Thus a lowering of the MWL below SWL takes place since n is negative and this 

 wave- induced change is called setdown. The integration is not straightforward 

 since all three variables k, d, and E can be dependent upon the horizontal 

 coordinate x for this problem. 



It is also possible to express n at a given depth d as a function of the 

 7ater condit 

 His results are 



deepwater conditions H and L (or a , k ) as discussed by Gourlay (1978) 



a^k 

 loo coth^kd 



4 n slnh 2kd 



(31) 



H^ 



d 



n = - ^ f (^) (32) 



o o 



with the form of the function f(d/L ) shown in Gourlay (1978) as plotted 

 against a normalized setdown. Wave setdown is zero in deep water and in- 

 creases rapidly as the depth increases. The maximum setdown is limited by 

 wave breaking in shallow water which voids the assxjmption of constant energy 

 flux. Using shallow-water approximations and a breaking criteria as discussed 

 later, the maximum setdown at the breaker line is approximate 5 percent of the 

 wave height at the breaker. 



The most questionable assumptions in this theory are the use of S based 

 on linear wave theory and the neglect of bed shear in the region approaching 

 wave breaking. 



c. Wave Setup . Shoreward of the breakers, internal turbulence from wave 

 breaking and bottom shear both drain energy from the waves in the surf zone. 

 Since S^j^^ varies directly with E in shallow water (n -> 1), or as H^, the re- 

 duction of wave height toward the shoreline_means a negative gradient of S^^ 

 must be balanced by a positive gradient of r\ in the x-direction. This is 

 called wave setup. The key question is how the wave height H varies from the 

 first breakpoint to the shoreline. 



(1) Dissipative-Type Beaches . Spilling-type breakers are found on 

 wide, flat dissipative beaches. After breaking, the wave height continuously 

 decreases as the waves and bores propagate shoreward as schematized in Figure 

 21. No truly satisfactory theory exists to explain when, where, and why waves 

 break. Also, very little is known about energy dissipation rates in the surf 

 zone for various types of breakers and beach profiles. Consequently, simpli- 

 fying assumptions primarily based upon experimental evidence have been em- 

 ployed to develop wave setup theories. For spilling-type breakers on dissipa- 

 tive beaches, the assumption commonly employed is that the breaker index, y 

 (ratio of breaking wave height to mean depth at breaking) remains a 



"b \ E 



(rT4d)^ h^ h 



(33) 



74 



