J.L. Hench et al. / Continental Shelf Research 22 (2002) 26152631
2617
Fig. 1. Computational grids used in momentum balance analyses. (a) idealized inlet I (0.5 1.0 km), (b) idealized inlet II
(3.0 1.0 km), (c) idealized inlet III (0.5 3.0 km), (d) idealized inlet IV (3.0 3.0 km), where inlet dimensions are given in parentheses.
Thick dashed lines indicate locations of open boundary forcing. The other boundaries are treated as land, with zero normal flow
boundary conditions applied. Axes distances are given in kilometers.
transform (see Eqs. (A.1)(A.4)). Momentum was
parameter was used corresponding to latitude 34.5
conserved at all grid points in both the x and y
degrees N. The lateral viscosity was set to a
constant value of 4 m2 s1, and a constant bottom
directions, as well as the s and n directions,
typically to within one percent of the largest term
friction coefficient of 0.0025 was used. The models
in the local momentum balance. Conservation was
were spun-up from rest and run for 4 days to
not perfect due to the finite precision arithmetic in
dynamic equilibrium using a time-step of 4 s.
the numerical integration of the momentum terms,
2.2. Momentum balance calculations
but the errors were small enough not to affect
interpretation of the momentum balances. Rotated
momentum fields were interpreted using the s2n
Velocity and elevation fields from the models
were used to evaluate each term in the x2y
momentum equations (also derived in Appendix A)
momentum Eqs. (2) and (3) at every computa-
qZ Cf Us2
qUs
qUs
Us
g
0;
4
tional node. Each term was evaluated using exactly
s
qt
qffls} |fflffl{zq} |fflfflffl{Hfflffl }
zffl
fflffl
|{z}
|fflfflfflfflffl{zfflfflffl ffl
the same integration, assembly scheme, and run
streamwise streamwise nonlinear
local
parameters as in the circulation model (see
streamwise Bernoulli pressure
bottom
acceleration acceleration gradient
Luettich et al., 1992 for details) so that the
individual momentum terms were consistent with
Us2
qa
qZ
the computed flow fields. For visualization and
fUs g
0;
5
Us
|ffl{zffl} |fflffl{zqffln
fflt
R
|ffl {zq}
ffl}
interpretation purposes, a rotational transform
|ffl{zffls
}
Coriolis
local
centrifugal acceleration normal
was applied to the precomputed x2y components
rotary acceleration
direction
of each term in the momentum equations, which
pressure
acceleration
gradient
yielded the corresponding momentum term values
in a streamwise-normal s2n coordinate system.
where Usx; y; t is the streamwise velocity,
Rsx; y; t is the flow radius of curvature, and
Appendix A details the coordinate rotation and
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