The solution of the two-dimensional elliptic mild-slope wave equation is a well-

accepted method for modeling surface gravity waves in coastal areas (e.g. Chen &

Houston, 1987; Chen, 1990; Xu & Panchang, 1993; Mei, 1983; Berkhoff, 1976; Kostense

et al., 1986; Tsay and Liu, 1983). This equation may be written as:

(

)

∇ ⋅ *CC*g ∇ η +

σ2 η = 0

$

$

(1)

where

η(x, y) =

complex surface elevation function, from which the wave

$

height can be estimated

σ

=

phase velocity = σ/k

C(x,y)

=

group velocity = σ / k =nC with

Cg(x,y) =

1

2kd

n=

1 +

(2)

2 sinh 2 kd

wave number (= 2π/L), related to the local depth d(x,y)

k(x,y)

=

through the linear dispersion relation:

σ2 = gk tanh (kd)

(3)

Equation 1 simulates wave refraction, diffraction, and reflection (i.e. the general

wave scattering problem) in coastal domains of arbitrary shape. However, various other

mechanisms also influence the behavior of waves in a coastal area.

The mild-slope

equation can be modified as follows to include the effects of frictional dissipation

(Dalrymple et al 1984; Chen 1986; Liu and Tsay 1985) and wave breaking (Dally et al

1985; De Girolamo et al 1988):

6

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