The compressible-boundary-layer stability can be considerably influenced by base flow distortion. The distortion may originate from perturbations of flow parameters, such as the Mach number. In this paper, sensitivities of the boundary layer stability to certain flow parameters are derived analytically by utilizing the homotopy analysis (with codes shared), in conjunction with a direct-adjoint stability theory. The sensitivities can be categorized according to the routes the distortion evolves. Route I is that parameters distort the base flow (Sensitivity A), which, in turn, affect the eigenvalue of the linear stability equation (Sensitivity B). Route II gives rise to the effects of flow parameters onto eigenvalues caused by direct perturbation of the linear operators (Sensitivity C). Results indicate that Sensitivity A is characterized by the only peak found on the sensitivity profile that corresponds to the maximum gradient of base flow; for Sensitivity B, production terms, e.g., the mean-shear terms, are found to be significant, while for Sensitivity C, which is rarely discussed in existing literature, the pressure gradient terms in the momentum equations are dominant in affecting the stability via route II. Furthermore, route II can be more significant than route I. Having examined the variation of the mean shear gradient, d(ρ¯du¯/dy)/dy, near the critical layer yc, it is proven that the sensitivity of the eigenvalue to the velocity or temperature distortion is negative at yc under certain assumptions, particularly for the temperature-relevant sensitivity that has hardly been discussed before.

This paper investigates a Mach 6 oblique breakdown via direct numerical simulation in conjunction with stability and quadrant analyses. Particular emphasis is placed on, first, the heat transfer and mean flow distortion in the near-wall and outer transitional boundary layer, and, second, the flow events that are responsible for the production of the Reynolds stress. Energy budget reveals that enhancement of viscous dissipation due to mean flow distortion dominates the heat transfer overshoot, while the dissipation due to fluctuations is less but not negligible. Downstream of the location of the peak mean heat flux, the wall temperature gradient (nondimensionalized by the freestream temperature and local boundary layer thickness) varies little, owing to the occurrence of breakdown and the establishment of self-similarity. Renormalized by the boundary layer thickness, a new correlation of the Stanton number shows no overshoot or difference between the original overshoot region and the turbulent region, which indicates the possibility of similarity once breakdown has occurred. Because of successive modal growth and nonlinear saturation, the contributions of the primary oblique mode, streak mode, and a superharmonic to the outer advective heat transfer are found to compete near the location of the peak heat flux. Quadrant analysis highlights the broadly distributed joint probability density function (PDF) of the fluctuating velocities during transition, which results in overproduction of the Reynolds stress. The flow event Q2 (ejection) overtakes Q4 (sweep) in the transitional region, mainly owing to the primary mode, while the two events become attenuated when transition is complete.

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