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 U₀ in a stably stratified and compressible fluid of constant Brunt–Väisälä frequency N , sound speed cₛ 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 θ with respect to the vertical direction of stratification. The stability analysis is performed using both numerical and theoretical methods for all the values of θ and Froude number F= U₀ / (LN) . When non-Boussinesq and compressible effects are negligible ( L/ H 1 and U₀ / cₛ 1 ), the boundary layer flow is found to be unstable for any F as soon as θ = 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 θ 1 ). In this limit, the instability is associated with the emission of internal-acoustic waves.