Optimal disturbances in the supersonic boundary layer past a sharp cone

Optimal disturbances for the supersonic flow past a sharp cone are computed in order to assess the effects due to flow divergence. This geometry is chosen because previously published studies on compressible optimal perturbations for flat plate and sphere did not allow to discriminate the influence of divergence alone, as many factors characterized the growth of disturbances on the sphere (flow divergence, centrifugal forces and dependence of the edge parameters on the local Mach number). Flow-divergence effects result in the presence of an optimal distance from the cone tip for which the optimal gain is the largest possible, showing that divergence effects are stronger in the proximity of the cone tip. By properly rescaling the gain, wavenumber and streamwise coordinate due to the fact that the boundary layer on the sharp cone is √3 thinner than the one over the flat plate, it is found that both the gain and the wavenumber compare fairly well. Moreover, results for the sharp cone collapse into those for the flat plate when the initial location for the computation tends to the final one and when the azimuthal wavenumber is very large. Results show also that a cold wall enhances transient growth.