c. A numerical scheme in which the effect of wave diffraction could be 

 included. 



d. A statistical characterization of wave climate and longshore energy 

 flux. 



Examples of recent prototype analysis and prediction of shoreline 

 evolution by mathematical modeling are Apalachicola Bay by Miller (1975) 

 and the Oregon coastline by Komar, Lizarraga-Arciniega, and Terich (1976) 

 Both studies are based on numerical schemes related to the Pelnard- 

 Considere (one-line) formulation. 



VII. CONCLUSIONS 



There are two methods of approach to the problems related to littoral 

 processes. The first one, typified by the previously discussed reports, 

 consists of analyzing global effects. The method essentially based on 

 establishing "coastal constants" for a model by correlation between 

 long-term evolution and wave statistics and subsequently, to use the 

 model for predicting future effects. It appears that this method is the 

 most promising for engineering purposes and could be termed the macro- 

 scopic view. The main results are summarized in Table 2. 



The second approach, the microscopic view of the problem, consists 

 in analyzing sediment transport, step-by-step, on a rational Newtonian 

 approach, starting with wave motion, threshold velocity for sand trans- 

 port, equilibrium profiles of beaches, etc., until the individual com- 

 ponents can be combined into an overall model to predict shoreline 

 evolution. The second method or scientific approach has not progressed 

 to the point where it can be applied to engineering problems in the 

 foreseeable future. 



However, much progress has been made in the last 5 years toward 

 understanding the hydrodynamics of the surf zone through application of 

 the "radiation-stress" concept. In theory, establishing a reliable 

 mathematical model of surf zone circulation should permit a determina- 

 tion of the resulting sediment transport. Practically, however, inter- 

 action between a movable bed and the surf zone circulation, and the 

 inherent instability of longshore currents limit this approach to the 

 realm of research. Among the problems that make this approach difficult 

 are the refraction and diffraction of water waves, uncertainty in pre- 

 dicting rip current spacing, and the effect of free turbulence generated 

 by breaking waves on the rate of sediment suspension. 



Finally, the complexity of mathematical formulation, based on the 

 radiation-stress concept, makes it difficult to use as a predictive tool 

 when dealing with forcing functions expressed by statistical multi- 

 directional sea spectra. This method is promising in explaining local 

 effects (e.g., near groins), rhythmic topography, beach cusps, and short- 

 term evolution due to unidirectional sea states. All these effects are 



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