2

4

'j

4

m

2

ση

(II-1-147)

'

2

0

where *m*0 is the zero-th moment of the spectrum. Physically, *m*0 represents the area under the curve of *E(f)*.

The area under the spectral density represents the variance of a random signal whether the one-sided or two-

sided spectrum is used.

(l)

The moments of a spectrum can be obtained by

4

m

i ' 0,1,2,...

(II-1-148)

0

(m) We now use the above definition of the variance of a random signal to provide a third definition of

the significant wave height. As stated earlier, this gives an estimate of the significant wave height by the

wave spectrum. For Rayleigh distributed wave heights, *H*s may be approximated (Longuet-Higgins 1952)

by

II-1-84

Water Wave Mechanics

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