************** EXAMPLE PROBLEM 



*************** 



GIVEN : A breaking wave with height, Hj, = 4 feet; period T = 7 seconds. 

 Surf observations indicate that the wave crest at breaking makes an 

 angle, ajy = 6° with the shoreline. 



FIND ; 



(a) The longshore component of wave energy flux. 



(b) The angle the wave made with the shoreline when it was in deep 

 water, Uq. 



SOLUTION : Calculate 



Hfe 4.0 



-— = r = 0.00254 . 



gT^ 32.2 (7.0)2 



Enter Figure 4-34 to the point where the line labeled aj, = 6" crosses 

 H2,/gT2 = 0.00254 and read Pji/pg^ "f "^ = 6.7 x lO"** from the left axis 

 and a(-) = 18° from the bottom axis. 



The longshore energy flux can then be calculated as, 



Pg = 0.00067 pg2 Hi T , 



Pg = 0.00067 (2) (32.2)2 (4 q)2 (70) . 



Pg = 155.6, say 160 ft.-lb./ft.-sec. , 



and 



«o = 18° • 



************************************* 



For offshore conditions, the group velocity is equal to one-half the 

 deepwater wave speed C^, where C^ is given by Equation 2-7, and the 

 refraction coefficient, K^, can be determined by the methods of Section 

 2.32. Hence, 



P£s = ^T(H^K^)2 3i„2a, . (4-30) 



Figure 4-35 also presents the longshore component of wave energy flux 

 in a dimensionless form, P£,/(pg^ H^ T), as a function of deepwater wave steep- 

 ness, H^/gT^, and the angle the wave crest makes with the shoreline in 

 either deep water, a^, or at the breaker line, a^,. Refraction by 

 straight parallel bottom contours is again assumed. As illustrated by 



4-93 



