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 entropylayer 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. Disturbances in the entropy-layer interact non-linearly with each other through the oblique breakdown mechanism, inducing streamwise streaks in the boundary-layer. These undergo further destabilization downstream leading to turbulence onset. Different mechanisms of interest are extracted with modal decomposition techniques best suited for each. Dynamic mode decomposition (DMD) reveals sinuous subharmonic oscillations induced by the entropic-disturbances as the dominant streak instability mechanism. On the other hand, spectral proper orthogonal decomposition (SPOD) elicits the slanted hook -shaped structures in the temperature perturbations, which are attributable to the Orr like-mechanism in the entropy-layer. Furthermore, cross-bispectral mode decomposition (CBMD) shows that the temperature perturbations amplify on the crests of the low-speed streaks in the entropy-layer and generates disturbances through triadic interactions. These newer disturbances further interact, resulting in the transfer of perturbation energy into the boundary-layer. This eventually leads to spanwise homogenization and near-wall streak generation, reflecting late nonlinear stages of transition. Towards the end of 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.