theory which suggested that surf beating between particular pairs of incom- 

 ing waves led to the resonant growth of long-period edge waves. However, 

 wave breaking was not permitted in this model. To study resonant inter- 

 action conditions in the presence of breaking waves, Bowen and Guza (1978) 

 conducted a series of carefully designed laboratory tests. It was found 

 that theoretical resonance can be produced in a wave basin with incident 

 wave breaking present. When resonance conditions for edge wave growth 

 from the theory were satisfied in the experiments, the response at the 

 beat frequency was in the form of the theoretically predicted edge wave 

 mode. It was concluded that these results suggest (strongly) that surf 

 beat is predominantly an edge wave phenomenon. The reverse is also true 

 to provide a mechanism for generation of long-period edge waves with 

 resulting large rip spacings on flat dissipative beaches. 



(2) Intersecting Wave Trains . A second wave interaction mech- 

 anism to produce rips is the intersection of incident wave trains with 

 the same periods, but from different directions (Dalrjmiple, 1975; 

 Dalrymple and Lanan, 1976). Large rip spacings are possible from the 

 theory (no maximum limit). However, as pointed out by Dalrymple (1978), 

 the amount of time natural conditions (separate distant storms, refrac- 

 tion, diffraction, local reflection) produce wave intersections at real 

 beaches is unknown. Synchronous, progressive cross-waves can also be 

 excited in a wave basin with a sloping beach as demonstrated by the lab- 

 oratory experiments of Maruyama and Horikawa (1977). The cross-waves are 

 shown to be component waves, with angles different from 90° to the wave 

 maker, and not edge waves. Numerical simulations, agreed well with 

 observed flow patterns which included rip currents. It was concluded that 

 the interaction of the incident and cross-waves produced the longshore 

 variation in breaker height causing nearshore circulations and rip currents. 



(3) Wave-Current Interaction . Finally, rip currents have been 

 observed where there is no wave topography, wave wave, or wave structure 

 interaction. There is no obvious external reason for a longshore variation 

 in breaker height. Bowen and Inman (1969) stated this case clearly for 

 perpendicular wave incidence on a plain noneroding beach: 



"In theory, the set-up at the beach can be in equilibrium 

 with the momentum input of a uniform wave train over any 

 width of beach, provided that the conditions are uniform 

 in the longshore direction. However, as this condition 

 is not observed in nature and not observed even in the 

 laboratory unless the beach width is quite small, it has 

 been suggested that the equilibrium might not be stable. 

 That is, a small temporary disturbance might cause a com- 

 plete breakdown of the two-dimensional equilibrium." (p. 5480) 



They then presumed that a small disturbance could excite edge waves in the 

 region and their incident edge wave theory ensued. It is also conceivable 



12 II 



GALLAGHER, B. , Generation of Surf Beat by Non-linear Wave Interactions,' 



Journal of Fluid Medhanics^ Vol. 47, No. 1, Sept. 1971, pp. 1-20 Cnot in 



bibliography) . 



51 



