Numerical investigation of unsteady plane wakes at supersonic speeds

The two-dimensional stability behavior of the supersonic plane wake at transitional Reynolds numbers is investigated using direct numerical simulations. A spatial model is used, with the domain of interest placed around the base of a twodimensional body aligned with the flow. The complete two-dimensional compressible Navier-Stokes equations are solved in a Cartesian coordinate system. They are discretized spatially using fourthorder split finite differences. For time integration, a fourth-order Runge-Kutta scheme is employed. Several free-stream boundary conditions were investigated. The flow at two free-stream Mach numbers was considered. At M = 2.46, no absolute instability was found at Reynolds numbers (based on base thickness) up to Re = 100,000. However, sinuous disturbances produce an oscillation in the recirculation region which decays exponentially in time, with the decay rate decreasing with increasing Reynolds number. At M - 1.20 and Re = 4,000 the flow was found to be absolutely unstable, with disturbances growing exponentially until a finite amplitude periodic state is reached. As a consequence, the recirculation region oscillates strongly, and a Karman vortex street is formed downstream. The mean flow properties of this state differ significantly from a steady flow computation.