Shorelines are usually irregular, and a more general method for estimating 

 fetch must be applied. A recommended procedure for determining the fetch 

 length consists of constructing nine radials from the point of interest at 3- 

 degree intervals and extending these radials until they first intersect the 

 shoreline. The length of each radial is measured and arithmetically 

 averaged. While 3-degree spacing of the radials is used in this example, any 

 other small angular spacing could be used. 



2. Simplified Wave-Prediction Models . 



Use of the wave prediction models discussed in Chapter 3, Section III 



(Wave Field) requires an enormous computational effort and more meteorological 



data than is likely to be found outside of a major forecasting center or 

 laboratory. 



The U.S. Navy operates an oceanic forecast facility at Monterey, 

 California, and the Corps of Engineers is developing a wave climate for U.S. 

 coastal areas using a sophisticated numerical model. The results of the 

 latter study are being published as a series of climatological reports by the 

 U.S. Army Engineer Waterways Experiment Station. 



Computational effort required for the model discussed in Chapter 3, 

 Section 111,1 (Development of a Wave Field) can be greatly reduced by the use 

 of simplified assumptions, with only a slight loss in accuracy for wave height 

 calculations, but sometimes with significant loss of detail on the distribu- 

 tion of wave energy with frequency. One commonly used approach is to assume 

 that both duration and fetch are large enough to permit an equilibrium state 

 between the mean wind, turbulence, and waves. If this condition exists, all 

 other variables are determined by the windspeed. 



Pierson and Moskowitz (1964) consider three analytic expressions which 

 satisfy all the theoretical constraints for an equilibrium spectrum. 

 Empirical data described by Moskowitz (1964) were used to show that the most 

 satisfactory of these is 



E(a)) do) = (ag2/a)5)e"^^'^^^'^'*^ do) (3-31) 



where 



_3 

 a = 8.1 x 10 (dimensionless constant) 



3 = 0.74 (dimensionless constant) 



g = acceleration of gravity 



U = windspeed reported by weather ships 



0) = wave frequency considered 



Equation (3-31) may be expressed in many other forms. Bretschneider 

 (1959, 1963) gave an equivalent form, but with different values for a and 3 

 A similar expression was also given by Roll and Fischer (1956). The condition 

 in which waves are in equilibrium with the wind is called a fulty av%sen 

 sea . The assumption of a universal form for the fully arisen sea permits the 



3-42 



