j^ = 0.14 tanh {(0.8 + 5S) 2-nd^/L^} S < 0.1 

 b 



j^ = 0.14 tanh {(0.13) 27rd,/L, } S > 0.1 



(9) 



b 



To obtain the breaking wave characteristics, the two offshore 

 parameters (sin a/C*, C4) must be known where 



a = angle of incidence 



C = wave phase speed C = C/(gT) 



g = gravity acceleration 



T = wave period 



C4 = T yj {(^)^ n sin a)}-^/4 



d = Stillwater depth 



1 ,, 2kd , 



2 sinh2kd 



k = 2tt/L 



L = wavelength 



In the deepwater limit this implies that wave height, Hq, angle 

 of incidence, ag, and wave period must be known independently. The 

 solution requires an iteration process and nomographs are presented 

 to facilitate the operations. 



The method for determining breaking wave characteristics sug- 

 gested by Ostendorf and Madsen (1979) has been compared with experi- 

 mental data (Kamphuis, 1963), and it was found that the predicted 

 breaking wave angle is too large, especially for smaller wave steep- 

 nesses (see Table 1). This is easily explained when considering the 

 plot of wavelength transformation shown in Figure 10. Although 

 cnoidal theory predicts wave height well up to breaking, it overpre- 

 dicts wavelengths significantly. Cnoidal theory, in fact, predicts 

 an increase in wavelength and therefore, also in wave angle when H/d 

 is sufficiently large. This increase is, as previously mentioned, 

 not reflected by known data (Ippen, 1966; Fig. 11), which are fitted 

 quite well by linear theory. As another consequence, the wave break- 

 ing criterion, again, a result which is difficult to defend. 



Dean (1974) determined wave breaking angles using his stream 

 function theory, but with a slope- independent semiempirical breaking 

 criterion. A comparison of his results with the experimental ob- 

 servations of Kamphuis (1963) is also presented in Table 1. The 



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