expected to provide an accurate approximation under typical wave conditions, 

 for which the breaking wave angle is small (less than 30). The linearization 

 method was introduced by Perlin and Dean (1978) for use with the CERC formula, 

 Equation 2. The method was extended by Kraus and Harikai (.1983) to account for 

 an additional contribution arising from a systematic change in breaking wave 

 height alongshore COzasa and Brampton 1980), as caused, e.g., by wave diffrac- 

 tion. These references should be consulted for details. The final result is 

 that the transport rate at the new time step can be expressed in the form 



Q i = E i (y i-1 + y P + F i (15) 



where E! and F! are functions of the incident wave parameters. Substitu- 

 tion of Equation 13 into Equation 15 gives a tridiagonal system of equations 

 for the Q! . A tridiagonal system can be solved by an efficient standard 

 algorithm, called the double-sweep algorithm. The solution is based on the 

 following recurrence relation: 



Q! = EE! Q! , + FF! (16) 



l l 1+1 l 



where 



B! 



EE i = 1 + B! (2 - EE! ,) (17) 



l 1-1 



F! + E! (yc. , - yc.) + B! FF! , 



FF . - -i 1 ^ —1 1 Izl ( 18 ) 



l " 1 + B! (2 - EE! .) V l0; 



l 1-1 



B! = B E! (19) 



li 



63. The solution procedure, prior to making any corrections to account 

 for the seawall, is as follows: 



a. Specify a boundary condition at i = 1 in terms of EE! and 



FF! . 



l 



b. Solve Equations 17 and 18 for i = 2 to N, in ascending order. 

 This constitutes the first sweep. 



c. Specify a boundary condition for Q' 1 



26 



