H

Pmax = - ρgz + ρg

(135)

Z

2

The wave phase angle β is obtained from

η2

$

β = arctan

(136)

η1

$

The cosine of β varies from -1 to 1, and is written as output.

The wave amplitude A is obtained from

A = η1 + η2

(137)

$

$

A ` nap-shot'of the sea surface elevation at time = 0.0 is obtained from

s

[]

η = ℜ ηe-iωt = [ 1 cos ω t + η2 sin ω t]

η

(138)

$

$

$

A floating dock inside the computational domain may be treated following the

formulation of Tsay & Liu (1983). If the distance from the bottom of the bed to the

surface of the floating body is d (x, y ) and the wave number corresponding to this depth is

k (x, y ) , the governing equation for region under the floating body is

∇ ⋅(p∇ η) = 0

(139)

$

where

2

2kd

1 σ

1+

p=

(140)

2 k

sinh 2 kd

σ2 = gk tanh kd

(141)

Note that the second term of Equation 1 has been neglected in Equation 139. This

40

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