Effects of shear and sharp gradients in static stability on two-dimensional flow over an isolated mountain ridge

We have investigated the effects of shear and sharp gradients in static stability and demonstrated how a mountain wave and its associated surface winds can be strongly influenced. Linear theory for two-dimensional, nonrotating stratified flow over an isolated mountain ridge with positive shear and constant static stability shows that the horizontal wind speeds on both the lee and upslope surfaces are suppressed by positive shear. The critical F(= U/Nh where U is the basic wind speed, N the Brunt-Vaisala frequency, and h the mountain height) for the occurrence of wave breaking decreases when the strength of the positive shear increases, while the location for the wave-induced critical level is higher in cases with larger positive shear. The linear theory is then verified by a series of systematic nonlinear numerical experiments. Four different flow regimes are found for positive shear flow over a two-dimensional mountain. The values of critical F which separate the flow regimes are lower when the strength of the positive shear is larger. The location of stagnation aloft from numerical simulations is found to be quite consistent with those predicted by linear theory. We calculate the strongest horizontal wind speed on the lee surface (Umax), the smallest horizontal wind speed on the upslope surface (Umin), the reflection (Ref), and the transmission (Tran) coefficients for different combinations of the stability ratio between the upper and lower layers (i.e. λ12 = N2/N1) and z1 (interface height) in a two-layer atmosphere from linear analytical solutions. Both Ref and Tran are found to be functions of log(λ12) but not the interface height (z1). Ref is larger when λ12 is much different from 1, no matter whether it is larger or smaller than 1. However, Tran decreases when log(λ12) increases and approaches 0 when log(λ12) is large. The magnitude of the largest Umax (smallest Umin) increases (decreases) as the absolute value of log(λ12) increases. It is found that the largest Umax occurs when the nondimensional z1 is near 0.25 ± n/2 for cases with a less stable upper layer or when z1 is near n/2 for cases with a more stable upper layer. These results are confirmed by nonlinear numerical simulations. We find that linear theory is very useful in qualitative analysis of the possibility of high-drag state for different stability profiles. The location of stagnation aloft in a two-layer atmosphere from numerical simulations agrees very well with those predicted by linear theory. The above findings are applied to investigate the Boulder severe downslope windstorm of 11 January 1972. We find that the windstorm cannot develop if the near mountain-top inversion is located at a higher altitude (e.g., z = 6.7 km). However, if there exists a less stable layer right below the tropopause, the windstorm can develop in the absence of a low-level inversion. These results indicate the importance of partial reflection due to the structured atmosphere in influencing the possibility of severe downslope windstorms, although partial reflection may not be the responsible mechanism for the generation of windstorms.