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

Integrated Publishing, Inc. |