the Generalized Wave-Continuity Equation (GWCE). Fundamental components
of the GWCE are the depth-integrated continuity and Navier-Stokes equations
for conservation of mass and momentum. The assumption of incompressibility
and the Boussinesq and hydrostatic pressure approximations were applied. The
primitive, nonconservative form of the governing equations, given in spherical
coordinates, as applied in the model are (Flather 1988; Kolar et al. 1993)
∂UD ∂ [UV cos (φ)]
∂ζ
1
+
+
=0
(2)
∂t R cos (φ) ∂ϕ
∂φ
∂U 1 ∂U tan (φ)
∂U
1
+
+ V
-
U+ f V
U
∂t R cos (φ) ∂ϕ R ∂φ R
(3)
τSϕ
∂ PS
1
+ g (ζ - ξ ) +
=-
- τ*U
R cos (φ) ∂ϕ ρ0
ρ0 D
∂V 1 ∂V tan (φ)
∂V
1
+
+ V
-
U+ f U
U
∂t R cos (φ) ∂ϕ R ∂φ R
(4)
τ
1 ∂ PS
+ g (ζ - ξ ) + Sφ - τ*V
=-
R ∂ϕ ρ0
ρ0 D
where t is time, ϕ is degrees longitude (east of Greenwich is taken positive), φ is
degrees latitude (north of the equator is taken positive), ζ is the free-surface
elevation relative to the geoid, U is the depth-averaged velocity component
parallel to the east-west axis, V is the depth-averaged velocity component
parallel to the north-south axis, R is the radius of the earth, D = ζ + h is the total
water-column depth, h is the ambient depth relative to the geoid, f = 2Ωcos(φ) is
the Coriolis parameter, Ω is the angular speed of the earth's rotation, Ps is the
atmospheric pressure at the free surface, g is the acceleration due to gravity, ξ is
water, τsϕ and τsφ are the applied free-surface stresses, and τ* is the bottom stress
The time-differentiated form of the conservation of mass equation is
combined with a space-differentiated form of the conservation of momentum
equation to develop the GWCE (Westerink et al. 1992) given by
13
Chapter 3
Modeling Approach
Previous Page
