58 Observations and Measurements of Ocean Waves 



(in Fig. 27 in the right portion of the CCS-curves) and 5 % at the long-wave 

 end are supposed to be cut off. In this way, we get the limit periods T u and 



T , which, together with T and r max , define the total period characteristics. 

 These limit values are given for different wind speeds in Table 106. Neumann 

 (1954) has shown that the theoretical values agree very well with the ob- 

 servations. 



The determination of the "average wave length L" of the composite sea 

 motion is more difficult. It is not allowed to compute L from the classical 



formula valid for harmonic waves with T. Using the theoretical wave spectrum 

 for a fully arisen sea, Pierson (1953) has computed the average "apparent 



wave length" L as a function of the average "apparent period" T and found 



L = Vf^ 2 = 0-577 ^r- ■ (HI. 16) 



3 2n 2ti 



This relation is valid only for infinitely long wave crests. Taking into account 

 the length of the wave crests, Pierson derived an other relation between 

 the average values of the apparent wave length and the apparent period 

 by extending the energy spectrum to two dimensions: 



t-3%-. (III. 17) 



Thus, the average apparent wave length of short-crested wind-generated waves 

 is only two-thirds of that value which can be computed from the apparent wave 

 period by means of the classical formula. This relation is not yet verified 

 by observations, but we know that in general the application of the classical 

 formula with the apparent wave period gives too large apparent wave lengths. 

 The characterizations of wave height data in terms of the average wave 

 height H, the height of the highest third of the waves (£ highest, or significant 

 waves) // 1/3 , or the highest tenth of the waves (1 to 10 highest waves) H i:i0 , 

 give useful descriptions of the ocean wave pattern for many practical purposes. 

 Observations indicate that, in general, a similar distribution of wave heights 

 prevails in the wave pattern generated by different winds, although the absolute 

 heights and the wind speed vary considerably. According to a summary by 

 Munk (1952), the ratios of the average wave heights H, and of the average 

 of highest 10% 7/ 1/10 , to significant wave heights (H l!z ) are 



H/H m = 065 

 #i/io/#i/8 = 1 29 



(computed from wave records). (III. 18) 



As was shown by Longuet-Higgins (1952), the distribution of the ap- 

 parent wave heights can be computed with the following assumptions: 



