Nonlinear transition mechanism on a blunt cone at Mach 6: Oblique breakdown

Direct numerical simulations (DNS) were carried out to investigate laminar-turbulent transition for a blunt (right) cone (half-angle) at Mach 5.9 and zero angle of attack. First, (linear) stability calculations were carried out by employing a high-order Navier-Stokes solver and using very small disturbance amplitudes in order to capture the linear disturbance development. Contrary to standard linear stability theory (LST) results, these investigations revealed a strong 'linear' instability in the entropy-layer region for a very short downstream distance for oblique disturbance waves with spatial growth rates far exceeding those of second-mode disturbances. This linear instability behaviour was not captured with conventional LST and/or the parabolized stability equations (PSE). Secondly, a nonlinear breakdown simulation was performed using high-fidelity DNS. The DNS results showed that linearly unstable oblique disturbance waves, when excited with large enough amplitudes, lead to a rapid breakdown and complete laminar-turbulent transition in the entropy layer just upstream of the second-mode instability region.