PART III: SOLUTIONS FOR SHORELINE EVOLUTION 

 INVOLVING COASTAL STRUCTURES 



60. In the previous chapter, the incident wave crests were restricted 

 to be parallel to the x-axis. In such a case, an initially straight beach 

 will always remain straight, unless material is supplied in an irregular way. 

 If the waves arrive at the same angle to the shoreline everywhere, the beach 

 will also be stable if it is initially straight. However, if an obstacle on 

 the beach disturbs the equilibrium transport conditions, a change in shoreline 

 position occurs in order to achieve a new steady-state configuration. Exam- 

 ples of such obstacles are groins, jetties, detached breakwaters, and sea- 

 walls. In order to treat such complex cases analytically, the situation has 

 to be idealized to a large degree. Properties which generally vary continu- 

 ously along the shoreline (breaking wave angle, amplitude of the sand trans- 

 port rate, etc.) usually must be approximated by means of a series of coupled 

 solutions of simpler problems. Within each solution area the properties are 

 held constant but are allowed to vary from one area to another. 



Shoreline Change at Groins and Jetties 



61. The analytical solution for beach change at a groin or any thin 

 shore-normal structure which blocks alongshore sand transport was first ob- 

 tained by Pelnard-Considere (1956). Initially, the beach is in equilibrium 

 (parallel to the x-axis) with the same breaking wave angle existing every- 

 where, thus leading to a uniform sand transport rate along the beach. At time 

 t = a thin groin is instantaneously placed at x = , blocking all trans- 

 port. Mathematically, this boundary condition can be formulated as (see 

 Equation 7) 



P- = tan a x = (62) 



8x o 



This equation states that the shoreline at the groin is at every instant 

 parallel to the wave crests. The wave crests make an angle a with the 

 x-axis according to Figure 28, giving rise to longshore sand transport in the 

 negative x-direction. 



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