yHi,2 



2.5 



(31) 



Equating Fj^ and F^j 



N/2 

 16 Z [a2(n) + b2(n)]Cg(^) cos ct^ 

 n=l 



:2 /7 



0.4 



(32) 



Note that neglecting wave refraction in the breaking depth determination does 

 not result in very large errors; e.g., for a wave direction at the gages of 

 30°, the error in breaking depth would be less than 6 percent. For a more 

 realistic overall wave direction of 20°, the associated error in breaking depth 

 is less than 3 percent. 



c. Transformation of Wave Components to Shore . With the breaking depth 

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

 refraction and shoaling as based on linear wave theory. Wave refraction was 

 computed in accordance with Snell's law and the assumption that straight and 

 parallel contours existed between the gage and breaking locations, 



Cb(n) = sin 



-1 



'CR(n) 



aj^(n) 



(33) 



Shoaling was based on linear theory, resulting in the value of the sums of 

 the squared FFT coefficients at the breaker line of 



cos a (n) [C (n)] 



in which the first and second ratios on the right side of the equation repre- 

 sent the effects of refraction and shoaling, respectively. 



d. Computation of ?^^ at the Surfline ^ With the wave energy and direction 

 known at the breaker line, the value of the wave energy flux factor, P^g* is 

 readily determined. 



Pj^s = g{2y E [a2(n) + b2(n)]b Cgb(n) [cos a (n) sin a(n)]b (35) 

 I n=l I 



where the factor G is given by the ratio 



G = 



TOT 



(36) 



as defined in and discussed in relation to equation (28). 



34 



