PART III: SHORELINE MODEL AND THE SEAWALL BOUNDARY CONDITION 

 Shoreline Model Review 



33. The theory of the shoreline model originated with Pelnard-Considere 

 (1954). He assumed that the beach bottom, not necessarily of planar slope, 

 always remains in equilibrium and, as a consequence, moves in parallel to it- 

 self down to a certain depth, herein called the depth of closure. Therefore, 

 one contour, or "line," is sufficient to describe changes in beach planform. 

 This line is conveniently taken as the shoreline. Pelnard-Considere did not 

 develop a numerical model but did give closed-form mathematical solutions for 

 certain idealized cases and verified the results through laboratory experi- 

 ments. Details of the numerical formulation of the model may be found in, 

 e.g., Komar (1976, 1983), Le Mehaute and Soldate (1978) and Hanson and Kraus 

 (1980). 



34. The purpose of the shoreline model is to simulate long-term evolu- 

 tion of the shoreline or the beach planform. The governing equation for the 

 shoreline position is obtained from the continuity equation for beach sediment 

 (assumed to be cohesionless sand). A predictive formula for the sand trans- 

 port rate is necessary to solve the governing equation. Sand transport and 

 the resultant shoreline change depend on the local wind, waves, and currents, 

 beach planform, boundary conditions, and constraints such as the one produced 

 by a seawall. It will be assumed here that the longshore sand transport is 

 produced solely by obliquely incident waves; other transport mechanisms are 

 possible, such as coastal, tidal, and wind-generated currents. 



35. In the present work, it will be sufficient to use the equation for 

 the shoreline position in its most basic form: 



^U±^ = (1) 



3t D 3x 



where 



y = shoreline position, m 



t = time, s 



D = depth of closure, m 



Q = volume rate of longshore sediment transport, m-Vs 



x - distance alongshore, m 



15 



