Instability and Transition Induced by Distributed Roughness in High-Speed Boundary Layer

This study investigated distributed-roughness-induced instability and boundary-layer transition in high-speed boundary layers using direct numerical simulation, BiGlobal linear stability analysis, and plane-marching parabolized stability equations. Sinusoidal roughness patterns with different wavelengths and freestream Mach numbers were examined. Despite changes in the geometric parameters of the roughness, two types of counter-rotating streamwise vortex pairs were consistently observed to distort the local boundary layer and generate high-strength shear layers. The stronger vortex pair develops from the vortices passing through the lateral portion of the last row of sinusoidal humps, while the weaker pair comprises the two vortices shedding from the center of the sinusoidal humps. At Mach 3.5, the roughness patch with a smaller sinusoidal wavelength can induce earlier transition and a greater variety of instability modes. The symmetric mode associated with the strong lateral vortex pair is consistently the dominant instability source in the transition process. Conversely, the most unstable mode around the weak center vortex pair changes from symmetric to asymmetric as the sinusoidal wavelength decreases. As the Mach number increases to 6.0, two types of antisymmetric modes around each vortex pair become dominant; however, they have lower growth rates and cannot induce transition.