7.2.2 Bottom and surface kinematic boundary conditions

The bottom of the ocean is a material surface. The corresponding kinematic boundary condition, as derived in Section 4.3.1, is given by

 

$$- {\bf u}_{h} \cdot \nabla_{h} H \qquad z = -H(\lambda,\phi).$$ w = (7.15)

The details of how MOM realizes this boundary condition on the discrete grid are given in Section 22.3.3.

The ocean surface is generally permeable to fresh water fluxes. The surface kinematic boundary condition, as derived in Section 4.3.2, is given by

 

$$(\partial_{t} + {\bf u}_{h} \cdot \nabla_{h}) \, \eta = w + q_{w} \qquad z = \eta(\lambda,\phi,t).$$ (7.16)

where q_w is the flux of fresh water, in units of velocity (volume per unit time per unit area), crossing the ocean surface. The presence of horizontal advection of the free surface height makes this equation nonlinear.