52. In the same way, shoreline evolution of a bay formed in a circular 

 segment may be calculated. Equation 42 is superimposed with opposite sign on 

 a beach of width p (pitch height) . Figure 22 shows the solution. 





0.3- 





t 1 - i 













1 .0 









s. 









3J 



0.2- 



0.6 









o 



0.4______^— - 

















i- 

























01 













o 





0^2^^'^ 









kJ 













-z. 















0.1 - 



o.\s^ 









a; 

 o 









t'= 



ct 



CO 









a 2 







o/ 











0.0- 















1 



1 



i i 



0.5 1 1.5 



ALONGSHORE DISTANCE (x/a) 



Figure 22. Shoreline evolution of an initially circular 

 segment cut in a beach (a = 45 deg) 



Rhythmic Beach 



53. A beach with a rhythmic shoreline in the form of a cosine wave at- 

 tenuates with time but maintains its rhythmic character. The initial condi- 

 tion is 



y(x,0) = A cos ax 



(43) 



where A represents the amplitude of the rhythmic form such as cusps along 

 the beach, and a denotes the wave number of the shoreline oscillation or 

 cusp. The quantity a can be expressed also as 2tt/L , where L is the 

 beach cusp wave length. The solution to this case is found to be 



36 



