Ocean Wave Spectra and Shtp Appltcattons 
waves coming from other directions. Figure il shows how the an- 
gular resolutions varied with the frequencies of the waves. As dis- 
cussed previously, the angular resolution increases with increasing 
wave period and the theoretical value of S*(k, ,w) is -0.5 at di- 
rection 0,., (k, -k,) = a ; The measured angular resolution agrees 
fairly well with the theoretical value. However, away from the peaks, 
S*(k,;w) oscillated with a much higher value than one would expect, 
especially for the wave periods of 2.5 and 3 seconds. The irregu- 
lar wave results do not agree as well with the tehoretical value. 
Figure 12 shows the resulting directional wave spectra of irregular 
wave trains generated at the North bank. It indicates that the waves 
were all coming from the North bank and the peak values of the spec- 
tra are between 6.5 and 8. In comparison with the regular wave 
measurements of Figure 7, the peak value is decreased. However, as 
the tail value also decreases, one concludes that the mixture of the 
frequencies in the same direction does not affect the angular spread- 
ing significantly. 
Figure 13 shows the measured directional spectra under a 
different wave condition. From it is concluded that there were long 
waves of period 2.5 to 3 seconds coming from the West and short 
waves of period 1.6 seconds propagating to the South. The direc- 
tional distribution of the 2.0 second period wave is meaningless. 
However, the actual wave field was different from the one pictured 
above. An irregular wave train was generated at the North bank and 
a regular wave of period 2.5 seconds was generated at the West 
bank. The loss of accuracies of the wave directions for the waves 
with wave frequencies near that of the regular wave is clear, Figure 
14 illustrates the same phenomena, For this case the period of the 
regular wave was 2.0 seconds and the amplitude was smaller in 
comparison with the previous case. The loss of information on the 
wave directions in this case was not as serious as in the previous 
case. The presence of the 2.0 second period wave reduced the peak 
value of the 2.4 second period wave but increased that of the 1.6 
second period wave. Figure 15 shows the measured directional wave 
spectra for the case of two low-amplitude irregular wave trains pro- 
pagating at 90 degrees to each other. The directional distribution of 
the wave is reasonable. 
By examining the calculated cross-spectra we found that the 
method used in estimating the cross spectrum was responsible for 
the errors which appear in Figures 13 and 14. Special care is neces- 
sary when analyzing the directional wave fields in these cases. By the 
use of a narrower frequency band-width, the result was improved ; it 
is shown in Figure 16. 
1345 
