914
JOURNAL OF PHYSICAL OCEANOGRAPHY
VOLUME 33
U
U
U
2
kinematics, progress has been made in describing the
U
V
fV
g
U
dynamics of inlet flow. Imasato (1983) used results from
t
x
y
x
a two-dimensional barotropic idealized inlet model to
U2
V2
H
Cf
construct a simple set of conceptual force balance car-
U
0
(2)
toons. Imasato (1987) used the same model to compute
selected momentum terms along a single transect ad-
V
V
V
2
U
V
fU
g
V
jacent to an inlet. These ideas were extended by Imasato
t
x
y
y
et al. (1994) who used a three-dimensional idealized
inlet model to compute vertical profiles of selected mo-
U2
V2
H
Cf
V
0,
mentum terms at two points within the inlet. The most
(3)
complete dynamical analysis to date appears to be by
Ridderinkhof (1988), who computed term-by-term mo-
where x and y are horizontal coordinates aligned east
mentum balances for a two-dimensional model of Wad-
and north directions, respectively; U(x, y, t), V(x, y, t)
ar( depth-integrated velocities; H(x, y, t)
h(x, y)
den Sea inlets. However, his analysis was confined to
e
x, y, t) is the total water column height; (x, y, t) is
the limiting cases of steady flow (near maximum ebb
and maximum flood). These studies have provided much
the vertical displacement of the surface from still water;
insight into inlet dynamics, although they were all lim-
f is the Coriolis parameter; g is the gravitational con-
st2ant; is the lateral eddy exchange coefficient; 2
ited in space, time, and/or the portion of the dynamics
/ x2
2 / y 2 is the horizontal diffusion operator; and
analyzed.
In this paper, we extend these prior studies with a
detailed and systematic examination of the transient mo-
(1) is transformed into a waveequation formulation,
mentum balances at two complementary shallow tidal
and the resulting coupled system of equations is dis-
inlets. Model results from both inlets are dissected to
cretized using a finite-element method in space and a
assess the contribution of each term in the momentum
finite-difference scheme in time (see Luettich et al.
equations to gain an understanding of the spacetime
1992). The model has been previously verified in studies
patterns of the dynamics. An idealized inlet is used to
of natural tidal inlets (Luettich et al. 1999; Militello and
identify generic behaviors. These results are contrasted
Zarillo 2000) and should faithfully simulate the physics
with those from a highly detailed model of a natural
of barotropic flow.
inlet to illuminate the confounding roles of irregular
bottom topography and shoreline geometry. Herein, we
b. Numerical model domains
1) describe the numerical models and the streamline
Two inlet models with differing degrees of geometric
coordinate system used for the momentum balance anal-
and bathymetric complexity were used. The first is an
ysis, 2) describe the modeled circulation fields, 3) an-
idealized inlet model, which was constructed to corre-
alyze the transient momentum balances over a partial
spond to the general features of Beaufort Inlet, with a
tidal cycle, and 4) discuss the dynamics and their im-
domain comprised of two basins connected by an inlet
plications for inlet exchange.
that is 1 km wide and 0.5 km long (Fig. 1). Water depths
in the sound and inlet were set uniformly to 5 m. Off-
2. Methods
shore the depth increased linearly from 5 to 14 m at the
a. Numerical model formulation
open ocean boundary. Flow separation and adverse pres-
sure gradients are significant flow features in inlet prob-
As a necessary step toward understanding time-de-
lems and adequate grid resolution is essential for ac-
pendent, three-dimensional, baroclinic momentum bal-
curately modeling these processes. The finite-element
ances on irregular bathymetry and geometry, we focus
method and the use of unstructured grids are particularly
here on barotropic dynamics and assume density gra-
useful for studying inlet circulation since they permit
dient effects are dynamically small. These conditions
selective resolution of a wide range of length scales and
are common at shallow inlets where vertical mixing is
complex shoreline geometries while keeping computa-
strong, and is often the case at Beaufort Inlet, North
tional requirements tractable. For the idealized inlet
Carolina, which is the shallow inlet prototype consid-
model, horizontal grid resolution varied from 1 km at
ered in this study. Assuming barotropic conditions and
the open ocean boundary to a uniform 50 m in the
small vertical shears, we solve the fully nonlinear, shal-
vicinity of the inlet.
low-water equations using the circulation model AD-
The second model is of Beaufort Inlet, which has an
CIRC (Luettich et al. 1992). In the absence of wind and
inlet width of about 1 km at its narrowest point and a
tidal potential forcing, and assuming a constant lateral
nominal length of 0.5 km (Fig. 2). Depths range from
viscosity, the governing continuity and momentum
2 to 10 m along the ebb delta, while the inlet's main
equations used in the model are
channel (dredged for navigation) is about 15 m at the
VH
UH
deepest. The flood delta is cut by several connecting
0
(1)
t
x
y
sloughs. Model bathymetry came from a 1998 National
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