A Nonlinear Control Strategy for Finite-amplitude Perturbations in a Boundary-layer Flow

AbstractThe present work describes an optimal control strategy, based on the full Navier-Stokes equations, aiming at hampering the rapid growth of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow. An optimization strategy is used to find the blowing and suction control law at the wall providing the maximum damping of the perturbation energy at a given target time. Two optimally-growing finite-amplitude initial perturbations have been employed to initialize the flow. The nonlinear control procedure can drive such perturbations back to the laminar state, provided that the target time of the minimisation and the region in which the blowing and suction is applied have been suitably chosen. On the other hand, an equivalent control procedure based on the linearized Navier-Stokes equations is much less effective, being not able to lead the flow to the laminar state when finite-amplitude disturbances are considered