Investigation of influence of local cooling/heating on nonlinear instability of high-speed boundary layer with direct numerical simulations

The influence of local cooling/heating on two types of nonlinear instabilities of the high-speed boundary layer, namely, the First and Second Mode Oblique Breakdown (FMOB and SMOB), is studied using direct numerical simulations. Local cooling and heating are performed at the weak and strong nonlinear stages of the two types of nonlinear instabilities. It is found that for the FMOB, local cooling at the weak nonlinear region will suppress the increase of the fundamental mode, leading to transition delay. Opposite to local cooling, local heating at the weak nonlinear region of the FMOB will promote the growth of the fundamental mode, resulting in the occurrence of more upstream transition onset. However, if local cooling and heating are performed at the strong nonlinear region, the influence of both local cooling and heating on the FMOB can be neglected. Remarkably, both local heating and cooling can delay the SMOB for different mechanisms. Performing local cooling at the weak nonlinear region of the SMOB, the low amplitude of higher spanwise wavenumber steady mode caused by local cooling lies behind transition delay. When local cooling is set at the strong nonlinear region, the low amplitude of harmonic modes around the cooling area can cause transition delay. Additionally, local heating will suppress the SMOB for the slowing amplification rate of various modes caused by the local heating at both the weak and strong nonlinear stages of the SMOB.