(c) Waves are completely absorbed at shorelines. 



Fetch distances determined in this manner usually are less than those 

 based on maximum straight- line distances over open water. This is true 

 because the width of the fetch places restrictions on the total amount of 

 energy transferred from wind to water until the fetch width exceeds twice 

 the fetch length. 



While 6° spacing of the radials is used in this example, any other 

 angular spacing could be used in the same procedure. 



3.5 SIMPLIFIED WAVE-PREDICTION MODELS 



Use of the wave-prediction models discussed in Section 3.3, Wave 

 Field, requires an enormous computational effort and more meteorological 

 data than one is likely to find outside of a major forecasting center. 

 The Fleet Numerical Weather Center, Monterey, California began using this 

 model on an experimental basis for a small part of the globe early in 1972. 

 Expansion to larger regions is planned. Wave prediction begins with a com- 

 putation of the existing wave field (often called a zero-time prediction), 

 and continues with a calculation of the effects of predicted winds on the 

 waves. A few years after this system is operational, it should be possible 

 to supply the needs for wave-hindcast statistics by compilations of zero- 

 time predictions. In the meantime, engineers who require wave statistics 

 derived by hindcasting techniques for design consideration must accept 

 simpler techniques. 



Computational effort required for the model discussed in Section 3.31, 

 Development of a Wave Field, can be greatly reduced by the use of simpli- 

 fied assumptions with only a slight loss in accuracy for wave height cal- 

 culations, 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 equi- 

 librium state between the mean wind, turbulence, and waves. If this 

 condition exists, all other variables are determined by the wind speed. 



Pierson and Moskowitz (1964) consider three analytic expressions which 

 satisfy all of the theoretical constraints for an equilibrium spectrum. 

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

 most satisfactory of these is 



-flCw^/w*) 

 E(co)da; = (ag^/co*) e " dco , (3-20) 



where a and 3 are dimensionless constants, a = 8.1 x 10 3, g = 0.74 

 and too - g/U, where g is the acceleration of gravity and U is the 

 wind speed reported by weather ships, and o) is the wave frequency 

 considered. 



Equation 3-20 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 



3-33 



