Topological flow structures in an L-shaped cavity with horizontal motion of the upper lid

The flow patterns in a steady, viscous L-shaped cavity are investigated using both analytic solutions combined with methods from nonlinear dynamical systems and numerically using the finite element method. A boundary value problem is formulated for the case of Stokes flow, which is solved analytically, ψ, expressed as an infinite series of eigenfunctions which depend on h1 and h2 which are related to the heights of the L-shaped domain. The (h1,h2) control space diagram is constructed for exhibiting the mechanism by which new eddies are obtained in the cavity.