49. For notational convenience, a prime on a quantity will denote its 

 value at the next (future) time step; an unprimed quantity is evaluated at the 

 present time step. Quantities at the present time step are known. In custom- 

 ary notation, the next time step is denoted by a superscript n + 1 and the 

 present time step is denoted by a superscript n . The customary notation 

 will be used in certain applications to follow. 



50. For the purpose of implementing a boundary condition, or con- 

 straint, the explicit model is convenient since (a) only immediately neigh- 

 boring values of Ch and y* are involved, and (b) the implementation only 

 involves the present shoreline position and present transport rates; no quan- 

 tities at the next time step are used. 



51. If the shoreline moves landward of the position of the seawall at a 

 certain grid point, thus violating the seawall constraint, the longshore sand 

 transport rate must be corrected to conserve sand volume. The (nonphysical) 

 erosion, or retreat, of the shoreline to a position behind a seawall, as shown 

 in Figure 7, results in a nonphysical additional transport of sand out of the 

 associated calculation cell. The transport rates at the cell faces must 

 therefore be corrected to prevent the shoreline from moving behind the sea- 

 wall. The correction must be made with consideration of the direction of 

 transport at the two faces of the particular cell violating the seawall con- 

 straint. Only minus cells and regular cells may require correction. The sea- 

 wall constraint is never violated at a plus cell, because the shoreline always 

 advances in a plus cell. 



52. The calculation procedure is described in detail next. An overview 

 is as follows. First, the transport rates along the beach are calculated in 

 order to determine the transport directions and to identify minus, plus, and 

 regular cells. Then, as required, corrections start at either a seawall bound- 

 ary or the first minus cell encountered in the search. After the starting 

 cell is corrected, corrections to regular cells are made as necessary follow- 

 ing the direction(s) of the longshore transport, until either a plus cell or a 

 lateral boundary is reached. This procedure is repeated at each time step. 



Correction at a 



minus cell (Figure 7a) 



53. Since correction is necessary, the shoreline position y! lies 

 behind the seawall. The general principle governing transport corrections is 

 that the transport rate at a downdrift cell face should be reduced to a value 



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