Optimal control of Tollmien-Schlichting waves in a developing boundary layer

Optimal control theory is used to determine the wall transpiration (unstead y blowing/suction) with zero net mass flux capable of attenuating Tollmien- Schlichting waves in a spatially developing boundary layer. The flow state is determined from the parabolized stability equations, in a linear setting . An appropriate cost functional is introduced and minimized iteratively by the numerical solution of the equations for the state and the dual state, coupled via transfer and optimality conditions. Central to the control is t he determination of the wall Green's function expressing the receptivity of the flow to wall inhomogeneities. The optimal wall velocity is obtained in few iterations and a reduction of several orders of magnitude in output di sturbance energy is demonstrated, as compared to the uncontrolled case, for control laws operating both over the whole wall length and over a finite s trip. Finally, white noise disturbances are applied to the optimal wall vel ocities already determined, to assess the influence of an imperfectly opera ting controller on the final result, and to decide on the practical feasibi lity of the approach. (C) 2001 American Institute of Physics.