Observations and Measurements of Ocean Waves 



59 



(1) The wave spectrum is composed of a frequency band which must 

 not be too wide. 



(2) The ocean wave pattern is formed by the supersposition of a large 

 number of waves of small amplitude and a random distribution of phases. 



It has proved convenient to express all quantities by the energy E defined 

 in equation (III. 10). It represents the sum of the squares of the amplitudes 

 of the individual component wave trains, which go to make up the actual 

 wave motion as it is observed; E is with equation (III. 10) related to total 

 potential energy of the composite wave motion, and can be calculated for 

 any stage of wave development by equation (III. 8). Table 8 a contains the 

 statistical height distribution of apparent waves in a wind generated wave train. 



Table 8a. Statistical distribution of the heights of apparent waves 

 in a composite ocean wave pattern 

 (after Longuet-Higgins, 1952) 



In long observation series there occur: 



10% of all waves higher than 304 j/E 



20% of all waves higher than 2' 54 j/E 



30% of all waves higher than 2-20 J/E 



40% of all waves higher than 1*92 j/E 



50% of all waves higher than 1*66 j E 



60% of all waves higher than 1*42 j E 

 70% of all waves higher than 1*20 \ E 

 80% of all waves higher than - 94 j/E 

 90 % of all waves higher than 064 j E 

 100% of all waves higher than 000 - E 



The most important characteristics of wave height data can be found 

 from the 



most frequent value (mode) H/= 1414] E 



average value (mean) H = 1-772 | E 



significant value 7/i 3 = 2 832 j E j 



average of highest ten percent Hi M = 3-600 | E ) 



(III. 19) 



It follows 



HjH v .z = 625 and H ll0 /H 13 = 1 27 



(III. 20) 



which is in good agreement with equation (III. 18). These results demonstrate 

 that the statistical theory is capable of reflecting the actual conditions in 

 a very satisfactory manner, and it seems that the statistical distribution of 

 apparent wave heights does not so much depend on the width of the frequency 

 band. As an example of the application of the theoretical results we will 

 consider the case of a fully arisen sea at a wind speed of 30 knots 

 (v = 15-43 m/sec -1 ). Equation (III. 12) gives U = 27-4 erg cm" 2 or E = 5-48 m 2 . 

 The same value can be obtained from Fig. 33. Then the characteristic heights 



are: H = 4 1 m, H ll3 = 6-6 m and H lll0 = 8-4 m. According to Table 8a, 

 10% of the total waves present will be higher than 71 m, 20% higher than 



6 m, 30% higher than 515 m, 



40% 



higher than 4 5m and 50% higher 



