such a complex scheme, which is plagued with numerical instabilities, 

 are shown in Fig. 18. Even though the results show how oblique waves 

 initiate an erosion pattern that might eventually lead to the formation 

 of hooklike beaches, they do not show that the beaches represent a good 

 fit to segments of a logarithmic spiral. 



Rea and Komar (1975) developed an approach to overcome the numeri- 

 cal instability encountered by Leblond. They combined two orthogonal, 

 one-dimensional arrays as shown on Fig. 19. In this way, deformation of 

 the beach can proceed in two directions without the necessity of a two- 

 dimensional array. The wave configuration in the shadow zone was 

 described by various simple empirical functions which resulted in beach 

 configurations fairly approximated by a logarithmic spiral. 



The main interest in the work of Rea and Komar (1975) is that they show 

 the lack of sensitivity of the shoreline evolution in the shadow zone to 

 the actual pattern of incident waves used. Also, the sensitivity of the 

 beach shape to the energy distribution seems to be small. 



VI. PROTOTYPE APPLICATIONS 



The application of mathematical models of shoreline evolution to pro- 

 totype conditions is not very well documented in the literature. It is 

 certain that, at least in its simplified form such as given by Pelnard- 

 Considere, the method has been used by practicing engineers and designers. 

 It has been reported in unpublished reports but very little has appeared 

 in the open literature. 



Weggel (1976) has formulated a numerical approach to coastal process- 

 es which is particularly adapted to prototype situations. In particular, 

 it includes: 



a. A method for determining the water depth beyond which the onshore- 

 offshore sediment transport is negligible. This information is particu- 

 larly useful in determining the quantity D used in Pelnard-Considere' s 

 theory and others. It is also useful in determining the effect of a 

 change of sea level. Beach profile data are plotted on semilog paper 

 and the base elevation of the most seaward point varied until an approxi- 

 mate straight line is obtained (see Fig. 20). He found D = 70 feet at 

 Pt. Mugu, California. 



b. The effect of a change in sea level, a situation pertinent to the 

 Great Lakes, is also taken into account in a way proposed by Bruun 

 (1962). Using the principle of similarity of shoreline profile, the 

 shoreline recession Ay is related to the change of water level a by 

 the relationship (Fig. 21): 



44 



