Two-dimensional direct numerical simulation (DNS) of stabilization of supersonic boundary layers over a shallow grooved wavy plate at Mach=5.9 is carried out. Numerical experiments are conducted for propagation of disturbances generated by a suction-blowing actuator placed on the wall. Numerical data obtained for a flat plate are consistent with the linear stability theory (LST) and stability experiments in the "Transit-M" wind tunnel of the Institute of Theoretical and Applied Mechanics. It is

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... shown that high-frequency forcing excites unstable disturbances in the flat-plate boundary layer relevant to the second-mode instability. The wavy wall leads to damping of these disturbances in a wide frequency band of the forcing.