7.4.1 Bottom stress

At the ocean bottom, there is a stress arising from two terms. The first is a stress associated with variations in the model's resolved bottom topography

$${\bf\tau}_{bottom-resolved} = \rho_{o} \, A \, (\nabla_{h} H) \cdot (\nabla_{h} {\bf u}).$$ (7.52)

For a model with full bottom cells, this term appears as a direct result of discretizing horizontal momentum friction and bottom topography on the velocity cells. For the partial bottom cells discussed in Chapter 26, there are added terms which occur due to variations in the bottom cell thickness. In addition to bottom stress from resolved topography, there is the possibility of adding a parameterized stress which can be used to account for subgrid scale (SGS) effects. MOM assumes this stress to take the aerodynamic form (see equation (4.31))

$${\bf\tau}_{bottom-sgs} \rho_{o} \, C_D\, \vert{\bf u}_h\vert\,{\bf u}_h.$$ = (7.53)

This stress is formally associated with the vertical friction term evaluated at the ocean bottom

$$\rho_{o} \, C_D\, \vert{\bf u}_h\vert\,{\bf u}_h = \kappa_m {\bf u}_z \qquad z= -H(\lambda,\phi).$$ (7.54)

The stress ${\bf\tau}_{bottom-sgs}$ is what the model calls the ``bottom momentum flux.'' The default in MOM is to set C_D to zero, which means that all bottom stress arises from the resolved topography. The introduction of a bottom boundary layer (Chapter 36) in MOM also affects the presence or absence of SGS bottom stress.

Note that the treatment of the ocean bottom is identical in both the rigid lid and free surface methods.