Inviscid instability of a stably stratified compressible boundary layer on an inclined surface

The three-dimensional stability of an inflection-free boundary layer flow of length scale L and maximum velocity U-0 in a stably stratified and compressible fluid of constant Brunt-Vaisala frequency N, sound speed c(s) and stratification length H is examined in an inviscid framework. The shear plane of the boundary layer is assumed to be inclined at an angle theta with respect to the vertical direction of stratification. The stability analysis is performed using both numerical and theoretical methods for all the values of theta and Froude number F = U-0/(LN). When non-Boussinesq and compressible effects are negligible (L/H << 1 and U-0/c(s) << 1), the boundary layer flow is found to be unstable for any F as soon as theta not equal 0. Compressible and non-Boussinesq effects are considered in the strongly stratified limit: they are shown to have no influence on the stability properties of an inclined boundary layer (when F/sin theta << 1). In this limit, the instability is associated with the emission of internal-acoustic waves.