Ocean Wave Spectra and Shtp Appltecattons 
The water surface elevation was measured by an array of sonic probes 
and the directions of the waves were then estimated from those mea- 
surements. The results indicate that the measurements obtained by 
the probes are indeed suitable for analyzing directional spectra. 
However, the technique used in estimating the cross spectra between 
different probes was not sufficiently accurate for determining the 
wave directions in the case where a regular wave train and an irre- 
gular wave train are propagating at 90 degrees to each other. 
This paper reports on the experimentally determined direc- 
tional wave spectra and a study of the application of the two-parameter 
wave spectrum model. 
UNIDIRECTIONAL WAVE SPECTRA 
One is aware of the variety of the ocean spectra, yet one must 
establish some order in this chaos for practical application. For es- 
timating the seakeeping qualities of ships, Cummins “ }] proposed a 
technique which makes use of a two-parameter wave spectrum of the 
general Bretschneider form, This two-parameter spectral formu- 
lation was studied by applying it to North Atlantic hindcast wave data 
[5]. The analysis procedure and results are given below. 
Bet x(t; he Hy3 ) be the response of a ship in a seaway 
which has average wave period T, and significant wave height Hy ; 
where t is time. If x is linear, its variance X(T, »Hys ) is given 
by 
Se cy =E x" (ts baa Wel = | Hx p( w) Sp(w;T ),H) 75) dw 
0 (1.1) 
where E[a] represents the average value of a, Sp(w) is the wave 
spectrum, Fp is the frequency response function of the ship and w 
is the wave frequ y. By the use of the wave spectrum form recom- 
mended by ITTCL?J , that is 
2 
173 H 4 
I 1/737 *EGoite 
Sp(w) = Sp(w) = 5 = ee) (1:22) 
T, w 
where sh (w) is the idealized two-parameter spectrum. The statis- 
tics of the response X(T, : Hy3 ) are completely determined by the 
statistics of T,; and Hy3 if co is a deterministic function. The 
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