Trapped mountain waves with a critical level just below the surface

Abstract

The trapped mountain waves produced when the incident wind near the surface is small compared with its value aloft are analyzed with a theory adapted from Long (1953) and compared with fully nonlinear simulations performed with the Weather Research and Forecasting model (WRF). Although small near‐surface incident winds occur naturally in fronts via a combination of the thermal wind balance and the boundary layer, they pose at least two problems in mountain meteorology: zero surface incident winds produce no wave in the fully linear case; they also correspond to places where mountain waves have a critical level.Despite these problems, theory and WRF show that, for small mountains, trapped lee waves (a) can occur and (b) are favored when the surface Richardson number J = N 2/(∂u/∂z)2 is small. This last result is related to the theoretical fact that the surface absorption of stationary gravity waves increases when J increases. The relation with flow stability is corroborated further by the fact that the trapped lee waves resemble the Kelvin–Helmholtz (KH) modes of instability that exist when J < 0.25.For medium mountains, some aspects of the theory still hold but need to be adapted, the more intense winds and foehn that occur along the lee side of the mountain having a tendency to increase the surface flow stability. For “initially” small J, this can limit the onset of trapped lee waves, again consistent with the fact that mountain‐wave surface absorption increases with surface flow stability. For large J, the dynamics produces wave breaking on the lee side, destabilizing the flow in the wake of the mountain. In the region where the Richardson number is small, trapped waves develop despite the fact that the surface Richardson number can be quite large, suggesting that the trapped lee waves now result from an absolute instability of the wake.