* ■ Q o( 2a o - 2 If) (8) 



13. If the amplitude of the longshore sand transport rate and the inci- 

 dent breaking wave angle are constant (independent of x and t) the follow- 

 ing equation may be derived from Equations 1, 2, and 8: 



. 4 - H (9) 



where 



2Q 

 £=-/ (10) 



14. Equation 9 is formally identical to the one-dimensional equation 

 describing conduction of heat in solids or the diffusion equation. Thus, many 

 analytical solutions can be found by applying the proper analogies between 

 initial and boundary conditions for shoreline evolution and the processes of 

 heat conduction and diffusion. The coefficient e , having the dimensions of 

 length squared over time, is interpreted as a diffusion coefficient expressing 

 the time scale of shoreline change following a disturbance (wave action) . A 

 high amplitude of the longshore sand transport rate produces a rapid shoreline 

 response to achieve a new state of equilibrium with the incident waves. Fur- 

 thermore, a larger depth of closure indicates that a larger part of the beach 

 profile participates in the sand movement, leading to a slower shoreline 

 response. 



15. If the amplitude of the longshore sand transport rate is a function 

 of x , the governing differential equation for the shoreline position will 

 take a different form: 



2 



3 y , de 3y _ de , 3y nn 



„ 2 dx 3x o dx 3t 



3x 



where it is assumed that the depth of closure is constant. Equation 11 makes 

 it possible, in a simplified way, to account for diffraction behind a groin, 

 where the wave height varies with distance alongshore. However, the 



11 



