λ
gh
=
T
(5)
∆x
∆x
where λ is the wavelength, ∆x is the grid size, g is the gravitational constant, h is
the water depth, and T is the tidal period of interest. The λ/∆x ratio is generally
set at a constant value to create a graded variable mesh. This implies that the
element size should decrease with decreasing bathymetry along with decreasing
wavelength to maintain the constant ratio value.
The λ/∆x ratio does not call for increased resolution in the vicinity of steep
topographic gradients such as the continental shelf break and slope and rise.
Nonetheless it has been demonstrated that increased resolution is necessary to
correctly capture the changes occurring in these regions. The topographic length
scale is another grid generation technique that has been developed in recent years
(Hannah and Wright 1995). This one-dimensional criterion calculates the grid
size as:
αh
∆x ≤
(6)
h, x
where ∆x is the grid size, h is the water depth, h,x is the bathymetric gradient, and
α is the mesh generation criterion set to a constant value of ∆h/h ≤ α over any
element. This ratio creates a relationship that will incorporate both the bathyme-
try and the change of bathymetry relative to the grid size. TLS indicates the need
for resolution in areas with steep topographic gradients, such as at the continental
shelf break and slope, which the wavelength to grid-size ratio would tend to
underresolve. Unfortunately the TLS criterion will fail as h,x becomes small
requiring that the wavelength to grid-size ratio criterion be applied as well.
The combination of the wavelength to grid-size ratio and the TLS criteria can
be shown to create grids similar to more sophisticated grid development tech-
niques based on localized truncation error analysis (Hagen, Westerink, and Kolar
2000; Hagen et al. 2001). The Eastcoast 2001 grid, as shown in Figure 7, was
100 or more, and the TLS criterion was aimed at 1.00. The Eastcoast 2001 grid
has a defined minimum element size generally ranging from 1 to 4 km along the
land boundaries and a defined maximum element size equal to 25 km in the deep
ocean. The maximum element size of 25 km in the deep ocean was defined to
ensure that the computations did not have long-term stability problems (Roe
1998). Once these minimum and maximum mesh sizes were set, the combined
λ/∆x and TLS grid generating criteria were used to develop the rest of the grid.
The wavelength to grid-size ratio was implemented first, indicating much needed
resolution near the coastline and areas of shallow depths. The TLS criterion was
implemented next, which necessitated additional resolution in the vicinity of the
shelf break and slope. The resulting grid-size distribution throughout the domain
is shown in Figure 8 while the λ/∆x and TLS values are shown in Figures 9 and
10, respectively. Along the coastline, the wavelength to grid-size ratio (λ/∆x)
ranges between 100 to 500 wherever waters are shallow. In the deep ocean, the
λ/∆x ranges between 200 and 1,000. Although the targeted λ/∆x was 100 or
11
Chapter 3 Eastcoast 2001 Grid Development
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