Theoretical and Computational Study of the Wake Control Problem

In the present paper we are concerned with the problem of active drag minimization in the incompressible wake flow generated by a circular cylinder with turbulent Reynolds number. The objectives of the work are twofold: first, we show evidence coming from numerical simulations that a properly designed open-loop algorithm is indeed capable of performing effective flow control resulting in significant drag reduction, and then, with this motivation, we outline a rigorous feedback algorithm based on Optimal Control Theory. In both cases control is performed by rotary motion of the circular cylinder whose boundary we denote Γ0. The flow domain Ω extends to infinity. By an open-loop algorithm we mean a scheme in which the control is determined a priori, without any reference to the instantaneous flow field information and/or its history. Because of computational limitations, throughout the paper we will study two-dimensional (2D) flows only.