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lagoon near both shores but no obvious return flow can be detected against the wind
in the deep basin. The model was then used to simulate the 3D structure of currents
under the same wind conditions but with the water column divided in eight 1-m-
thick layers. Results of the 3D simulation verified the initial hypothesis: the return
flow does occur close to the bottom in the deeper basin, in a direction opposite to
the winds. Surface currents in this case are still oriented downwind. These results
should have significant implications for studies of lagoon ecosystem dynamics. For
example, a stronger current near the bottom will enhance water and dissolved oxygen
renewal for benthic species. It is suggested that, when attempting to model ecosystem
dynamics in a coastal lagoon, currents used should be computed using a 3D modeling
approach.
A
PPENDIX
9.2.A:
T
HE
MIKE3-HD N
UMERICAL
M
ODEL
As discussed in
Chapter 3
and
Chapter 6,
the circulation and mixing processes
in coastal lagoons are governed by the time-dependent, nonlinear equations of
conservation of mass and momentum in three spatial dimensions. In some
instances, 1D inlet-basin equations or 2D vertically integrated equations can be
used. However, anticipating dynamic changes in the vertical dimension due to
local wind stress, freshwater inflow from rivers, and mixing with denser oceanic
waters, it is appropriate to start a lagoon hydrodynamics study by using the 3D
governing equations of motion. Then, depending on local conditions (see Chapter
6), the equations can be simplified to one or two dimensions in space.
9.2.A.1
Governing Equations
The 3D governing equations of the MIKE3 numerical model are:
13
1.
The mass conservation equation:
1
c
∂
∂
P
t
∂
∂
u
x
j
j
+
=
S
ss
ρ
2
2.
The momentum conservation equations, or the Reynolds-averaged Navier-
Stokes equations in three dimensions, including the effect of turbulence
and variable density:
∂
∂
+
∂
(
u
u
x
)
1
∂
∂
P
x
u
t
i
i
j
g
+
2
Ω
u =
−
+
i j
j
i
∂
ρ
j
i
∂
∂
∂
+
∂
∂
2
3
u
x
u
x
i
j
+
"
−
k
+
ν
δ
u S
t
i
ss
i j
∂
x
j
j
i
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