A new theory for downslope windstorms and trapped mountain waves

Linear mountain gravity waves forced by a nonlinear surface boundary condition are derived for a background wind that is null at the surface and increases smoothly to reach a constant value aloft and for a constant buoyancy frequency. In this configuration, the mountain waves have a critical level just below the surface that is dynamically controlled by the surface and minimum Richardson number J. When the flow is very stable (J≳1), and when the depth over which dissipations act is smaller than the mountain height, this critical-level dynamics easily produces large downslope winds and foehns. The downslope winds are more intense when the stability increases and much less pronounced when it decreases (when J goes below 1). In contrast, the trapped lee waves are very small when the flow is very stable, start to appear when J≈, and can become pure trapped waves (e.g., not decaying downstream) when the flow is unstable (for J < 0.25). For the trapped waves, these results are explained by the fact that the critical level absorbs the gravity waves downstream of the ridge when J > 0.25, while absorption decreases when J approaches 0.25. Pure trapped lee waves follow that when J < 0.25 the absorption can become null in the nondissipative limit. In the background-flow profiles analyzed, the pure trapped lee waves also correspond to neutral modes of Kelvin-Helmholtz instability. The validity of the linear approximation used is tested a posteriori by evaluating the relative amplitude of the neglected nonlinear terms.