3490.1976.tb00678.x