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

Abstract

AbstractThe three-dimensional stability of an inflection-free boundary layer flow of length scale$L$and maximum velocity${U}_{0} $in a stably stratified and compressible fluid of constant Brunt–Väisälä frequency$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\ll 1$and${U}_{0} / {c}_{s} \ll 1$), the boundary layer flow is found to be unstable for any$F$as soon as$\theta \not = 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 \ll 1$). In this limit, the instability is associated with the emission of internal-acoustic waves.