Unsteady Stratified Circulation in a Cavity

An attempt is made, by introducing empirically defined, depth-dependent expressions for eddy diffusivity and eddy viscosity into the governing equations for two-dimensional behavior, to solve the problem of steady-state stratified flow in a lake subjected to surface shear. The set of four relevant partial differential equations (two momentum equations, mass conservation and the temperature diffusion equation) is transformed to a pair of nonlinear differential equations in the stream function and density. Integral conditions corresponding to the solution of these equations are established through the weighted residual concept, and finite element representations of the integrals are constructed. The resulting system of nonlinear algebraic equations is solved by means of quasilinearization technique. An extensive series of numerical solutions is presented to demonstrate that the results obtained are of the type measured in the analogous field situation of wind-driven stratified lakes.