Nonlinear Evolution of Azimuthally Compact Crossflow-Vortex Packet over a Yawed Cone

Hypersonic boundary-layer flows over a circular cone at moderate incidence angle can support strong crossflow instability and, therefore, a likely scenario for laminar-turbulent transition in such flows corresponds to rapid amplification of high-frequency secondary instabilities sustained by finite amplitude stationary crossflow vortices. Direct numerical simulations (DNS) are used to investigate the nonlinear evolution of azimuthally compact crossflow vortex packets over a 7-degree half-angle, yawed circular cone in a Mach 6 free stream. Simulation results indicate that the azimuthal distribution of forcing has a strong influence on the stationary crossflow amplitudes; however, the vortex trajectories are nearly the same for both periodic and localized roughness height distributions. The frequency range, mode shapes, and amplification characteristics of strongly amplified secondary instabilities in the DNS are found to overlap with the predictions of secondary instability theory. The DNS computations also provide valuable insights toward the application of planar, partial-differential-equation based eigenvalue analysis to spanwise inhomogeneous, fully three-dimensional, crossflow-dominated flow configurations.