A Diagnostic Barotropic Finite-Element Ocean Circulation Model

Abstract

The finite-element method possesses many advantages over more traditional numerical techniques used to solve systems of differential equations. These advantages include a number of conservation properties and a natural treatment of boundary conditions. The method's piecewise nature makes it useful when dealing with irregular domains and similarly when using variable horizontal resolution. To take advantage of these properties, a finite-element representation of the linearized, steady-state, barotropic potential vorticity equation is developed. The Stommel problem is used as an initial test for the model. A fourth-order eddy viscosity term is then added, and the resulting problem is solved in both simply and multiply connected domains under both slip and no-slip boundary conditions. The beta-plane assumption is then relaxed, and the model is reformulated in spherical coordinates. A realistic geography and topography version of this model is also used to examine the barotropic circulation in the North Atlantic Ocean. Results are found to agree very well with those of previous diagnostic calculations. In particular, the Gulf Stream separates at the correct latitude with the inclusion of the JEBAR (joint effect of baroclinicity and relief) term.