The receptivity of supersonic boundary layers due to the interaction of a twodimensional acoustic wave with a three-dimensional roughness is numerically investigated over a 5-degree sharp tipped straight cone at a free stream Mach number of 3.5 and a high Reynolds number of 10 6 /inch. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the fifth-order accurate weighted essentially non-oscillatory (WENO) scheme for spatial discretization and

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... g third-order totalvariation-diminishing (TVD) Runge-Kutta scheme for temporal integration. The simulations are performed with different roughness heights and roughness locations. The steady computations with the roughness reveal that the perturbations induced by the roughness remain very close to the wall and do not penetrate to the outer part of the boundary layer. The effects of the roughness persist for about 10 boundary layer thicknesses downstream of each element. The unsteady simulation shows the generation of unstable three-dimensional first mode disturbances within a short distance from the roughness. However, the amplitudes of the instability waves are very small near the neutral point, on the order of 10 -4 compared to the free stream disturbances. The receptivity coefficients due to the roughness elements located very close to the tip are one order of magnitude smaller than those due to the roughness elements located closer to the neutral point.