133. The wavelength Is calculated from the dispersion relation, 



L - L tanhp^j (13) 



To minimize computer execution time, a rational approximation (Hunt 1979) with 

 an accuracy of 0.1 percent is used to solve the transcendental Equation 13. 



134. The equation for depth -limited wave breaking is given by 



H b - 7Db (14) 



in which Dj, is the depth at breaking and the breaker index 7 is a function 

 of the deepwater wave steepness and the average beach slope (Smith and Kraus , 

 in preparation) : 



7 - b - a — (15) 



in which a = 5.00 [1 - exp(-43 tan/9)] and b = 1.12/[1 + exp(-60 tan/3)]. 



135. The wave angle at breaking is calculated by means of Snell's law, 



sing b = sin *i ,, 6) 



Lb Li 



in which 9 b and Lj, are the angle and wavelength at the break point, and 

 8 X and h x are the corresponding quantities at an offshore point. 



136. The three unknowns, H b , Dj, , and 8 h , are obtained at inter- 

 vals alongshore by iterative solution of Equations 9, 14, and 16 as a function 

 of the wave height and angle at the reference depth and the wave period. 



137. Wave refraction models provide the undiffracted breaking wave 

 angle 8 h in the fixed coordinate system. With reference to Figure 10, the 

 breaking wave angle to the shoreline required to calculate the longshore sand 

 transport rate, Equation 2, is obtained as 



(17) 



65 



