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JOURNAL OF PHYSICAL OCEANOGRAPHY
VOLUME 33
affected with 17% difference in M 4 SEMA and 21% in
on land boundaries, the sound, and along the shore-
perpendicular offshore boundaries to obtain onshore
M 4 PHA. Here, M 6 changed the most with 16% differ-
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 Cf
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 , M10 , and steady constituents) to
M 6 velocities, the total model response in these sensi-
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-
M 2 tide, as well as the major nonlinear overtides (and
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-
e. Momentum balance calculations
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
d. Model sensitivity
(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 xy 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 (sn) 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 xy to sn transformation.
2%, and M 2 velocity phases (PHA) differed by 8%. The
The sn 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
Cf U 2
Us
g
0,
s
because previous model verification work (Luettich et
(4)
t
s
s
H
al. 1999) showed this value provided good agreement
l
with observed tidal constituents. A run with Cf 0.0030
ocal
streamwise
streamwise
nonlinear
showed 5% difference in M 2 SEMA and 10% difference
streamwise
(Bernoulli)
pressure
bottom
gradient force
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