^ = 6.88x10^ m \ (3-35) 



Note that T, /n is given as 0.95 1^ . The preceding equations are valid up 

 to the fully developed wave conditions given by 



-1 

 — r^ = 2.433x10 (3-36) 



"a 



1^ 



"a 



= 8.134 (3-37) 



££. = 7 1 "iirin^ 

 ^A 



y = 7.15x10 (3-38) 



where 



H = the spectrally based significant wave height 

 m 

 o 



T = the period of the peak of the wave spectrum 



F = the fetch 



t = the duration 



Ua = the wind-stress factor 



Often in applying the wave growth formulas, the engineer must determine if the 

 design situation is fetch limited or duration limited. In these cases 

 estimates of a one half- to 5-, etc. hour windspeeds with some return period 

 (often 25 or 50 years) may be available. The objective is to find the largest 

 wave height that occurs under these conditions. For example, a given return 

 period, the 30-minute windspeed, will be higher than the 1- to 3-, etc. hour 

 windspeeds, but because of its short duration it may produce a smaller wave 

 height than the 1-hour windspeed. 



A given calculation for a duration should be checked to ensure that it has 

 not exceeded the maximum wave height or period possible for the given wind- 

 stress factor and fetch. The nomograms in Figures 3-23 and 3-24 show wave 

 prediction curves of empirical values which can be used to check the 

 reasonableness of the mathematical solutions. For example, for U^ = 20 

 meters per second a duration of 5 hours yields a height of 2.5 meters. 

 However, if the fetch were only 30 kilometers long, the maximum wave height 

 can only be 1.75 meters for a wind-stress factor of 20 meters per second. If 

 the wind-stress factor is 20 meters per second and its duration is only 3 

 hours, the fetch-limited wave height of 2.5 meters for a fetch of 30 

 kilometers would not be reached; therefore, the wave height is duration 

 limited. It is essential that fetch-limited wave calculations be checked to 

 see if they are duration limited; likewise, duration-limited cases should be 



3-47 



