The role of entropic-instabilities in laminar-turbulent transition on a blunted flat plate

Abstract: The effects of entropic-instabilities on the laminar-turbulent transition dynamics of a blunted flat plate at Mach~$4$ are numerically investigated through linear and nonlinear approaches. Linear wavepacket analysis reveals amplifying oblique first-modes as well as planar and oblique entropy-layer disturbances. The receptivity of entropic-instabilities is found to be largest for actuation seeded in the entropy-layer; the corresponding linear evolution is characterized by an intensification in the wall-normal plane, coupled with streamwise tilting. The transition process that arises from entropy-layer wave interactions via the oblique breakdown mechanism is examined in detail. Oblique entropy-layer disturbances interact non-linearly with each other and induce streamwise streaks in the boundary-layer. These undergo further destabilization downstream, through a combination of lift-up and Orr-like mechanisms, leading to turbulence onset. Sinuous subharmonic oscillations induced by the entropic-disturbances are the dominant streak instabilities. Slanted hook-shaped structures are observed in the temperature perturbations, and are attributed to an Orr-like mechanism in the entropy-layer. Further, temperature perturbations amplify on the crests of the low-speed streaks in the entropy-layer and generate disturbances through triadic interactions. These disturbances aid in the transfer of perturbation energy into the boundary-layer, eventually leading to spanwise homogenization and near-wall streak generation. Towards the end of the breakdown region, spectral broadening accompanied by the appearance of an inertial sub-range in the boundary-layer indicates the approach of the flow towards turbulence.