Page 47 - Marine Structural Design

24 Part I Structural Design Principles

x in the above equations denote fetch.
However, the Ochi 6-parameter spectrum provides a better method to represent all stages of
development of a sea in a storm (Ochi, 1978). They start with a basic form as:

(2.10)

where r(A) is a gamma function and the parameter HS is the significant wave height, A is a
shape parameter and the Ochi 6-parameter spectrum reduces to the Bretschnerder form when
A= 1 . By adding two of these forms, Ochi (1 978) obtained a six-parameter spectral form as:

where j =1, 2 stands for the lower- and higher-frequency components, respectively. The size
parameters, H,, , H,, , w,, , w,, , A, and A, may be determined numerically to minimize the
difference from a specific observed spectrum.
Figure 2.3 compares the Bretschneider wave spectrum with the JONSWAP wave spectra of
various sharpness parameters (Hs and Tp are unchanged). Both Bretschneider and JONSWAP
(~3.3) wave spectra are frequently used in the calculation of extreme values and fatigue
damage.
Figure 2.4 shows the relationship between a time-domain solution of the waves (Eq. (2.3)) and
the fiequency-domain representation of the waves by a wave spectrum S(w) .

2.2.4 Moments of Spectral Density Function
The moments of a spectral density function S(w) may be expressed as (Bhattacharyya, 1978),

m, = g o"S(w)do (2.12)
where n is an integer. The zero moment, mo , is the area under the energy density spectrum
curve.

=
mo = J'sc~)~ %~(w)cim (2.13)
where f is the cyclic frequency, that is 2m. Hence the following relation may be derived.
S(f) = 2x S(w) (2.14)

%(f) = p's(f)dr= (2x)-"m, (2.15)