Direct numerical simulation of complete transition to turbulence via first- and second-mode oblique breakdown at a high-speed boundary layer

Complete transition to turbulence via first- and second-mode oblique breakdown in a high-speed boundary layer at Mach 4.5 is studied by direct numerical simulations (DNS) and linear stability theory (LST). The initial frequency and spanwise wavenumbers for both types of oblique breakdown are determined from LST. Then, DNS is employed to study the main features of the two oblique breakdown types in detail, which has rarely been discussed in previous studies. This includes the main flow structures and evolution of various modes during the linear, nonlinear, and breakdown stages, and both different and similar features for the two oblique breakdown types are summarized. Compared with only one type of low-speed streak existing for first-mode oblique breakdown, two types occur in the second-mode oblique breakdown, and the generation mechanism, evolution process, and role of the low-speed streaks are studied. Subsequently, the generation mechanism of both the heat transfer and skin-friction overshoot during both oblique breakdowns is illustrated with emphasis on the heat transfer overshoot for the second mode, which occurs at the laminar stage. Finally, both types of oblique breakdown are the likely path to a fully developed turbulent flow, although the unstable region for the second-mode oblique waves is short and for the first-mode oblique waves is amplified slowly.