A COMPARISON OF DIFFERENTIAL-SYSTEMS AND NUMERICAL-METHODS FOR THE COMPUTATION OF SMOOTH OCEANOGRAPHIC FLOWS

Recently, a new system of equations which can be used to describe accurately approximately hydrostatic and incompressible oceanographic flows has been developed. The 'approximate system' is derived by slowing down the speed of the fast waves instead of increasing their speed to infinity as in the primitive equations. Whereas the initial-boundary value problem for the primitive equations is always ill posed, boundary conditions can be chosen for the approximate system so that the initial-boundary value problem is well posed. The new system is not restricted to the mid-latitudes and its continuum error is an order of magnitude less than that of the quasi-geostrophic system. In this paper a model based on the proper mathematical limit of the approximate system, the 'reduced system', is compared with models based on the primitive and quasi-geostrophic systems for a fixed grid and numerical method. This illuminates some of the advantages of the reduced system compared with the traditional systems. A series of reduced models based on different numerical methods are then compared in terms of their accuracy and efficiency.