Low-dimensional control of the circular cylinder wake

Many wake flows exhibit self-excited flow oscillations which are sustained by the flow itself and are not caused by amplification of external noise. The archetypal example of a self-excited wake flow is the low Reynolds number flow past a circular cylinder. This flow exhibits self-sustained periodic vortex shedding above a critical Reynolds number. In general, control of such hows requires stabilization of many globally unstable modes; the present work describes a multiple-sensor control strategy for the cylinder wake which succeeds in controlling a simplified wake model at a Reynolds number above that at which single-sensor schemes fail. Representation of the flow field by a finite set of coherent structures or modes, which are extracted by proper orthogonal decomposition and correspond to the large-scale wake components, allows the efficient design of a closed-loop control algorithm. A neural network is used to furnish an empirical prediction of the modal response of the wake to external control forcing. This model avoids the need for explicit representation of the control actuator-wake interaction. Additionally, the neural network structure of the model allows the design of a robust nonlinear control algorithm. Furthermore the controller does not necessarily require velocity field information, but can control the wake using other quantites (for example flow visualization pictures) which characterize the structure of the velocity field. Successful control of a simplified cylinder wake model is used to demonstrate the feasibility of the low-dimensional control strategy.