Ocean Wave Speetra and Shtp Appltcattons 
N 
S(k;#) © ad [+ oe cos n(k, -k,) D| (2. 11) 
ea 
At k, =kp the approximation S(k,;w) has its maximum value of 
C() D 1 ilo Lae C(w)D, 1 
aaa Seas iN) At kK - Ky) = Wp one bas S(k, 30) = = Nes) 
It is a factor of -1/(1+2N) smaller than the maximum value. The 
approximation of equation (2.8) to the narrow band directional spec- 
trum, equation (2.9) of kg = 0, is shown in Figure 6. From this 
figure, one sees how a narrow-band directional wave-spectrum is 
directionally spread out as a function of-“= D in this approach. The 
loss of accuracy, i.e., increase of spreading, with decreasing-“—D, 
which has been discussed previously, is clearly shown in the 
figure. 
EXPERIMENT 
The basic approach described in the previous section was ap- 
plied to the measurement of the directional spectrum of waves gene- 
rated in NSRDC's seakeeping basin. Wave measurements were 
taken with sonic probes, using three separate array configurations, 
which are shown in Figure 7. For the linear arrays, the fundamental 
distance between the probes was 2.5 feet and the total array length 
was 32.5 feet . This arrangement enables one to approximate the 
Fourier series of the directional wave spectrum up to the ninth har- 
monic. This configuration was suggested by Pierson - “Phe 
reason this arrangement was used rather than the optimum array sug- 
gested by eetomaea (FE is that in Barber's configuration the total 
array length would have been only 22.5 feet ; a greater length was 
preferred. The linear array was arranged in two orientations 
relative to the wave generators. In the first case the array was 
mounted parallel to the West bank of the basin and at a distance of 
100 feet from the bank, as shown in Figure 3. In the second case the 
same array was rotated 45 degrees clock-wise to the North. The 
third array consisted of a pentagon arrangement, and employed six 
probes : one in the center and five outside forming an equilateral pen- 
tagon. The sides were designed to be 10 feet long. The orientation 
is shown in Figure 3. 
The seakeeping basin has wave generators along both the West 
and North banks and the wave generators on the two banks are operated 
independently. During the study three kinds of directional wave fields 
were generated. These were : wave coming from West bank, waves 
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