First-mode-induced nonlinear breakdown in a hypersonic boundary layer
The mechanisms underlying transition of a Mach 6 flat plate boundary layer with adiabatic wall conditions are explored with Direct Numerical Simulations (DNS) using a high-order hybrid upwind-centered method. The forcing employed is obtained from linear stability theory (LST), which is used to identify Tollmien–Schlichting (T-S) or first-mode instability in the hypersonic boundary layer (HBL). At small amplitudes, the DNS displays linear growth, and matches those obtained from LST, including the spanwise structure of the most amplified oblique wave in the first-mode as well as the spreading angle of the turbulent wedge induced by the oblique wave under transitional scenarios. The main emphasis of the paper is on the nonlinear breakdown process, obtained by forcing the DNS at a higher amplitude so that the linear amplification region yields to nonlinear saturation and breakdown of the first-mode. The oblique waves are seen to first evolve into lambda-vortices with peak perturbation amplitudes around the generalized inflection point (GIP) of the HBL. The fundamental forcing frequency gives rise to progressive superharmonics: These first appear within the foot region of the lambda-vortices, and spread in the spanwise direction into the ring-shaped vortices that develop along the symmetry plane of the oblique waves. Transition and loss of symmetry is initiated upon saturation of the fundamental and harmonics. A modal analysis used to extract each frequency component yields further insight into streak-formation in these modes, resulting in localized regions of peak skin friction near the transition location. The near-wall boundary layer in the transitional zone displays coherent spanwise structures, which represent compressed regions of fluid and induce high gradients over the surface. Towards the end of the breakdown region, the flow displays a broadband spectrum, and the anticipated inertial sub-range appears inside the boundary layer, as a prelude to self-similar turbulent boundary layer evolution.
Computers & Fluids