Optimal open-loop control of the recirculation length in the wake of a cylinder

We consider steady equilibrium solution of the 2-D Navier-Stokes equations describing the flow around a circular cylinder. It is well known that, for moderate Reynolds numbers, the recirculation length is an increasing function of the Reynolds number. We first express the recirculation length as a cost-functional and then use a Lagrangian-based optimization procedure to compute the linear sensitivity of the recirculation length with respect to base flow modifications, localized bulk point forces and blowing and suction at the cylinder wall. The results are compared to nonlinear steady-state computations. The influence of a shortened or increased recirculation on the stability of the flow above threshold (Re=47) is finally discussed.