If the wave crests make an angle, a with the shoreline, the energy flux 

 in the direction of wave advance per unit length of beaah is 



PgH^ 

 P cos a = — — C cos a , (4-26) 



8 * 



and the longshore component is given by 



— Pg 1 



?£ = P cos a sin a = -^ H C cos a sin a , 



8 * 



or since cos a sin a = 1/2 sin 2a 



Pp = 77 H^ C sin 2a . (4-27) 



* lo * 



The surf-zone approximation of Pj^, is written as P^.^. 



Pfi. = ll^S '^2ai, . (4-28) 



Usable formulations of this surf- zone approximation can be obtained by 

 several methods. The principal approximation is in evaluating C^ and H 

 at the breaker position. It is standard practice to approximate the group 

 velocity, Cg, by the phase velocity, C, at breaking. The phase velo- 

 city may then be approximated by either linear wave theory (Equation 2-3) 

 or by solitary wave theory (Equation 4-13). 



Figure 4-34 presents the longshore component of wave energy flux in 

 a dimensionless form, P^/pg^ H? T, as a function of breaker steepness, 



Hi/gT^, and the angle the wave crest makes with the shoreline in either 

 deep water a^, or at the breaker line, ai^. Figure 4-34 is based on 

 Equation 4-28 using linear wave theory to determine C^ and assuming that 

 refraction is by straight parallel bottom contours. Figure 4-35 can be 

 used to determine the longshore component of wave energy flux when breaker 

 height, H^,, period, T, and angle, aj,, are known- -for example, for 

 surf observation data. The use of Figure 4-34 is illustrated by an 

 example problem below. 



For linear theory, in shallow water, C^ « C and 



P«. = ^ Hfc C sin 2aj, , (4-29) 



where H^j and a^ are the wave height and direction at breaking and C 

 is the wave speed from Equation 2-3, evaluated in a depth equal to 1.28 

 Hi. 



4-91 



