EM 1110-2-1100 (Part II)
30 Apr 02
EXAMPLE PROBLEM II-1-3
FIND:
(a) The maximum horizontal and vertical displacement of a water particle from its mean position when
z = 0 and z = -d.
(b) The maximum water particle displacement at an elevation z = -7.5 m (-24.6 ft) when the wave is in
infinitely deep water.
(c) For the deepwater conditions of (b) above, show that the particle displacements are small relative to
the wave height when z = -L0 /2.
GIVEN:
A wave in a depth d = 12 m (39.4 ft), height H = 3 m (9.8 ft), and a period T = 10 sec. The corresponding
deepwater wave height is H0 = 3.13 m (10.27 ft).
SOLUTION:
(a)
L0 ' 1.56T 2 ' 1.56(10)2 ' 156 m (512 ft)
d
12
' 0.0769
'
L0
156
From hand calculators, we find
2πd
sinh
' 0.8306
L
2πd
' 0.6389
tanh
L
When z = 0, Equation II-1-34 reduces to
H
1
A'
2
2πd
tanh
L
and Equation II-1-35 reduces to
H
B'
2
Thus
3
1
' 2.35 m (7.70 ft)
A'
2 (0.6389)
H
3
' 1.5 m (4.92 ft)
B'
'
2
2
Example Problem II-1-3 (Continued)
Water Wave Mechanics
II-1-19
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