Variational model for lake circulation.

Steady-state, wind induced circulation in a large lake is considered. The effects of surface wind stress, different bottom topographies, rotation of the earth, bottom friction, and interior islands are included in the analysis, and the coefficient of eddy viscosity is assumed to decrease parabolically with depth. The vorticity equation is solved by the finite element method using different approaches and the results are compared with those obtained by the finite difference method. The solution of the vorticity equation, which is of the elliptic type, by the finite element method shows that approximate variational principles can be developed for non-self-adjoint problems if the initial assumptions are forced to be consistent with the finite element shape function model adopted for the analysis. The versatility and high efficiency of the finite element method in handling complicated boundary conditions is demonstrated by the solution of a physical problem in a multiple connected domain. (A) .