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JOURNAL OF PHYSICAL OCEANOGRAPHY

VOLUME 33

affected with 17% difference in *M * 4 SEMA and 21% in

perpendicular offshore boundaries to obtain onshore

offshore tidal propagation as seen at Beaufort Inlet, and

ence in SEMA and 55% in PHA; this was expected since

elsewhere along the South Atlantic Bight (Redfield

1958; Pietrafesa et al. 1985). The Beaufort Inlet model

However, the change to the overall flow is fairly insig-

nificant since *M * 6 makes up 10% of the total velocity.

was forced at three open boundaries (two within the

sound and one on the ocean; see Fig. 2) with specified

Grid resolution effects were studied by rerunning the

elevations for the *M * 2 , *M * 4 , *M * 6 , and steady tidal con-

Beaufort Inlet model with double the resolution in the

stituents obtained from the larger domain circulation

near-inlet region (25 m). Tidal harmonics were inter-

model of Luettich et al. (1999). Zero normal-flow

polated to a common set of about 500 uniformly spaced

boundary conditions were imposed along land bound-

near-inlet stations, and rms differences between the runs

7

0.0025,

aries. Both models used constant *C*f

were: 0.5% *M * 2 SEMA and 1% *M * 2 PHA, 2% *M * 4 SEMA

1

m s (the minimum for model stability) and a time

2

and 4% *M * 4 PHA, and 2% *M * 6 SEMA and 9% *M * 6 PHA.

step of 2 s. The Coriolis parameter in both models was

The higher harmonics showed greater differences as

set to a value corresponding to latitude 34.5 N. The

they benefited more from increased resolution of the

models were spun up for 6 days to dynamic equilibrium;

shorter wavelengths.

results from days 68 were harmonically analyzed (us-

ing *M * 2 , *M * 4 , *M * 6 , *M * 8 , *M*10 , and steady constituents) to

obtain tidal constituents and for the momentum balance

tivity studies was 10% of the baseline run. We con-

analyses.

clude that the Beaufort Inlet model results were not

In our initial modeling efforts at Beaufort Inlet (Luet-

overly sensitive within a reasonable range of model pa-

tich et al. 1999), model results compared well with

rameters. The grid is highly converged for the barotropic

moored instrument data from 16 elevation and 10 ve-

locity stations distributed within the sound. Drogue ob-

tidal residuals). Sensitivity runs with the idealized inlet

servations during flood tide (Churchill et al. 1999) also

showed even smaller differences.

provided encouraging comparisons with the earlier

model. The model used in the present study uses a sub-

domain of the previous model and includes several re-

finements. High-resolution bathymetry and updated

shoreline geometry were incorporated into the grid near

Velocity and elevation fields from the models were

Beaufort Inlet (described above), and grid resolution

used to reconstruct momentum terms at each compu-

was doubled to better resolve small-scale (subkilometer)

tational node throughout a tidal cycle. Each term was

flow features.

evaluated using exactly the same integration, assembly

scheme, and run parameters as in the circulation model

(see Luettich et al. 1992 for details) so that the indi-

vidual momentum terms would each be consistent with

Model runs were conducted to determine sensitivity

the computed flow fields. To simplify dynamical inter-

to parameter values and grid resolution. The Beaufort

pretation, the *x**y *components of each term in equations

Inlet model was much more computationally difficult

(2) and (3) were rotated at each node into a local stream-

due to the steep bathymetry and geometric complexity

and was the focus of our sensitivity studies.

wisenormal (*s**n*) coordinate system aligned with the

In selecting a lateral viscosity, we followed the phi-

instantaneous velocity vector. This ``streamline'' coor-

losophy of Geyer and Signell (1992): use as little vis-

dinate system was defined with the *s *direction positive

cosity as possible (in combination with high grid res-

in the direction of flow, and the *n *direction positive left

olution) in order to model advective processes explicitly.

of the flow. The local acceleration terms were treated

10 m 2 s 1

We reran the Beaufort Inlet model with

with a forward-Euler two time-level finite difference

and compared tidal ellipse parameters at about 500 uni-

scheme, where the streamline velocities and angles were

formly spaced stations within a 3-km radius of the Inlet.

defined relative to the initial time level. The appendix

Rms differences for *M * 2 semimajor axes (SEMA) were

provides a derivation for the *x**y *to *s**n *transformation.

2%, and *M * 2 velocity phases (PHA) differed by 8%. The

The *s**n *momentum equations and their physical inter-

higher harmonics were more affected with 12% differ-

pretations are

ences in *M * 4 SEMA and 21% difference for *M * 4 PHA.

We used the canonical drag coefficient value 0.0025

Us

Us

Us

g

0,

because previous model verification work (Luettich et

(4)

t

s

s

al. 1999) showed this value provided good agreement

l

with observed tidal constituents. A run with *C*f 0.0030

ocal

streamwise

streamwise

nonlinear

showed 5% difference in *M * 2 SEMA and 10% difference

streamwise

(Bernoulli)

pressure

bottom

gradient force