Low-dimensional Modeling and Dynamics of a Driven Cavity Flow: on the Modeling and Control of Vortex Breakdown in a Closed Cavity

The flow in a lid driven cavity with a rotating rod has been studied by numerical simulations. The flow is suitable for studying vortex breaksdown. Breakdowns bubbles of the steady flow and unsteady flow can be controlled by the rotation of the rod. Transition of the flow was studied and the frequencies appearing in the time varying flow were determined by applying a Fast Fourier Transform (FFT). By applying Proper Orthogonal Decomposition (POD) and the newly developed Sequential POD (SPOD), one can extract a limited amount of data characterizing the flow. The modes resulting from the decomposition form a basis in the phase space on which a Galerkin projection of the equations of motion can be performed. One obtains a low-dimensional model consisting of a reduced set of Ordinary Differential Equations (ODE). This set of equations has been used for analyzing bifurcations. A method has been developed for contructing low- dimensional models with more than one free parameter. The resulting model allows one of the free parameters to appear in the inhomogeneous boundary conditions without the addition of any constraints.