This equation, which is also presented in Figure 4, predicts the relative 

 transport at point y. To obtain the fraction of transport between two y 

 coordinates, the integral of equation (25), from yi to y2, must be 

 used. 



^x = ^x 



Ji J yi 



-e 



[(y2+ a)/(1.25 y^^)]^ (26) 



QxCND] is dimensionless; therefore, to compute a value in, say, cubic feet per 

 second, it must be multipled by the total transport along a perpendicular to 

 the shoreline obtained from the total longshore transport equation used in 

 the model 



Q = C H^^/^ sin (2 a^^) (27) 



See Appendix A for a discussion of the constant C. It is noted that the 

 transformation of qx(y) to qx(h) can be effected by multiplying by the 

 one-dimensional Jacobian (Ay/^h). This latter form (qx(h)) is more useful 

 here because the present model simulates the changes in contour position (Ay) 

 rather than changes by depth (Ah). 



In the numerical model, Qx (I, J) (see Fig. 1) is determined using 

 equation (26) except for the shoreline contour, J=l, and the farthest 

 offshore contour simulated, J = JMAX. The shoreline contour longshore 

 transport, Qx (1,1), in order to include swash transport, uses equation 

 (16); however, the first term is set equal to 1.0. The seawardmost contour 

 transport, Qx (I, JMAX), in order to include any longshore transport not yet 

 accounted for, neglects the second term of equation (26) (i.e., it accounts 

 for transport from y(I,JMAX) to infinity). The dimensionless numbers are 

 then multiplied by Q determined from equation (27). This method is based on 

 parallel contours which may not exist. In order to compensate for the 

 nonparallel nature of the contours (note that refraction does account for it 

 as far as the wave field is concerned), the term sin (2ab) of equation (27) 

 is replaced by sin (2aL) shoreward of the breakpoint, where aL represents 

 the angle between the "local" wave angle and the "local" contour. It can be 

 argued that for a spilling breaker, the remaining surf zone at any point 

 "sees" a total transport similar to equation (27), where a[j and H^ are 

 the local values. The problem is that the constant of proportionality was 

 determined for the entire surf zone and for nearly straight and parallel 

 contours. This not being the case, the equation was altered on intuitive 

 grounds to reflect the fact that the contours are no longer straight and 

 parallel . 



21 



