J.L. Hench et al. / Continental Shelf Research 22 (2002) 26152631
2616
momentum balances over a tidal cycle for both a
qU
qU
qU
qZ
U
V
fV g
natural inlet and a complementary idealized inlet.
qt
qx
qy
qx
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi!
These studies have provided valuable insight into
Cf U 2 V 2
fundamental circulation dynamics. However, gi-
2
nr U
U 0;
2
H
ven that each study has used different tidal forcing,
inlet geometry, latitude, and bathymetry, two
qV
qV
qV
qZ
questions arise. First, how comparable are the
U
V
fU g
qt
qx
qy
qy
results between the differing inlets, and second,
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi!
how well do these intensive studies compare with
Cf U 2 V 2
2
V 0;
3
nr V
other systems where the circulation is known to
H
some degree, but the dynamics have not been
thoroughly analyzed?
where x; y are horizontal coordinates aligned in
East and North directions; U x; y; t; V x; y; t are
In this study we examine these questions with a
depth-integrated velocities; H x; y; t hx; y
set of numerical experiments on a series of
Zx; y; t is the total water column; Zx; y; t is the
idealized inlets (Section 2). In Sections 3 and 4,
we use the velocity and elevation fields from the
vertical displacement from the still water surface;
f y is the Coriolis parameter; g is gravity; n is the
models to compute term by term momentum
lateral eddy viscosity/dispersion coefficient; r2
balances and Rossby numbers to identify the
q2=qx2 q2=qy2 is the horizontal diffusion opera-
primary dynamical balances. The emphasis is on
lateral dynamics, but we include the streamwise
momentum balances as well to more fully under-
coefficient. The model has been previously verified
stand cross-stream balances. Section 5 uses the
in studies of natural tidal inlets (see Luettich et al.,
insight gleaned from the momentum balance
1999; Militello and Zarillo, 2000) and should
analyses to develop an inlet classification scheme
faithfully simulate the physics of barotropic flow.
where the results from this study are compared
Four idealized inlet models (IIV) were run, all
with those from 20 previous inlet studies. Finally,
identical except for inlet geometry (Fig. 1). The
Section 6 provides discussion and conclusions.
inlet geometries were selected to be representative
of a range found in nature. The computational
domains consisted of two rectangular basins,
representing an ocean shelf and a sound (also
2. Methods
known as a bay or lagoon), and connected by a
single inlet. Basin dimensions were the same in
2.1. Circulation modeling
each of the models to isolate the effects of inlet
geometry. The bathymetry for each of the models
We focus on barotropic dynamics and assume
was also the same, with water depths in the sounds
density gradients are dynamically small, as these
and inlets uniformly 5 m, while offshore the depths
conditions are common at shallow tidal inlets
increased linearly from 5 to 14 m at the open
where vertical mixing is strong. These assumptions
boundaries. Grid resolution ranged from 1 km at
permit the use of the depth-integrated fully non-
the open boundaries to a uniform 50 m in the
linear barotropic shallow-water equations, which
vicinity of the inlets. All four models were forced
are solved using the circulation model ADCIRC
along an offshore ocean boundary with specified
(Luettich et al., 1992). Assuming no wind or tidal
elevations of 0.15 m amplitude and zero phase at
potential forcing, and a constant lateral viscosity,
the governing continuity and momentum equa-
produce maximum velocities in the inlet throat of
tions used in the model are
about 1 m s1 for the two ``narrow'' inlets (I and
II). The remaining boundaries were treated as
qZ qUH qVH
land, with zero normal velocity boundary condi-
0;
1
qt
qx
qy
tions. For all model runs, a constant Coriolis
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