and 



^1 SO 



^ = ^or H^ = 1.67 H^ 



*************************************** 



Goodknight and Russell ( 1963) analyzed wave gage observations taken on an 

 oil platform in the Gulf of Mexico during four hurricanes. They found 

 agreement adequate for engineering application between such important para- 

 meters as Hg , Hj^Q , H^Tjax, ^rns » ^^^ ^ » although they did not find 

 consistently good agreement between measured wave height distributions and the 

 entire Rayleigh distribution. Borgman (1972) and Earle (1975) substantiate 

 this conclusion using wave observations from other hurricanes. These findings 

 are consistent with Figures 3-3 and 3-4, based on wave records obtained by 

 CERC from shore-based gages. The CERC data include waves from both extra- 

 tropical storms and hurricanes. 



3. Energy Spectra of Waves . 



The significant wave analysis, although simple in concept, is difficult to 

 do objectively and does not provide all the information needed in engineering 

 design. Also, it can be misleading in terms of available wave energy when 

 applied in very shallow water where wave shapes are not sinusoidal. 



Figure 3-1 indicates that the wave field might be better described by a 

 sum of sinusoidal terms. That is, the curves in Figure 3-1 might be better 

 represented by expressions of the type 



N 



n(t) = I a. cos (oj.t - i>.) (3-11) 



j = I J ^ J J / 



where n(t) is the departure of the water surface from its average position 

 as a function of time, aj the amplitude, wj the frequency, and (j)</ the 

 phase of the j wave at the time t = . The values of o) are arbitrary, 

 and (1) may be assigned any value within suitable limits. In analyzing 

 records, however, it is convenient to set o) . = 2iij/D , where j is an 

 integer and D the duration of the observation. The a,- will be large only 

 for those co . that are prominent in the record . When analyzed in this 

 manner, the significant period may be defined as D/j , where j is the value 

 of j corresponding to the largest a • . 



It was shown by Kinsman (1965) that the average energy of the wave train 

 is proportional to the average value of [n(t)]^ . This is identical to 

 a , where a is the standard deviation of the wave record. It can also be 

 shown that 



a2 = i Z a2 (3-12) 



J = 1 ^ 



In deep water, a useful estimate of significant height that is funda- 

 mentally related to wave energy is defined as 



3-11 



