Dynamic boundary conditions

At the bottom boundaries, no-slip conditions are prescribed for the horizontal velocity components:

$$u=0, \quad v=0.$$ (8)

With (7), also $w=0$ holds at the bottom. It should be noted already here, that the bottom boundary condition (8) is generally not directly used in numerical ocean models, since the near-bottom values of the horizontal velocity components are not located at the bed, but half a grid box above it. Instead, a logarithmic velocity profile is assumed in the bottom layer, leading to a quadratic friction law, see section 8.13.9.

At the surface, the dynamic boundary conditions read:

$$\begin{array}{l} (\nu_t+\nu) \partial_z u=\alpha \tau^x_{s}, \\ \\ (\nu_t+\nu) \partial_z v=\alpha \tau^y_{s}, \end{array}$$ (9)

The surface stresses (normalised by the reference density) $\tau_s^x$ and $\tau_s^y$ are calculated as functions of wind speed, wind direction, surface roughness etc. Also here, the drying parameter $\alpha$ is included in order to provide an easy handling of drying and flooding.