*C*

(

)

$ + g σ2 + *i*σ*w *+ *iC*g σγη = 0

∇ ⋅ *CC*g ∇ η

(4)

$

*C*

where w is a friction factor and γs a wave breaking parameter. Following Dalrymple et al.

i

(1984), we have used the following form of the damping factor in CGWAVE:

2nσ2f r

ak 2

w=

(5)

k 3π (2kd + sinh 2kd )sinh kd

user. The coefficient fr depends on the Reynolds number and the bottom roughness and

may be obtained from Madsen (1976) and Dalrymple et al. (1984). Typically, values for fr

s

n.

function of (x,y) allows the modeler to assign larger values for elements near harbor

entrances to simulate entrance loss. For the wave breaking parameter γ we use the

,

following formulation (Dally et al 1985, Demirbilek 1994, Demirbilek et al. 1996b):

χ Γ2 d 2

γ 1 -

=

(6)

d

4a 2

where χ is a constant (a value of 0.15 is used in CGWAVE following Dally et al (1985))

and Γ is an empirical constant (a value of 0.4 is used in CGWAVE).

In addition to the above mechanisms, nonlinear waves may be simulated in the

MSE. This is accomplished by incorporating amplitude-dependent wave dispersion, which

has been shown to be important in certain situations (Kirby and Dalrymple 1986). The

nonlinear dispersion relation used in place of Equation 3 is

7

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