Example Problem II-1-5 (Continued)

which gives L = 88.5 m (290.3 ft). The wavelength from the linear (Airy) theory is

2π*d*

tanh

' 80.6 *m *(264.5 *ft*)

2π

To check whether the wave conditions are in the range for which cnoidal wave theory is valid, calculate *d/L*

and the *Ursell number = L*2H/d3:

3

1

' 0.0339 <

0.K.

'

88.5

8

1

' 290 > 26

0.K.

'

3

2

Therefore, cnoidal theory is applicable.

(b) Wave celerity is given by

88.5

' 5.90 *m*/*s *(19.36 *ft*/*s*)

'

15

while the linear theory predicts

80.6

' 5.37 *m*/*s *(17.63 *ft*/*s*)

'

15

Thus, if it is assumed that the wave period is the same for cnoidal and Airy theories, then

.1

'

(c) The percentage of the wave height above the SWL may be determined from Figure II-1-11 or II-1-12.

Entering these figures with *L*2H/D3 = 290, the value of *(y*c -d)/H is found to be 0.865, or 86.5 percent.

Therefore,

Example Problem II-1-5 (Continued)

II-1-46

Water Wave Mechanics

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