Modern developments in the study of breaking waves through 1976 are re- 

 viewed in Longuet-Higgins (1976). A new numerical method is revealed which 

 uses a mixed Eulerian-Lagrangian technique in that both a velocity potential 

 and marked particles are employed. This numerical method can follow the 

 development of the jet in a plunging-type breaker, as shown in Figure 31 

 (from Cokelet, 1978). Details of the development of the simulation technique 

 can be found in Longuet-Higgins and Cokelet (1976), and Cokelet (1978), and 

 it continues to be researched in subsequent papers on the subject (e.g.. 

 Peregrine and Cokelet, 1980). Much of the initial effort has concentrated 

 on deepwater wave breaking. 



In July 1978 a research colloquim, Euromeoh 102^^, was held with the ex- 

 press purpose to present the latest developments in wave breaking research. 

 Natural waves break for a large number of reasons: surface winds, shoaling, 

 depth or current refraction, wave-wave interactions, wave energy concentra- 

 tion, reflections, and by relative motion between the water and a solid 

 boundary. Peregrine (1979) stated that whatever the cause, the local motion 

 of the water particles involved in the breaking process can be very similar. 

 Thus for many applications, research can concentrate on the actual breaking 

 process rather than the cause. It was also concluded that the theoretical 

 study of breaking waves is in its infancy (Peregrine, 1979). 



However, for longshore currents in the nearshore zone, wave breaking 

 caused by nonlinear shoaling processes is of greatest interest. Sakai and 

 Battjes (1980)^^ used Cokelet' s (1978) theory to calculate two-dimensional 

 shoaling of finite-amplitude waves on a gradual slope. The results were found 

 to agree with laboratory experiments except near breaking where the theory 

 predicted wave heights higher than the measured values. In the long run, 

 numerical simulation of wave breaking processes is expected to provide much 

 clearer empirical relations to determine when, where, and why waves break. 



c. Surf Zone Energy Dissipation . After breaking, turbulent energy is 

 produced at the expense of potential energy and wave height decay results 

 across the surf zone. The longshore current models usually assume a constant 

 value for the breaker index y^ * 



For large-amplitude waves with spilling-type breakers over gentle slopes, 

 Divoky, LeMehaute, and Lin (1970)^^ derived theoretically (using energy 

 balance principles) a wave height decay relationship which depended upon 

 bottom slope, bottom friction, and the breaking ratio y,. Theories from 



^^E-uromech 102 (1978), "Breaking Waves; Surf and Run-up on Beaches," University 



of Bristol, England, July 18-21 (file copy of Abstracts Only in CERC Library, 



Fort Belvoir, Va.) (not in bibliography). 

 3^ SAKAI, T. and BATTJES, J.A. , "Wave Shoaling Calculated from Cokelet's 



Theory," Abstracts, t7th Conference on Coastal Engineering, Sy dney , 



Mar. 1980, pp. 65-66 (not in bibliography). 

 ^^ DIVOKY, D. , LeMEHAUTE, B. , and LIN, A. "Breaking Waves on Gentle Slopes," 



Journal of Geophysical Research, Vol. 75, No. 9, Mar. 1970, pp. 1681-1692 



(not in bibliography). 



109 



