M8, and M10 overtides and the MN, SM, MNS2, 2MS2, 2MN2, 2SM2, MN4 MS4,
constituents were used as the basis of comparison to measured harmonically
decomposed field data at the 101 defined elevation recording stations.
A time-step of 5 sec was used yielding a maximum Courant number based on
wave celerity of approximately one for the Eastcoast 2001 grid. This require-
ment on the Courant number is associated with the explicit treatment of the
nonlinear terms. It is noted that Courant number is less than 0.4 over most of the
domain, between 0.4 and 0.5 in the Bahamas, around Cuba, north of Jamaica, and
north of the Dominican Republic, and between 0.5 and 0.8 in the Bahamas and in
a small region south of Cuba. Elsewhere the Courant number is significantly
smaller. The time weighting factors for the three-level implicit scheme in the
GWCE equation are 0.35, 0.30, and 0.35 for the future, present and past time
levels respectively. A two-level Crank-Nicholson scheme is used for the
momentum equations.
The nonlinear finite amplitude option, which determines how the finite
amplitude component of the total depth is considered, was utilized with wetting
and drying enabled. The hybrid fully nonlinear bottom friction option was used.
This option defines a Darcy-Weisbach type friction law for water column depths
column depths below the break depth to:
γ
hbreak
θ
θ
= C f 1 +
C fapplied
(4)
H
This increases bottom friction for shallow waters in order to accommodate a
realistic wetting/drying front. The bottom friction parameters were specified as
Cf = 0.0025, hbreak = 1.0 m, θ = 10.0, and γ = 0.3333 throughout the domain. The
lateral eddy diffusion/dispersion coefficient was set equal to 5 sq m/sec. Finally,
due to the locally high Courant number, the advective terms were turned off.
Boundary and Interior Forcing
The domain was forced on the 60W meridian open boundary with O1, K1,
Q1, M2, N2, S2, and K2 tidal amplitudes and phases interpolated onto the open
ocean boundary nodes using data from Le Provost 1995 global model
(Le Provost et al. 1998). Le Provost created a worldwide ocean tidal database
from a finite element hydrodynamic model in 1994, designated FES94.1
(Le Provost, Bennett, and Cartwright 1995). In 1995, Le Provost revised
FES94.1 by assimilating a satellite altimeter-derived data set, thus creating
FES95.2. FES95.2 has better accuracy than FES94.1 because of corrections to
major constituents by TOPEX/POSEIDON mission data assimilation and
because of the increase in the number of constituents in the model. A compari-
son study of both FES94.1 and FES95.2 on the Eastcoast 2001 grid has shown
that FES95.2 provided better results, and thus was used to force the open ocean
7
Chapter 2 Governing Equations and 2-D Modeling
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