T he turbulent viscous and inviscid flow over a wavy wall with the freestream speed of transonic and supersonic range is studied by solving the Navier-Stokes and Euler equations. In the inviscid computation, the streamwise flow development through a series of shock waves and entropy production is investigate in depth. In the case of the supersonic freestream, the isentropy contours of the horse-shoe form as well as the staircase form are found. In the turbulent viscous computation, Beam-Warming-Steger method is applied to the full Navier-Stokes equations and thin later Navier-Stokes equations with Baldwin-Lomax turbulent modeling. Some numerical experiments are carried out to confirm the applicability of thin layer Navier-Stokes equations and Baldwin-Lomax turbulent modeling on the curved surface. The variations of flow characteristics due to the variation of freestream Mach number, boundary layer thickness, and wavy wall amplitude are investigated. And the progressive flow development due to the multiple shocks, their interaction with the boundary layer are investigated. The separation patterns are also investigated for various wavy wall amplitude.
