A General Pressure Gradient Formulation for Ocean Models. Part II: Energy, Momentum, and Bottom Torque Consistency

Abstract

A new formulation of the pressure gradient force for use in models with topography-following coordinates is proposed and diagnostically analyzed in Part I. Here, it is shown that important properties of the continuous equations are retained by the resulting numerical schemes, and their performance in prognostic simulations is examined. Numerical consistency is investigated with respect to global energy conservation, depth-integrated momentum changes, and the representation of the bottom pressure torque. The performances of the numerical schemes are tested in prognostic integrations of an ocean model to demonstrate numerical accuracy and long-term integral stability. Two typical geometries, an isolated tall seamount and an unforced basin with sloping boundaries, are considered for the special case of no external forcing and horizontal isopycnals to test numerical accuracy. These test problems confirm that the proposed schemes yield accurate approximations to the pressure gradient force. Integral consistency conditions are verified and the energetics of the ?advective elimination? of the pressure gradient error (Mellor et al) is considered. A large-scale wind-driven basin with and without topography is used to test the model?s long-term integral performance and the effects of bottom pressure torque on the transport in western boundary currents. Integrations are carried out for 10 years in each case and results show that the schemes are stable, and the steep topography causes no obvious numerical problems. A realistic meandering western boundary current is well developed with detached cold cyclonic and warm anticyclonic eddies as it extends across the basin. In addition, the results with topography show earlier separation and enhanced transport in the western boundary currents due to the bottom pressure torque.