predictions are consistently too high, especially for smaller wave 

 steepness, where predicted and observed a^ differ by a factor of 

 approximately 2. 



Table 1. Comparison of measured and predicted 

 breaking wave angles.^ 



Ho 



Lo 



■- ■ 

 0.0175 



0.04 



0.053 



0.062 



% 





20° 



40° 



60° 



20° 



40° 



20° 



40° 



20° 



40° 





Kamphuis 

 (1963) 



Ostendorf 

 and Mads en 

 (1979) 



Dean 

 (1974) 



5° 

 10° 



9.5° 



go 

 18.6° 



19° 



12° 

 24.3° 



22° 



8° 

 12.8° 



13° 



16° 



24.3° 



25° 



10° 

 13.9° 



14° 



20° 

 26.5° 



27° 



11° 

 14.5° 



14.5° 



22° 

 28.8° 



28° 



^Beach slope, S = .1 



2 . Solution Approach . 



To obtain reliable prediction of breaking wave characteristics, 

 this study proposes to use cnoidal theory to describe the transformation 

 of wave height while wavelength will be transformed using either linear 

 wave theory or third-order Stokes theory. The cnoidal wavelength is 

 then considered as an auxiliary parameter which cannot be identified as 

 the physical wavelength. Linear wave theory is simpler to use; however, 

 to retain some nonlinear effect in the transformation of wavelength the 

 third-order Stokes theory is also included. The wavelength computed 

 using the cnoidal third-order Stokes theory is shown in Figure 11. 



Due to the large wave heights near breaking, a higher order approxi- 

 mation to cnoidal waves given by Iwagaki (1968) was considered. A more 

 detailed discussion of this "hyperbolic" wave theory is given in the 

 Appendix. Note that this higher order theory suffers from the same prob- 

 lem of inhomogeneous convergence as, for example, plagues fifth-order 

 Stokes waves (Le Mehaute and Koh, 1966), and therefore gives poorer 

 results than the first-order cnoidal theory near breaking. 



The computation and shoaling of cnoidal waves have been given by 

 Svendsen (1974) and Svendsen and Brink-Kjaer (1972). It is convenient 

 to define the parameter 



U = — ^ = ^ mK^(m) (10) 



where 



= wave height 

 ^ = cnoidal wavelength parameter 



26 



