Direct numerical simulation and the theory of receptivity in a hypersonic boundary layer

Direct numerical simulation of receptivity in a boundary layer over a sharp wedge of half-angle $5.3\text{degrees}$ is carried out with two-dimensional perturbations introduced into the flow by periodic-in-time blowing-suction through a slot. The freestream Mach number is equal to 8. The perturbation flow field downstream from the slot is decomposed into normal modes with the help of the biorthogonal eigenfunction system. Filtered-out amplitudes of two discrete normal modes and of the fast acoustic modes are compared with the linear receptivity problem solution. The examples illustrate how the multimode decomposition technique may serve as a tool for gaining insight into computational results.