Assuming that the breaking wave angle, 0, , is small, that the waves will 

 break under shallow-water conditions, and that the ratio of breaking wave 

 height to depth is a constant, the breaking wave height, fL, is then given 

 by 



[ N/ 2 ) / GB \° * 2 



H b = I 16 [a(n) 2 + b(n) 2 ] C g (n) cos 0(n) 0' 4 ( — J 



(23) 



where GB is the ratio of root-mean-square (rms) breaking wave height to 



breaking depth, GB = H,/d, (here assumed GB = 0.78). With the breaking depth 



known, each wave component is transformed to shore accounting for both wave 

 refraction and shoaling based on linear wave theory. 



Wave refraction is in accordance with Snell's law and the assumption 

 that straight and parallel contours existed between the gage and breaking 

 locations 



b (n) = sin" 



C r (n)_ 



sin r (n) 



(24) 



where C is linear wave celerity (see the SPM, Ch. 2) in which the r sub- 

 scripts denote the "reference (gage)" location. 



With the wave energy and direction now known at the breaker line, the 

 value of the longshore energy flux, (Po s ) cm > is readily determined 



(P 9e ) 



£s 'cm 



R(Po c ) 



£s'c 



N/2 

 = R J2y I [a 2 (n) + b 2 (n)] b [C g (n)] b [cos 0(n) sin 0(n)] fa 

 n=i 



in which the factor R is given by the ratio 



En 



(25) 



R = 



J T0T 

 E 



as defined in and discussed in relation to equation (21). 



III. MAIN PROGRAM DOCUMENTATION 



The detailed programing steps in analysis for the longshore energy flux, 

 (Po ) , (which in this program is calculated in terms of rms wave height) are 

 presented in this section. Program steps are numbered to correspond to areas 

 in the program listing where computations are carried out. A program listing 

 with corresponding numbered steps follows the program documentation. Note 

 that preceding text has used the indexes j and n for time and frequency, 

 respectively, while the program which follows uses the index I for both time 

 and frequency. A listing of the main program is presented in Figure 2. 

 Program steps are as follows and refer to numbered parts of main program 

 listing: 



13 



