A general pressure gradient formulation for ocean models. Part II: Energy,momentum, and bottom torque consistency

A new formulation of the pressure gradient force for use in models with top ography-following coordinates is proposed and diagnostically analyzed in Pa rt I. Here, iris shown that important properties of the continuous equation s 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 chang es, 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 longterm integral stability. Tw o typical geometries, an isolated tall seamount and an unforced basin with sloping boundaries, are considered for the special case of no external forc ing and horizontal isopycnals to test numerical accuracy. These test proble ms confirm that the proposed schemes yield accurate approximations to the p ressure gradient force. Integral consistency conditions are verified and th e energetics of the "advective elimination" of the pressure gradient error (Mellor el 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 press ure 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 r ealistic meandering western boundary current is well developed with detache d cold cyclonic and warm anticyclonic eddies as it extends across the basin . In addition, the results with topography show earlier separation and enha nced transport in the western boundary currents due to the bottom pressure torque.