5. Momentum equation methods

This chapter describes the methods available in MOM for solving the momentum equations. There are two basic approaches: the rigid lid and the free surface. Each approach itself has two different methods: the rigid lid streamfunction, the rigid lid surface pressure, the explicit free surface, and the implicit free surface. Currently, development work is focused on the explicit formulation of the free surface. The other methods essentially remain in their MOM 2 form. Plans are to only support development of the explicit free surface in the future (post Summer 1999). The reasons for this focus can be summarized by the following:

• The rigid lid is less physically complete than the free surface. Most notably, it does not allow for a direct treatment of fresh water fluxes.
• The rigid lid in MOM has not been parallelized, nor are there plans to do so.
• Both the explicit and implicit free surfaces have been parallelized in MOM. The explicit free surface shows enhanced scaling properties over the implicit scheme.
• The explicit free surface has been formulated so that it can be of use for either global climate integrations or limited area models.
• The implicit free surface algorithm is more complex than the explicit free surface.
• As of Summer 1999, the explicit free surface has incorporated the effects of the undulating top cell thickness into the depth dependent equations. Hence, the model is conservative of tracers, including total salt in the presence of fresh water fluxes, as well as momentum.

Each of these points will become more clear in this chapter as well as Chapters 8 and 29.