I 

 observations by laboratory researchers. Swart (1974)^^, for complete plung- 

 ing, assumed that all the energy of the approaching wave immediately trans- 

 formed at the outer edge of the breaker zone. An abrupt water level change 

 occurs to balance the change in radiation stress at the breaker line and the 

 mean water surface is assumed level across the surf zone. Maximum setup was 

 found to be lower than for spilling breakers. This was cited as a limiting 

 case for natural beaches which have some combination of plunging- and spilling- 

 type breakers . ! 



Gourlay (1974) made allowance for the effect of a plunge point distance 

 X , between the breakpoint and plunge point of a curling breaker, where he 

 p^ostulated that energy dissipation began. Assuming a constant wave setdown 

 n, over this distance, no abrupt rise in setup at the plunge point and a con- 

 stant index y from the plunge point to the shoreline on a plain beach. 



For surging breakers, X was zero and equation (38) reduces to equation (37). | 

 The dimensionless plunge distance (X /H, ) must be found empirically, as by j 

 Galvin (1969), and is related to the beach slope. Maximum setup is again 

 lower than for spilling breakers. 



More assumptions are employed in the theory for plunging breakers. These 

 points are discussed when comparing theories to the observations in Chapter 4. i 



I 

 2. Oblique Wave Incidence . ; 



The more general case is when waves approach the beach at an angle. Wave ■ 

 refraction causes changes in wave height and length. The magnitudes of theo- 

 retical setdown and setup can be shown to depend on wave angle and all other j 

 factors that influence surf zone wave heights such as the induced longshore 

 current and resulting wave-current interaction processes. i 



All the analytic theories to date neglect the feedback of the current on 

 the wave motion. The partial differential equations are decoupled in this i 

 way to become two ordinary differential equations. The momentum equation per- J 

 pendicula^r to the shore (eq. 28) is solved independently so that calcula- 

 tion of n is independent of longshore current. Such a theoretical solution ] 

 for a profile with straight and parallel bottom contours but arbitrary shape I 

 (monotonously decreasing depth toward shore) was given by Jonsson and Jacobsen I 

 (1973). The shore-normal radiation stress is found from equation (23). ■ 



a. Wave Setdown . Outside the breaker line, the wave height is deter- ; 

 mined by assuming a constant energy flux between orthogonals and Snell's law ;; 

 (c/sin a = constant) to reference conditions to deep water. Interestingly, i 



2 3 SWART, D.H., "Offshore Sediment Transport an Equilibrium Beach Profiles," Pub- 

 lication No. 131, Delft Hydraulics Laboratory, The Netherlands, 1974 (not in 

 biblography) . 



76 



