Linear Mountain Waves Past a Mountain Range with Concavity and Convexity

It is well known that winds past a mountain range in a stable atmosphere cause internal gravity waves, resulting in wind deceleration in front of the mountain and wind acceleration in the lee of the mountain range. In recent years, several statistical analyses and numerical experimental investigations have been published on airflow over terrain that is convex on the upwind side (concave on the downwind side; Left Figure). Here, we computed analytic solutions for 3-D linear mountain waves based on Smith (1980) and Saito (1993) for airflow over such terrain.

Center figure shows the surface wind speed through the center of the convexity of the horizontal wind from the statics linear analytical solution. The horizontal wind speed increases within the concave topography on the downwind side of the mountain range, exceeding the NH/2 (=0.5 m/s) of the grated wind speed of the analytical linear solution for 2-D bell-shaped topography, but not exceeding the speed increase for 2-D cosine bell-shaped topography. On the other hand, the maximum wind magnitude for the downwind concave terrain was larger than that for the 2D terrain (right figure). This is due to the effect of asymmetric topography with a steeper slope on the downwind side than on the upwind side.

References:

Smith, R. B., 1980: Linear theory of stratified hydrostatic flow past an isolated mountain. Tellus, 32, 348-364.

Saito, K., 1993: A numerical study of the local downslope wind Yamaji-kaze in Japan. Part 2: Non-linear aspect of the 3-D flow over a mountain range with a col. J. Meteor. Soc. Japan, 71, 247-271.