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

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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