generally contains waves of many periods. Typical records from a recording 

 gage during periods of steep waves (Fig. 3-1) indicate that heights and 

 periods of real waves are not constant as is assumed in theory. Wavelengths 

 and directions of propagation are also variable (see Fig. 3-2). Further, the 

 surface profile for waves near breaking in shallow water or for very steep 

 waves in any water depth is distorted, with high narrow crests and broad flat 

 troughs (see Ch. 2,11,5 and 6 and higher waves in Fig. 3-1, a). Real ocean 

 waves are so complex that some idealization is required. 



1 . Significant Wave Hei ght and Period . 



An early idealized description of ocean waves postulated a significant 

 height and significant period that would represent the characteristics of the 

 real sea in the form of monochromatic waves. The representation of a wave 

 field by significant height and period has the advantage of retaining much of 

 the insight gained from theoretical studies. Its value has been demonstrated 

 in the solution of many engineering problems. For some problems this repre- 

 sentation appears adequate; for others it is useful, but not entirely 

 satisfactory. 



To apply the significant wave concept it is necessary to define the height 

 and period parameters from wave observations. Munk (1944) defined significant 

 wave height , as the average height of the one-third highest waves , and stated 

 that it was about equal to the average height of the waves as estimated by an 

 experienced observer. This definition, while useful, has some drawbacks in 

 wave record analysis. It is not always clear which irregularities in the wave 

 record should be counted to determine the total number of waves on which to 

 compute the average height of the one-third highest. The significant wave 

 height is written as H, -^ or simply H . 



The significant wave period obtained by visual observations of waves is 

 likely to be the average period of 10 to 15 successive prominent waves. When 

 determined from gage records, the significant period is apt to be the average 

 period of all waves whose troughs are below and whose crests are above the 

 mean water level (zero up-crossing method). Most modern gage record analyses 

 provide a wave period corresponding to the highest peak of the spectrum (see 

 Ch. 3, II, 3, Energy Spectra of Waves), which has greater dynamic importance 

 than significant period, although the two parameters are generaly comparable. 



2 . Wave Height Variability . 



When the heights of individual waves on a deepwater wave record are ranked 

 from the highest to lowest, the frequency of occurrence of waves above any 

 given value is given to a close approximation by the cumulative form of the 

 Rayleigh distribution. This fact can be used to estimate the average height 

 of the one-third highest waves from measurements of a few of the highest 

 waves, or to estimate the height of a wave of any arbitrary frequency from a 

 knowledge of the significant wave height. According to the Rayleigh distribu- 

 tion function, the probability that the wave height H is more than some 

 arbitrary value of H referred to as H is given by 



3-2 



