in sand transport, which might be in conflict with the imposed criterion 

 specifying transport direction. Furthermore, in such a case, the magnitude of 

 sand transport would increase as D decreased to reach a maximum if no energy 

 dissipation occurred. This is an incorrect description of what is expected to 

 occur, since a cutoff energy dissipation exists under which no sand transport 

 takes place. (See Kraus and Dean (1987) and Kraus , Gingerich, and Rosati 

 (1989) for empirical evidence of an effective cutoff in longshore sand 

 transport in the surf zone.) Consequently, the logical decision is to set q 

 to zero if D falls below D . Also, from Figure 48 it can be inferred 

 that the transport rate is small if D approaches D^^ (the situation 

 distant from the break point) . 



408. Physically, the equilibrium energy dissipation represents a state 

 in which the time-averaged net transport across any section of the beach 

 profile is zero. The equilibrium energy dissipation may be expressed in terms 

 of the beach profile shape parameter A in the equilibrium profile equation 

 (Equation 1) according to 



^e, = I4 PE,"'-y' A^'2 (35) 



where 7 is the ratio between wave height and water depth at breaking 

 (breaker index, Hj^/h^,) . In the derivation of Equation 35, Dean (1977) assumed 

 that the wave height existed in a fixed ratio with the water depth in the surf 

 zone. 



409. From Equation 34 it may be deduced that D inherently contains a 

 term proportional to the beach slope. The reason for incorporating an 

 explicit slope dependent term in the transport relationship (Equation 33) is 

 that regression analysis showed a dependence of q on slope for some of the 

 cases analyzed in Part V. Also, numerical stability of the model was improved 

 by inclusion of this term, as will be discussed below. Dean (1984) also 

 modified the equilibrium energy dissipation by reducing it depending on the 

 ratio between the local beach slope and the limiting slope for the sand 

 surface, thus including a further slope dependence (cf. Watanabe 1985). 



410. As discussed in Part V, the value of the transport rate coeffi- 

 cient K determined by comparison of calculated energy dissipation per unit 



168 



