Physical Processes - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 69

situation where our knowledge of initial conditions is limited. In the example of a
coastal lagoon we may still be in the situation to specify the water level (maybe
constant to a first approximation), but we surely do not know what the current
velocities are in the interior.
Fortunately, there is a way out of this dilemma. Many problems, after a
certain time, converge to a solution that is the same for different initial conditions.
These types of problems are therefore not sensitive to their initial conditions. An
example is a lagoon where a tidal elevation is prescribed on the inlet. In this
case the solutions of the hydrodynamic variables tend to converge even if different
initial conditions have been imposed. This is due to the fact that through the
tidal movement at the inlets, energy is created in the lagoon that is itself destroyed
by the frictional forces. After a while all energy that was in the system due to
the initial state has been dissipated, and from then on water movement in the
basin is due only to the forcing of the tide. The lagoon has “forgotten” its initial
state.
The duration of this memory effect depends mostly on the strength of the friction
(e.g., how long it takes to remove the initial energy from the system). In the case
of numerical simulations, this time is called the spin up time of the simulation. After
this initial spin up, the model is in equilibrium with the boundary conditions and
the effect of the unknown initial conditions has been damped out.

3.4.4.2 Conditions on Material Boundaries

Conditions on material (land) boundaries have to be specified for the scalar quantities
and the transports. On lateral material boundaries normally no-flux conditions are
applied for the scalar quantities. For example, there should be no heat or salinity
flux over (or exchange through) these material boundaries. These conditions take
into account the fact that there are actually no exchange processes going on through
material boundaries.
Two conditions must be considered for the current transports. The first is the
condition that the transport through a material boundary must be zero,

un
i

⋅ = 0

i

where n i denotes the direction of the normal of the boundary.
For flows with friction there is another boundary condition to be prescribed. On
material boundaries the fluid particles actually adhere to the wall, and in the very
vicinity of the wall there is no tangential movement of the fluid. This phenomenon is
observed only very close to the material boundary, as it is due to molecular friction.
However, the scale of the modeling is much larger than the molecular scale, and,
therefore, it is inadequate to impose no tangential flow along the boundary.
Although it is feasible to impose some lateral friction on the lateral boundary,
very often this lateral friction is set to zero. This is a suitable description if the
area-to-boundary ratio of the water body is high, meaning that the influence of
the lateral boundary can be neglected. In this case the boundary condition is called