Influence of dissipation on gravity waves propagating through a shear layer and on instabilities: validity of the linear approximation

Among the instabilities, we study those found by Drazin (1958) in an hyperbolic tangent wind profile, and another type which arises when stratification vanishes at the critical level. The interest of this last type of instabilities consists in the fact that they are propagating waves and can appear without rigid boundary conditions. The results we found concern linear approximation, which as is usually assumed, is valid for small amplitude waves. We found that in general the linear approximation is restricted to waves whose maximum horizontal induced velocity is less than 10% of the velocity scale of the mean flow. -from Authors