and/or rapidly varying flow. However, since the deep ocean, which comprises
the majority of the WNAT domain, is a vast region with very deep bathymetry
and a slowly spatially varying tidal response, which only require a relatively
coarse mesh, a high resolution uniformly graded grid would overdiscretize large
areas unnecessarily and only add to the computational cost. In general, tidal
wave propagation speeds and wavelengths decrease with decreasing depths.
Therefore, unstructured grid size should decrease along with bathymetry to
continue describing the flow at the same level of accuracy. In addition, varia-
tions in geometry and bathymetry impose gradients on the localized tidal eleva-
tion and especially velocity responses, particularly in shallow waters. This
requires that additional localized grid refinement be imposed in regions with high
bathymetric gradients. Thus, regions such as the continental shelf break and the
continental slope require higher grid resolution (Hagen, Westerink, and Kolar
2000; Hagen et al. 2001). Other areas needing local refinement include regions
exhibiting two-dimensional (2-D) response structures associated with complex
shorelines, 2-D topography and amphidromic points.
Several studies on grid generation techniques have been made in recent years
to provide a strategy for the methodical and optimal placement of nodes in
variable graded grids for large computational domains (Hagen, Westerink, and
Kolar 2000; Hannah and Wright 1995). Various techniques have been imple-
mented and studied over the years, but no technique has been proven to inde-
pendently work accurately enough to implement the appropriate grid spacing
based on the physical characteristics of the domain while being computationally
economical. The most widely used technique remains the wavelength to grid
size (λ/∆x) criterion that is based on computing an estimated wavelength using
one-dimensional linear constant depth long wave theory. However, this tech-
nique does not recognize gradients in response associated with changing
bathymetry, 2-D structure in boundaries and/or response. The topographic length
scale (TLS) criterion keys grid resolution to the rate of change in topography
(Kashiyama and Okada 1992; Hannah and Wright 1995). However, in and of
itself this criterion does not properly resolve constant depth or slowly varying
depth waters or account for 2-D response structures. A recent technique based on
localized truncation error analysis (LTEA) formally computes truncation error
and controls this by adjusting grid size (Hagen, Westerink, and Kolar 2000;
Hagen et al. 2001). Although the LTEA grid generation technique has been
successful in creating computationally more accurate and economical grids, the
process involved is long and tedious. However, a combination of the wavelength
to grid size ratio and the TLS criteria yields grids that are similar in performance
to LTEA based grids.
The WNAT domain has been used as a basis for unstructured graded grid
tidal computations since 1991. Westerink, Luettich, and Scheffner (1993) and
Westerink, Luettich, and Muccino (1994) developed Eastcoast 1991, a tidal
database of surface-water elevations and currents in the WNAT domain. The
Eastcoast 1991 grid, as shown in Figure 1, consists of 19,858 nodes and 36,653
elements with element sizes varying from 7 km at the coastline to approximately
140 km in the deep ocean, shown in Figure 2. This grid was generated using the
wavelength to grid-size ratio criterion and specifying a maximum element size
equal to 140 km. The Eastcoast 1991 bathymetry was constructed from the Earth
2
Chapter 1 Introduction and Objectives
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