Gravity Wave Drag Produced by Small Amplitude Elliptical Mountains for Sheared Wind Profiles

The analytical models of Teixeira et al. (2004) and Teixeira and Miranda (2004), where the gravity wave drag exerted by a sheared stratified flow on axisymmetric or 2D mountains is calculated, are extended here to mountains with an elliptical horizontal cross section. For the simple situations considered in this study, the normalized drag depends on only two parameters: the Richardson number at the surface, Ri, and the horizontal aspect ratio of the mountain. For a wind that varies linearly with height, the drag always decreases as Ri decreases, albeit at different rates depending on the aspect ratio. For a wind that rotates with height at a constant rate maintaining its magnitude, the drag generally increases as Ri decreases, but if the mountain is sufficiently elongated in the surface streamwise direction, this dependence changes sign. It is also shown that flow stagnation at the surface is strongly affected by variations of the windspeed with height, but weakly affected by variations of wind direction.