U M U2 ' U / 



and 



i^,f,(^,^l . C3) 



U / 



where g is the acceleration of gravity, T the wave period, U the 

 reference velocity of the wind, F the fetch length, t the duration 

 of the wind, and H the height. The functions fj and £2 cannot be 

 determined from dimensional analysis, but may be estimated from observa- 

 tions or theoretical considerations. Many secondary variables may be 

 included in equations (2) and (3) . Wiegel (1964) reviewed much of the 

 empirical data in support of this formulation and discussed the quality 

 of the data from various sources. Figure 4 is a compilation of data from 

 many individual studies (Wilson, 1955). The reference velocity used by 

 Wilson is an "anemometer wind." The importance of providing a precise 

 definition of the reference wind velocity was not fully recognized when 

 most of the data used by Wilson were gathered. Much of the later data have 

 been better documented, and at least three distinctly different definitions 

 of the reference velocity have been widely used. Similar figures have 

 been presented in other reports. The data in Figure 4 can be approx- 

 imated by a smooth curve, and for most of the figure, variability about 

 the smooth curve is no more than a factor of 2 or 3, although the dimen- 

 sionless wave height and period vary by factors of more than 100. A 

 relation which is reliable within a factor of 2 or 3 as the primary variable 

 changes by factors in excess of 100 represents a great deal of predictive 

 skill. However, it also leaves something to be desired for accurate 

 engineering calculations. 



Analytic equations for curves which summarize data of the type showrt 

 in Figure 4 (derived by many authors) are given in Table 1. Graphs of 

 these equations for comparison with Figure 4 are shown in Figure 5. Some 

 of the spread in data and in the curves is due to differences in the defini- 

 tion of the reference velocity. In some earlier studies, U was defined 

 as the anemometer wind without specifying the height of the anemometer or 

 other information relating the reference windspeed to the actual overwater 

 wind. An attempt was made to adjust many of the observations to a stand- 

 ard anemometer height of 10 meters, but the procedure employed in the 

 adjustment is not always clear. The curves diverge more for values of 

 gF/U^ > 10*^ than for shorter fetches. 



The equations derived by Bretschneider (personal communication, 

 1970-71) have been used in the construction of a nomograph for estimating 

 wave height and period from estimated values of windspeed, fetch, and 

 duration. This nomograph and the defining equation are in the "Shore 

 Protection Manual" (SPM) (U.S. Army, Corps of Engineers, Coastal Engineering 



16 



