Direct numerical simulation (DNS) method was performed on compressible boundary layer on flat plate with a local hump

and linear stability theory (LST) was applied to conduct the stability analysis based on the mean flow with Mach number of 4.5. The interactions between the disturbances with different frequencies and the local hump with various heights were simulated by solving the perturbation equations

and the effect of local hump on the stability was characterized by a transmission coefficient. The results show that

the local hump affectes the mean flow locally when the height of the local hump is smaller than 0.2 times of the boundary layer thickness. Local hump destabilizes the disturbances with frequency smaller than the most unstable disturbance frequency

and stabilizes the disturbances with frequency larger than the most unstable disturbance frequency

wherein the most unstable disturbance frequency is the frequency of the most unstable second modal disturbance of the boundary layer on flat plate at the center position of the local hump. Transmission coefficient quantitatively describes the effect of local hump on the instability. The local hump with height 0.2 times of the boundary layer thickness enables the correction of the N of e-N method 0.8

about 10% of N at the transition location

which can not be neglected in the transition prediction process.