ssc-367 - Ship Structure Committee

common probability distributions, the Gaussian (or normal)
distribution and-the Rayleigh distribution. These probability
distributions are used to define the distribution of wave elevations, n,
and of wave heights, H, respectively.
A.2.1
CharacteristicFrequencies and Periods
For design purposes sea spectra equations are selected to represent
middle aged seas that would exist some time after a storm, yet which
are still young enough to have a good dispersion of wave
frequencies. The primary assumption about the design seas is that
the wave elevations follow a Gaussian or normal distribution.
Samples of wave records tend to support this assumption. In
conjunction with the Gaussian distribution assumption, the wave
elevations are assumed to have a zero mean. Digitized wave records
tend to have a slight drift of the mean away from zero, usually
attributed to tide or instrument drift. The Gaussian distribution
assumption is equivalent to assuming that the phase angles of the
constituentwaves within a wave spectrum, are uniformly distributed.
The Gaussian distribution allows one to calculate statistical
parameters which are used to describe the random sea. The mean
elevation of the water surface is the first moment of the Gaussian
probability density function. The mean-square is the second moment
taken about zero, and the root-mean-square is the positive square
root of the mean-square. The variance is the second moment taken
about the mean value. The standard deviation is the positive square
root of the variance. Since the wave elevations are assumed to have
a zero mean value, the variance is equal to the mean-square, and the
standard deviation is equal to the root-mean-square. In present
practice, the area under a random wave energy spectrum is equated to
the variance.
In a similar way, the characteristic frequencies and periods of a
wave spectrum are defined in terms of the shape, the area, and/or the
area moments of the ~*a2 wave spectrum. Depending upon the
A-6
i
ij
-,,