The parameter A is determined from 

 o 1 



(A- 3) 



o L 3,2, 

 o o 



and Iwagaki found by empirical curve fitting 



1 H 



a = 1.3, n = 2 and m = tt for ^ < 0.55 



2 d - 



3 H 



a = 0.54, n = ^ and m = 1 for -y > 0.55 

 2 d 



Such that the elliptic integral, K, could be approximated by 



T/g/d 



Finally, in hyperbolic waves the wavelength is given by 



^1/2 2 H' 2 „ , „ 

 — = /2^ (— ) {1 _ _ (_) } [1 - 2 K d^ 

 o o o 



X {1 - a (^) } {1 _ (1 . --) --} (A-5) 



Again, it should be pointed out that equations (A-2) to (A-5) are only valid 

 for K > 3. 



To evaluate the hyperbolic wave theory the shoaling factor Kg is com- 

 pared with data and first-order cnoidal theory (Brink-Kjaer and Jonsson, 

 (1973). The results are shown in Figure A- 1 . 



It is evident that the results given by the hyperbolic theory are 

 worse than those obtained using linear cnoidal theory. For large wave 

 steepness the hyperbolic theory exhibits a decrease in K5 near breaking 

 similar to fifth-order Stokes waves which is also due to nonhomogeneous 

 convergence of the perturbation series. Finally, the wavelength predicted 

 by hyperbolic theory (not shown here) is quite close to the cnoidal wave- 

 length which is in itself questionable as examined earlier. Further 

 attempts at using hyperbolic wave theory to predict breaking wave character- 

 istics were abandoned because of the above shortcomings. 



42 



