Q = Q, 



, 3Q 



o 3a 



f a - a 1 

 o 



(2] 



in v\fhich Q denotes the transport, Q , when the angle of the wave 

 incidence is a . Substituting equation (1) into equation (2) yields: 



Q = Q. 



9Q 



Sy 



C3] 



During the interval of time, dt , the shoreline recedes (or accretes) by 

 a quantity dy . Therefore, the volume of sand which is removed (or 

 deposited) over a length of beach, dx , is D dx dy . The quantity is 

 equal to the difference of longshore transport during time, dt , between 

 X and X + dx; i.e.. 



Q dt and : and ( Q + ^r^ dx ) dt ; 



o X 



3Q 



ax 



dt 



Therefore, 



Substituting the expression for Q , a being small, and defining 



K - 1^ 

 D da 



(5) 



yield: 



9x 



9y 

 9t 



(6) 



which is the well-known diffusion or heat-flow equation. 



K is approximately constant at a given site, 

 .6 



Bakker (1968a) found 



K equal to 0.4 x 10" cubic meters per meter depth per year, at an exposed 

 site along the coast of the Netherlands. Equation (6) demonstrates that the 



gy- 

 rate of accretion or (erosion), ^^ , is linearly related to the curvature of 



ot 



