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Perturbations of flow control parameters may yield a significant alteration in the boundary layer stability. Based on the previously established parameter-associated sensitivity, the present work derives the optimal minor parameter perturbation analytically under the constraint of base flow energy variation. Specifically, the steady blowing-suction factor and the generalized Hartree parameter are examined at Mach number 4.5 to stabilize the mode S. Good agreement between the linear stability theory calculation, sensitivity theory, and Lagrangian approach is achieved for the optimal parametric state. The optimal state occurs if the contribution of the base velocity distortion has the greatest advantage over the temperature counterpart. Contributions of various physical sources to the growth rate behave similarly and collapse onto one correlation if normalized by the maximum, particularly for the major four: advection, mean shear, base temperature gradient, and pressure gradient. When the parameter perturbation further becomes finite, the optimal state is found on the constraint border of control parameters. Although the favorable pressure gradient and wall suction stabilize the broadband mode S, an unusual opposite tendency may occur for a single-frequency disturbance. In this unusual parametric range, positive contributions of both the major and minor physical sources to the growth rate are promoted. The contributive increase in major and minor sources are attributed to the enhancement of mean shear and viscous effect, respectively. Whether the parametric influence is stabilization or destabilization is intrinsically determined by the sensitivities, and the intermediate process is analyzed. Finally, given the modification to the critical Reynolds number, the input control parameter perturbation is inversely obtained and verified. [ABSTRACT FROM AUTHOR]

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. The 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 lesser but not negligible. Downstream of the location of the peak mean heat flux, the wall temperature gradient (non-dimensionalized 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. In the outer region, enhanced advective heat exchange strongly reshapes the mean temperature profile. 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. From the perspective of fluid motions, quadrant analysis highlights the evenly and broadly distributed joint probability density function (PDF) of the fluctuating velocities during transition, which results in overproduction of the Reynolds stress, while the PDF is concentrated around zero in the turbulent region. The flow event Q2 (ejection) overtakes Q4 (sweep) in the outer boundary layer of the transitional region, mainly owing to the primary mode, while the two events become attenuated and nearly achieve balance when transition is complete. [ABSTRACT FROM AUTHOR]