b = exp - 



m 



2 2 

 2 a f 

 m 



f is the frequency of the spectral peak, and a , a , and y are 

 coefficients either fit to an observed spectrum or calculated as functions of 

 dimensionless fetch (Hasselmann et al., (1973, 1976). This formula is called 

 the Joint North Sea Wave Project (JONSWAP) spectral shape after the field 

 experiment on which it is based. Frequently, a single peaked spectrum is 

 fitted to this form if parametric analytic spectra are required for mathe- 

 matical analysis. 



Similar formulas can also be developed empirically from wind and wave 

 observations. A combined empirical-analytical procedure was used by Sverdrup 

 and Munk (1947) in the first widely used wave prediction system. The 

 Sverdrup-Munk prediction curves were revised by Bretschneider (1952, 1958) 

 using empirical data. This prediction system is therefore often called the 

 Sverdrup-Munk-Bretschneider ( SMB) method. 



More recent field data (Mitsuyasu, 1968; Hasselman et al., 1973) have 



resulted in some revisions to this method. The resulting curves are given in 



the next section. This wave prediction system is convenient when limited data 



and time are available. 



3. Formulas for Predicting Waves in Deep Water . 



It is desirable to have a simple method for making wave estimates. This 

 is possible only if the geometry of the waterbody is relatively simple and if 

 the wave conditions are either fetch-limited or duration-limited. Under 

 fetch-limited conditions, winds have blown constantly long enough for wave 

 heights at the end of the fetch to reach equilibrium. Under duration-limited 

 conditions, the wave heights are limited by the length of time the wind has 

 blown. These two conditions represent asymptotic approximations to the 

 general problem of wave growth. In most cases the wave growth pattern at a 

 site is a combination of the two cases. Equations (3-33) to (3-38) (Table 

 3-2) were obtained by simplifying the equation used to develop the parametric 

 model (Hasselmann et al . , 1976). Two dimensionless plots for wave growth are 

 given in Figures 3-21 and 3-22, which also include adjustments for shallow 

 water discussed in Chapter 3, Section IV. 



In the fetch-limited case, the parameters required are the fetch, F and 

 the wind-stress factor Ua (adjusted windspeed), where U. has been adjusted 

 as described in Chapter 3, Section IV, and represents a relatively constant 

 average value over the fetch. The spectral wave height H and peak 

 spectral period T are the parameters predicted. o 



m 



— r^- = 1.6x10 "* m \ (3-33) 



gT 



■^= 2.857x10"^ l^ \ (3-34) 



3-44 



