the coast, the derivative of the longshore transport rate with respect 



to the angle of the wave incidence, 

 tional to the beach depth, D . 



dQ 

 da 



and inversely propor- 



The above equation will be recognized as the well-known diffusion 

 equation. A number of classical solutions of mathematical physics are 

 applicable to the diffusion equation when boundary conditions are 

 specified. Pelnard-Considere (1956) applied his theory to the case of 

 a littoral barrier or long groin. This case is reviewed below: 



The longshore transport rate along a straight, long beach is sudden- 

 ly stopped by the construction of a long groin built perpendicular to 

 the beach (see Fig. 2). The boundary conditions are: 



(a) y = o for all x when t = o which characterizes an 

 initial straight shoreline. 



(b) At the groin, the longshore transport rate Q = o which is 

 realized when the waves approach the shore normally; i.e., when 



9y = -tan a at x = o , 



37 



(c) 3y = o at a large distance updrift ( x ^ «> ) , and Q = Q 



Q is the steady-state longshore transport along a straight beach 

 for the given wave conditions. The solution for the given boundary 

 conditions is: 



^Kt exp (-U ) - X y/V E (u) 



(7) 



where u =^j^y/^^and E (u) is the Fresnel integral, 



E (u) 



Vtt~ 



C8) 



Values of E (u) or more frequently, (J) (u) = 1 - E (u) , can be found 

 in tabulated form as given in Table 1: 



16 



