Page 223 - Fundamentals of Ocean Renewable Energy Generating Electricity From The Sea

212 Fundamentals of Ocean Renewable Energy

Clamped Elevation
The free surface displacement is set to an externally prescribed value. This is
a popular boundary condition for tidal simulations, due in part to the smooth
spatial variability of elevation data, and readily available satellite-altimetry-
derived data (e.g. Section 8.1.3).

Clamped Normal Velocity
This condition simply sets the normal velocity component in the boundary cell
to an externally prescribed value.

Flather
Applied to the normal component of barotropic velocity, the Flather condition
is an adjustment to the externally prescribed normal velocity, based on the
difference between modelled and externally prescribed surface elevations. This
is a form of the classical radiation boundary condition.

Chapman
The corresponding boundary condition for water elevation (assuming an outgo-
ing signal) is Chapman.

8.3.3 Time Splitting
The presence of a free surface in a tidal model introduces waves in the domain
√
that propagate at a speed of gh. These waves impose a more severe constraint
on the model time step than any of the internal processes (Section 8.1.4).
Therefore, a split time technique is generally used in 3D modelling. The depth-
averaged equations are integrated using a ‘fast’ (barotropic) time step, and the
values of u and v used to replace those found by integrating the full equations
on a ‘slower’ (baroclinic) time step [11]. In general, it is recommended that the
ratio between barotropic and baroclinic time steps is in the range 10–20, but
this will depend on the scale of the problem. The purpose of time splitting is to
reduce the computational effort, because the 3D time step is considerably more
costly than the 2D time step.

8.4 WAVE MODELLING
There are two main classes of wave models: phase-resolving models and
phase-averaged models. In a phase-resolving model, the domain is discretized
onto a grid that is relatively fine compared with the wave length, and the
vertical displacement of the sea surface calculated in detail. Because such a
process is computationally expensive, phase-resolving models tend to be applied
to relatively limited domains, and are most appropriate in cases of strong
wave diffraction and reflection due to coastal structures. Examples of wave
resolving models are SWASH [12], CGWAVE, and FUNWAVE [13]. Although