Finally, processes such as tides and storm surges are
quite important aspects of shallow water circulation and to
simulate these effects, the rigid lid approximation has to be
revoked and free surface dynamics included. Since this results in
severe time step limitations due to constraints introduced by fast
external surface gravity wave motions, generated at the air--sea
interface, it becomes necessary to invoke mode splitting as a
solution strategy. Mode splitting consists of splitting the
solution into two parts, the barotropic (external mode) part
governed by the two-dimensional vertically integrated form of the
governing equations and the baroclinic (internal mode) part
governed by the full equations, as demonstrated in
section 5.5.
The baroclinic mode is solved less frequently relative to
the barotropic mode, consistent with the slower propagation speed
of the internal mode disturbances * vis-a-vis* the external mode.
Considerable savings accrue as a result. However care must be
taken to ensure that conservation properties are not violated by
mode-splitting.

- 5.1 Tides and Tidal Forcing
- 5.2 Governing Equations
- 5.3 Boundary Conditions
- 5.4 Transformation to Sigma Coordinates
- 5.5 Mode Splitting
- 5.6 Discretization