EM 1110-2-1100 (Part II)
30 Apr 02
EXAMPLE PROBLEM II-1-1
FIND:
The wave celerities C and lengths L corresponding to depths d = 200 meters (656 ft) and d = 3 m (9.8 ft).
GIVEN:
A wave with a period T = 10 seconds is propagated shoreward over a uniformly sloping shelf from a depth
d = 200 m (656 ft) to a depth d = 3 m (9.8 ft).
SOLUTION:
Using Equation II-1-15,
gT 2
9.8 T 2
' 1.56 T 2 m (5.12 T 2 ft)
L0 '
'
2π
2π
L0 ' 1.56T 2 ' 1.56(10)2 ' 156 m (512 ft)
For d = 200 m
d
200
' 1.2821
'
L0
156
Note that for values of
d
> 1.0
L0
d
d
'
L0
L
therefore,
d
1
> )
L ' L0 ' 156 m (512 ft) (deepwater wave, since
L
2
which is in agreement with Figure II-1-5.
By Equation II-1-7
L
156
C'
'
T
T
156
' 15.6 m/s (51.2 ft/s)
C'
10
For d = 3 m
d
3
' 0.0192
'
L0
156
Example Problem II-1-1 (Continued)
II-1-10
Water Wave Mechanics
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