Numerical investigation of streamwise vortex instabilities over an inclined cone at Mach 6: Modal excitation, evolution, and transition

This paper investigates the instability of streamwise vortices in the boundary layer of a flow field, focusing on modal excitation, the linear and nonlinear evolution of disturbances, and the evolution characteristics of skin friction and wall heat flux during the transition from laminar to turbulent flow. We conduct Bi-global stability analysis and direct numerical simulations of an inclined blunt cone with a 6° angle-of-attack, freestream Mach number of 6, and unit Reynolds number of 1.0 × 10 7 /m. Finite-amplitude disturbances introduced at the inlet consistently evolve into unstable outer modes downstream, ultimately triggering the transition of streamwise vortices. The receptivity coefficient of the modal disturbance excited by random perturbations is directly proportional to the boundary layer shear intensity in regions associated with streamwise vortices. A larger shear intensity corresponds to a greater initial disturbance amplitude. During modal linear evolution, inner/outer modes propagate downstream along the inward/outward vortices and gradually move away from the wall, reducing their ability to disturb the near-wall boundary layer. When the modal perturbations enter the nonlinear evolution stage and the amplitude of the Mean Flow Distortion (MFD) exceeds that of the fundamental disturbances, the disturbance waves diffuse toward the near-wall region, resulting in “transition stratification”, whereby the outer region of the streamwise vortex transitions while the perturbations in the near-wall region exhibit linear amplification. A negative MFD correction within the near-wall boundary layer reduces the local velocity and temperature gradients, leading to a local undershoot in wall friction/heat flux during the post-transition stage. This significantly influences the evolution of the wall heat flux/friction characteristics. Consequently, the heat flux uplift position in the streamwise vortex region significantly lags that in the crossflow region, resulting in the delayed V-shaped transition front observed in wind tunnel experiments.