where f Is fetch and u is windspeed. For a ^ 0.0081 



H(f c , h, a) -HCfc. h, 0.0081) (^j) < 7 > 



An alternate way to estimate (a/0.0081) 1 '' 2 is to use Table 2 where (a/0.0081) 1/2 

 is provided for peak frequencies from 0.05 to 0.34 and windspeeds from 10 to 100 

 miles per hour (5 to 50 meters per second). (See App. B for metric version of 

 tables.) Appendix A describes the comparison of this method to field data. 



IV. EXAMPLE PROBLEMS 



**************** EXAMPLE PROBLEM l*************** 



GIVEN: A wave spectrum measured offshore has a significant height of 18 feet (6 

 meters) with a peak frequency f = 0.08 and a value of 0.0101. 



FIND : The depth-controlled wave height (spectral) H in 45, 30, 15, and 3 feet 

 0~5, 10, 5, and 1 meter) of water. 



SOLUTION : Calculate f Q = 0.9 f = 0.072, using 0.07. From Table 1 using, 

 a = 0.0081, find 



H = 14.9 feet (4.5 meters) in 45 feet 



H = 12.3 feet (3.8 meters) in 30 feet 



H = 8.9 feet (2.7 meters) in 15 feet 



H = 4.0 feet (1.2 meters) in 3 feet 



These values must be adjusted to (a/0.0081) l ' 2 = 1.11, but the correction is 

 very small in each case. Examination of field data indicates that in depths 

 less than 13 feet (4 meters), wave spectral densities in frequencies less than 

 0.1 hertz can be substantially smaller than the upper bound value in equation 

 (2), probably due to frictional effects and turbulence; H(f c , h, a) can be an 

 overestimate. Also note that h representing actual water depth including 

 tide, surge, and wave setup is used. 



**************** EXAMPLE PROBLEM 2*************** 



GIVEN: Hindcasts on a lake indicate that under design storm conditions, peak 

 frequencies were not expected to be any lower than 0.17 hertz for windspeeds 

 of 68 miles per hour (30 meters per second). 



FIND : The depth-controlled (spectral) wave heights in 30, 15, 10, and 3 feet 

 (TO, 5, 3, and 1 meter) of water. 



SOLUTION : Calculate f c = 0.9 f p = 0.9(0.17) = 0.153, using 0.15. From Table 1 

 using a = 0.0081, find 



H = 5.1 feet (1.6 meters) in 30 feet 



H = 3.9 feet (1.2 meters) in 15 feet 



H = 3.2 feet (1.0 meter) in 10 feet 



H = 1.8 feet (0.6 meter) in 3 feet 



11 



