Effects of large amplitude periodic perturbationson boundary layer separation

It is known experimentally that finite-amplitude periodic excitations of a boundary layer may lead to a delay of separation or even to a reattachment of the initially separated flow. The transition from separated states to reattached ones is described by a curve in the perturbation frequency-amplitude parametric space. In this work we study a minimal model – a boundary layer on a flat plate subject to large amplitude excitations – to identify these transition curves and to understand the underlying physical mechanisms. Two settings are considered: when a finite-amplitude traveling-wave perturbations enter the boundary layer (a) at the leading edge and (b) through the free-stream flow. A discrete stream-function method, explicitly enforcing mass conservation, was applied to the incompressible Navier-Stokes system of equations on a staggered grid with second-order spatial and time numerical approximations. Simulations show, in particular, that perturbations in setting (a) lead to separation at lower amplitudes compared to setting (b). We also identified the conditions under which the boundary layer is reattached at large amplitudes of excitations and offer a theoretical explanation for the observed behavior.