Dynamical control for capturing vortices near bluff bodies

We investigate the vortex dynamics near a translating and rotating circular cylinder in a two-dimensional uniform viscous flow. In analogy with the point-vortex and Eulerian dynamics, there is an interesting scattering effect of vortices approaching the cylinder from far upstream. The vortex--boundary-layer interaction plays an important role in the scattering processes. We implement a modified Ott, Grebogi, and Yorke chaos control scheme, based on a low-dimensional Hamiltonian model of the flow, to capture and stabilize a concentrated vortex around the cylinder. This point-vortex-based control model can successfully be applied in a viscous flow when control is actuated by uniformly rotating the cylinder and actively changing the background flow velocity far from the body. We demonstrate that such a control mechanism can simultaneously control the vortex dynamics, and also suppress the vortex shedding. An analysis of the vortex--boundary-layer interaction is presented to explain the absence of vortex shedding during control simulations.