Secondary instability of Mack mode disturbances in hypersonic boundary layers over micro-porous surface

In laminar hypersonic boundary layers, it is known that secondary instability plays a crucial role in transition to turbulence. The secondary instability usually includes the fundamental mode, the subharmonic mode, and the detuned mode. Considerable research exists on the secondary instability mechanism in hypersonic boundary layers with the smooth wall condition. The topic of using micro-porous surfaces for disturbance stabilization has recently drawn interest. The stabilization and, thus, a possible delay in the transition arise due to a reduction in the growth rate of the primary Mack mode by the porous surface. This paper focuses on investigating whether the secondary instability mechanism of Mack modes can also be affected by a surface porosity condition. It is known that the primary Mack mode linear disturbances are changed significantly on the porous surface, and how it subsequently influences the secondary instability of the modified time varying basic flow is our concern. The analysis demonstrates that on the porous surface, as the amplitude of the primary Mack mode increases, the fundamental mode is not stable. Instead, the fundamental mode amplifies rapidly with increasing primary amplitudes. At larger secondary instability spanwise wavenumbers, when the primary amplitude exceeds a certain threshold value, the fundamental modes surpass the subharmonic modes and dominate the secondary instability. However, when the spanwise wavenumber is relatively small, especially at the spanwise wavenumber corresponding to the maximum growth rate of the subharmonic mode, the fundamental modes are weakened and lose their dominant position. We find that corresponding to different amplitudes of primary Mack mode disturbances affected by the porosity parameters, there are no strongly preferred interaction modes that dominate the secondary instability; this contrasts with smooth wall findings. We further find that the larger the pore size or porosity, the more severe the suppression of the fundamental mode.