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)
$
$
$
4.5 Floating Docks
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
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