Modeling Concepts - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 286

depth (see Section 6.3.3.6) for average wind, or if the water depth is much less than
the depth of the friction layer (see Section 6.3.3.2).
For a leaky lagoon the correct inclusion of the inlets between the barrier islands
in the computation defines the accuracy of the level variation and current predictions.
Here a simple rule can be applied: The more leaky a lagoon, the bigger the adjacent
sea area to be included in the computational grid.
Only a 3D approach is to be used if the local current or fluxes structure is studied
in the vicinity of the considerable local depth variations.
It is possible to use the ratio between the time scale of advective transport
and the vertical turbulent diffusion as one criterion for selecting the spatial
dimension of the hydrodynamic model. 39 If U and L are typical velocity and length
of advective admixture transport, then T adv L / U is the characteristic time of

advection. Similarly, if H 0 is the lagoon depth and K Z is the vertical turbulent
diffusion coefficient, then the time T diff

=

= H 0 2 / K Z characterizes the vertical diffusion

T diff / T adv illustrates the relationship between
the velocities of admixture spreading in depth and length. The use of a horizontal
2D model is reasonable if

processes. The dimensionless ratio ∆ =

∆ << 1. In all other cases, 3D models give more reliable

results.

6.3.5.3 Possible Simplification in the Physical Approach

The spatial scale of lagoons influences physical processes and the general hydro-
thermodynamic problem. For example, closed lagoon boundaries give rise to
gradient forces due to wind surge level inclination and inflow of rivers. In the
same way, the lagoon shallowness provides the basis for vertical mixing as tur-
bulence generated in the upper and bottom friction layers occupies nearly all the
water column. In this case, when freshwater inflow is low or wind-wave mixing
is strong enough to overcome the density stratification, the general task may be
reduced to a barotropic problem with density varying only in the horizontal
direction.
It is recommended to include the Coriolis force in 3D or 2D models regardless of
the ratio between spatial scale of the lagoon to the value of the Rossby radius (see
Section 6.3.3.7). The reason is that the Coriolis term (similar to diffusion terms) inserts
nonlinear cross-linkage between equations for three components of momentum ( see
Chapter 3) and the same one between water velocity components. Even if a scale
analysis shows that the Coriolis term is smaller than other terms in the equation of
motion, it provides a qualitative new linkage between velocity components and defines
the vorticity of currents, especially at the areas with low motion (see Section 6.3.3.7).
The substitution of the real task by a steady-state or static problem where
time dependence is omitted is reasonable only for barotropic solutions. However,
it is not reliable for baroclinic situations where the complete time-dependent
problem must be solved because even if the boundary conditions are time inde-
pendent, the baroclinic currents never tend to steady-state solution. This is a
fundamental property of fluid dynamics. Practically, in the presence of winds,
tides, or varying freshwater input the water motion in a lagoon is never kept
constant; it varies in time and space.