Barcilon (1978) used various models for the variation of Y through the surf 

 zone including one similar to that described above by Battjes (1978) based 

 on bore theory. Their case B = 32 gave 



X^ =-^+ 0.6 (114) 



Dalrymple (1978) concluded that no real progress in eigenvalue methods to 

 determine rip current spacings can be made until better surf zone energy loss 

 models are available. Also the use of time-average equations voids the possi- 

 bility to study real instability mechanisms, except those that evolve slowly. 

 Finally, it is also noted that neglect of the lateral shear-stress gradient 

 terms in the fundamental eqxiations also reduced the physical meaning of the 

 results. 



The primary motivation for solution of the fundamental equations is the 

 determination of nearshore currents, circulation patterns, rip currents, and 

 MWL variations. It quickly became obvious that for realistic bottom contours, 

 coastal planforms with manmade structures, and arbitrary incident wave con- 

 ditions, numerical solution methods were required. 



4. Numerical Models . 



Beginning with Noda (1972a), 11 efforts to build two-dimensional numeri- 

 cal models of nearshore circulation systems were uncovered. These are numbered 

 in Table 6 along with two other studies discussed below. Rese;archers at 

 Tetra Tech, Inc., Massachusetts Institute of Technology, University of Delaware, 

 and in Japan (Sasaki, 1977) and Holland (Vreugdenhil, 1980) have made major 

 contributions. Most of the models employed the finite-difference method 

 with some recent finite-element method efforts. 



a. Tetra Tech, Inc . As part of a research effort from 1968 to 1977 

 (summarized by Collins, 1977), researchers at Tetra Tech, Inc., Pasadena, 

 California, have developed a wave-induced circulation model (Noda, 1972a; Noda, 

 et al. , 1974) for regular waves. Wave-current interactions and shoaling were 

 included by a relaxation technique and the current refraction effects pro- 

 duced by even small currents resulted in major changes in the surf zone 

 driving forces and entirely different rip current patterns. The full motion 

 equations were not employed. For steady flows, the convective accelerations 

 and lateral turbulent mixing stresses were neglected. Tidal variations were 

 incorporated by making separate steady-state calculations every 3 hours. 

 Coastal flooding and water level setup were neglected. The pioneering ef- 

 forts of Noda, et al. (1974) are more valuable today for the refraction pro- 

 gram developed as part of the study. Because the study includes wave-current 

 interaction effects and is computationally efficient, it continues to be em- 

 ployed by coastal circulation modelers (Birkemeier and Dalrymple, 1976; 

 Ebersole and Dalrymple, 1979). 



b. Massachusetts Institute of Technology (MIT) . Liu and Mei (1975, 

 1976b) developed a finite-difference model to study the effects of offshore 

 and shore- connected breakwaters on nearshore circulation. A major part 



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