Algebraic growth in a Blasius boundary layer: optimal and robust control by mean suction in the nonlinear regime

Abstract

Optimal and robust control for the three-dimensional algebraically growing instability of a Blasius boundary layer is studied in the nonlinear regime. First, adjoint-based optimization is used to determine an optimal control in the form of a spanwise-uniform wall suction that attenuates the transient growth of a given initial disturbance, chosen to be the optimal perturbation of the uncontrolled flow. Secondly, a robust control is sought and computed simultaneously with the most disrupting initial perturbation for the controlled flow itself. Results for both optimal and robust control show that the optimal suction velocity peaks near the leading edge. In the robust-control case, however, the peak value is smaller, located farther downstream from the leading edge, and the suction profile is much less dependent on the control energy than in the optimal-control case.