A theory of mountain gravity waves produced when the incident wind is null at the surface and increases smoothly with altitude is presented. It inspires from the Long~(1953)'s mountain waves model and consider a linear set of inflow equations forced by a nonlinear surface boundary condition. In the model presented here, the mountain gravity waves have a critical level near below the surface upstream and downstream of the mountain which systematically produces large amplitude disturbance horizontal winds and buoyancy anomalies near the surface. In combination with the nonlinear boundary condition, this near critical level dynamics systematically produces large downslope winds and Foehn.

Downstream of the ridge, the critical level also prevents total wave reflection at the surface except when the surface Richardson number is lower than $0.25$. As in conjunction with turning point aloft, a total reflection is necessary for the development of trapped lee waves, it is shown that trapped lee-waves are highly favored when the background flow is unstable near the ground.

In the background flow profiles analyzed, trapped lee-waves also correspond to well known neutral modes of Kelvin-Helmholtz instability, establishing a direct correspondence between trapped lee-waves and stratified shear flow instabilities.

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*email: flott@lmd.ens.fr
*Preference: Oral