Dynamics and control of vortices in two-dimensional flows with a circular boundary

A detailed theoretical and numerical investigation is presented on the interaction of vortical structures with a circular cylinder embedded in a two-dimensional flow. A control mechanism is developed which can successfully modify the vortex dynamics, and actively stabilize a vortex around a cylinder in a viscous flow.;Firstly, we investigate the interaction of a vortex with an oscillating cylinder in an inviscid flow using a point-vortex model. The dynamics can be regarded as a scattering process and recent advances from the theory of chaotic scattering are used to characterize the vortex-cylinder interaction. We show there exists a chaotic set around the cylinder responsible for the finite-time trapping of the vortices. The average trapping time, the fractal dimension of the chaotic set, and the average Lyapunov exponent can be obtained from a multifractal analysis of the singularities in the time-delay function.;Next, we study the vortex dynamics in a viscous flow around a uniformly translating and rotating cylinder. We show that the vortex dynamics is strongly influenced by the vortex boundary layer interaction. For a non-rotating cylinder, a vortex approaching from upstream cannot penetrate the wake, and there exists a minimum distance for which the vortex can approach the cylinder. For a rotating cylinder, the vortex dynamics shows similarities with the corresponding point-vortex model, including a separatrix-like structure. For large rotation speeds we observe long-time trapping events.;To modify the vortex dynamics around a cylinder, we develop a control algorithm based on a simple point-vortex model of the flow. The control is actuated by uniformly rotating the cylinder and simultaneously actively changing the uniform background flow velocity. This procedure can simultaneously control the vortex and stabilize the boundary layer. A numerical and theoretical analysis of the boundary layer is also presented to explain the boundary layer stability.;Finally, as a possible application of the control scheme for an experimental plasma system, the problem of three point-vortices inside a cylindrical geometry is considered. As a main result, we develop a chaos control algorithm that can be applied for higher-dimensional systems.