914

JOURNAL OF PHYSICAL OCEANOGRAPHY

VOLUME 33

U

U

U

2

kinematics, progress has been made in describing the

U

V

f*V*

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

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

f*U*

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

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-

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

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-

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

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-

shore the depth increased linearly from 5 to 14 m at the

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

V*H*

U*H*

deepest. The flood delta is cut by several connecting

0

(1)

t

x

y

sloughs. Model bathymetry came from a 1998 National