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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