Optimal control of cylinder wake flow by electro-magnetic force based on adjoint flow field

A nonlinear adjoint-based optimal control approach of cylinder wake flow by using electro-magnetic forcing has been proposed and investigated numerically in the paper. A cost functional representing the balance between the enstrophy Ω2 and the interaction parameter N has been developed, and its corresponding adjoint equations have been derived. The sensitivity of the cost functional is found to be a simple function of the adjoint stream function in the adjoint field. Under the action of optimal force, N(t), the flow separation is suppressed successfully, the oscillations of drag and lift disappear and the total drag coefficient decreases dramatically. Furthermore, the global enstrophy is proved to be equal to the total squared strain during the control, which validates the conservation rule of Okubo-Weiss function.