ON THE NUMERICAL INTEGRATION OF THE PRIMITIVE EQUATIONS OF MOTION FOR BAROCLINIC FLOW IN A CLOSED REGION

Abstract

This paper considers the problem of numerically integrating the primitive equations corresponding to B 2-level model of the atmosphere bounded by two zonal walls on a spherical earth. Inertio-gravitational motions of the external type are filtered a priori; for such a constraint it is possible to define a stream function corresponding to the vertically integrated motions. A system of integration is developed for initial conditions which specify the shear wind vector, the specific volume, and the vorticity of the vertically integrated flow. Methods for reducing truncation error and for increasing the rate of convergence of the elliptic part are discussed. The question of boundary conditions is discussed at length. It is shown that the usual central difference methods yield independent solutions at alternate points, thus providing a source of computational instability to which the primitive equations are particularly sensitive. The solutions may be made compatible by suitable computational boundary conditions which can be deduced as sufficient conditions for insuring that the numerical solutions possess exact integrals. The application of these considerations to viscous flow is also discussed.