∂ ( DUU ) ∂ ( DUV cos (φ))
tan (φ)
∂
∂2ζ
∂ζ
1
1
+ τ0
-
+
- UVD
∂t R cos (φ) ∂ϕ R cos (φ)
∂t 2
∂ϕ
∂φ
R
τSϕ
∂
P
D
-2ωsin (φ) DV +
g (ζ - αξ) + S + τ*DU - τ0 DU -
R cos (φ) ∂ϕ
ρ0
ρ0
∂DVV ∂DVV cos (φ)
tan (φ)
1 ∂
1
(5)
+ 2ωsin (φ) DU
-
+
+ UUH
R cos (φ) ∂ϕ
R ∂φ
∂φ
R
τSφ
1 ∂ D ∂
P
g (ζ - αξ) + S + (τ* - τ0 ) DV -
-
R ∂φ R ∂φ
ρ0
ρ0
∂ VD
VD
tan (φ) - τ0
tan (φ) = 0
-
∂t R
R
The ADCIRC model solves the GWCE (Equation 5) in conjunction with the
primitive momentum equations given by Equations 3 and 4.
The GWCE-based solution scheme eliminates several problems associated
with finite-element models that solve the primitive forms of the continuity and
momentum equations (i.e., Navier-Stokes equations), including spurious modes
of oscillation and artificial damping of the tidal signal. Forcing functions include
time-varying water-surface elevation, wind stress, atmospheric pressure, and the
Coriolis effect.
The computational grid developed for this study is a large-domain circular
grid with a radius of 4 deg (276 miles) and center at 145 east longitude and
14 north latitude. The islands of Guam and Rota are located in the central
region of the grid. The large scale of the grid has two main advantages. First, the
tidal forcing boundaries are far from the region of interest such that island
shorelines are free from boundary effects. Second, because typhoons are large-
scale atmospheric phenomena, a large-domain grid is preferred to maximize the
interaction of the horizontal storm area with the computational grid, as well as
the storm track.
The grid developed for this study is shown in Figure 5. Grid resolution is
coarser in the open regions with increasing resolution toward the shore. Grid
parameters and range of scale of element sizes contained in the grid are given in
Table 3. Three Mariana Islands north of Guam were sufficiently large and close
that they are included in the grid: Rota, Saipan, and Tinian. The grid around
these islands was specified to be much coarser than the region surrounding
Guam. Initially, inclusion of detailed coastline and bathymetry around Rota was
an objective in developing the grid, so that one grid would serve for studies at
both Apra Harbor and Rota. However, this objective proved to be impractical.
14
Chapter 3
Modeling Approach
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