A numerical investigation of stably stratified, wind driven cavity flow by the finite element method

A model is presented to analyze steady state, stably stratified, wind driven circulation in cavities representing idealized lakes. A continuous but unknown density field is assumed. The density is stipulated on the surface and bottom of a cavity representing the minimum and maximum density difference. Viscosity, density gradient, diffusivity, and cavity length are represented by the Reynolds, Grashof, and Prandtl numbers, and the aspect ratio. Deep, square, and shallow cavities are analyzed for flow processes dominated by situations ranging from weak diffusion to strong nonlinear advection. In cases with strongly stratified flow or weak diffusion, two closed circulation cells form from the inability of the flow field to overcome density gradients. The velocity of the top cell is an order of magnitude more intense than the larger bottom cell. The circulation of the bottom cell is in the opposite direction to and driven by the surface cell. The results indicate the Reynolds, Grashof, and Prandtl numbers at which such cells first appear.