EM 1110-2-1100 (Part II)
30 Apr 02
EXAMPLE PROBLEM II-1-5
FIND:
(a) Using cnoidal wave theory, find the wavelength L and compare this length with the length determined
using Airy theory.
(b) Determine the celerity C. Compare this celerity with the celerity determined using Airy theory.
(c) Determine the distance above the bottom of the wave crest yc and wave trough yt .
(d) Determine the wave profile.
GIVEN:
A wave traveling in water depth d = 3 m (9.84 ft), with a period T = 15 sec, and a height H = 1.0 m
(3.3 ft).
SOLUTION:
(a) Calculate
H
1
' 0.33
'
d
3
and
g
9.8
' 15
' 27.11
T
d
3
From Figure II-1-13, enter H/d and T to determine the square of the modulus of the complete elliptical
integrals, k2:
k 2 ' 1 & 10&5
Entering both Figures II-1-13 and II-1-14 with the value of k2 gives
L 2H
' 290
d3
or
290 d 3
290 (3)3
L'
'
H
1
Example Problem II-1-5 (Continued)
Water Wave Mechanics
II-1-45
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