A New Theory for Downslope Windstorms and Trapped Mountain Waves

Abstract 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 , 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 , and can become pure trapped waves (e.g., not decaying downstream) when the flow is unstable (for ). For the trapped waves, these results are explained by the fact that the critical level absorbs the gravity waves downstream of the ridge when , while absorption decreases when J approaches 0.25. Pure trapped lee waves follow that when 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.