4.4 Kinematic Parameters
Once a solution for η is obtained in CGWAVE, the maximum wave velocity, maximum
$
wave pressures, wave phase angle and wave amplitude may be obtained from the values of
η . These quantities are obtained as follows.
$
The velocity potential for water particles of surface water waves may be written as
Φ (x, y, z, t) = [ 1 cos ω t + φ2 sin ω t] (z)
φ
Z
(122)
where
[
]
cosh k(z + h )
Z(z) =
(123)
cosh(kh )
The potential may be expressed in terms of η by substituting
$
g
Φ=
η
(124)
$
iω
into Equation 122; this gives
g
- i + ωt
π
Φ (x, y, z, t) = ℜ η(x, y)e
Z(z)
2
(125)
$
ω
where
η = η1 + iη2
(126)
$$
$
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