Spatial evolution of a monochromatically forced flat-plate wake

Nonlinear disturbance development in a two-dimensional, incompressible, spatially developing wake behind a thin flat plate aligned parallel to a uniform freestream is investigated by direct numerical integration of the Navier-Stokes equations. For the numerical integration, finite difference methods together with an alternating direction implicit/Adams-Bashforth time integration scheme are employed. The wake is harmonically forced at the inflow boundary at the frequency of maximum amplification predicted by linear stability theory. The response to this monochromatic forcing includes a disturbance component at the forcing frequency that grows very rapidly before saturating a short distance downstream. This saturation can be predicted qualitatively from a linear stability analysis of the distorted mean flow. Farther downstream, the disturbance energy is concentrated in the fundamental disturbance, the second harmonic, and the mean-flow distortion component. At large amplitudes, a Kármán vortex street forms. Variations in forcing strength do not alter the qualitative behavior of the forced wake. The results of these simulations compare well with both linear stability theory and experimental measurements.