where K/^ is the refraction coefficient 



K/? 



1/2 



CA-11) 



and K is the shoaling coefficient 



K„ = 



r \i/2 



K for later use may also be approximated by the breaker height index 



CA-12) 



K, 



b 



H 



CA-13) 



where Hi is the wave height at the point of breaking. Thus, 



E = k2 k2 E 



R s o 



so V^ becomes 



cos a \ /C 



cos a y I C ) o 



K^ K^ C E sin a cos a 



R s g o 



(A-14) 



(A-15) 



By substituting equations (A-11) and (A-12) into equation (A-15) and canceling 

 like terms , 



P.£ = ^go ^o ^°2 "^ sin a 



(A-16) 



Equation 2.68 of Wiegel (1964) gives that 



r 2 



1 + 



, d 



47T - 



sinh 



(- ^)J 



(A-17) 



where d is the water depth. To a good approximation, n is equal to 0.5 in 

 deep water, i.e., d/L > 0.5, and n is equal to 1.0 in shallow water, i.e., 

 d/L < 0.04. (Exact values of n at these limits are 0.5117 at d/L equal to 

 0.5, and 0.9795 at d/L equal to 0.04.) Equation (A-16) can be further modi- 

 fied using Snell's law (where C is the local wave speed given by equation 

 (2-3) in the SPM) , 



C sin a 



(A-IJ 



19 



