a. = ^^^ (3-47) 



.01 



^- V. 



and, for a decaying wave, 



F^ = a^ Ax (3-48) 



b. Wave Growth . For any given water depth, windspeed, and fetch length, 

 a maximum significant wave height Hg^ which is generated can be defined from 

 Figure 3-21. If the initial wave height H^ at the seaward or beginning edge 

 of the fetch segment is less than K , it is assumed that the wave will 

 increase in height. 



To find the wave growth, first determine an equivalent fetch length Fg 

 for the initial wave (obtained directly from Figure 3-21 using the given wave 

 height, windspeed, and water depth). Secondly, the adjusted fetch F^ as 

 discussed in Chapter 3, Section IV, 2, a is determined using equations (3-45) 

 and (3-46) and Figure 3-38. The total fetch is then given as 



F = F + F (3-49) 



e a 



Reentering Figures 3-21 and 3-22 with the fetch length F and the adjusted 

 windspeed factor Ua and water depth d the wave height and period at the 

 end of the fetch segment. Yip and T , are determined. 



c. Wave Decay . If the initial significant wave height H^ at the 

 seaward or beginning edge of a segment of fetch exceeds the maximum signifi- 

 cant wave height H-^ for the given water depth of the segment of fetch and 

 the given windspeed, it may be assumed that the effects of the bottom friction 

 will exceed the effects of the wind stress. Therefore, the wave will decay, 

 will lose height, and over a long distance will approach a wave height equal 

 to the maximum significant wave height. 



The following steps are used to predict the decay of a wave: 



(a) At the seaward end of fetch segment determine the maximum 

 significant wave height Hg^ that would be generated for a given 

 windspeed and water depth, assuming an unlimited fetch and using Figure 

 3-21. 



(b) Determine the maximum stable wave height F^ at the seaward edge 

 of the fetch segment, where 



H^ = 0.78 d (3-50) 



(c) Determine the fractional reduction R^ at the seaward edge of 

 the segment of fetch under consideration. This is given by 



(d) Determine an equivalent initial wave height H^g , assuming that 

 fractional wave growth is proportional to fractional wave decay, by 



3-70 



