observations are insufficient to provide quantitative trends. (Savage, 

 1957; Fairchild, 1958; Dorrestein, 1962; Galvin and Eagleson, 1965.) A 

 laboratory study by Saville (1961) indicated that for waves breaking on 

 a slope there would be a decrease in the mean water level relative to the 

 Stillwater level just prior to breaking, with a maximum depression or set- 

 down at about the breaking point. This study also indicated that from the 

 breaking point the mean water surface slopes upward to the point of inter- 

 section with the shore and has been termed wave setup. Wcwe setup is 

 defined as that super -elevation of the mean water level caused by wave 

 action alone. This phenomenon is related to a conversion of kinetic 

 energy of wave motion to a quasi-steady potential energy. 



Theoretical studies of wave setup have been made by Dorrestein (1962), 

 Fortak (1962), Longuet-Higgins and Stewart (1960, 1962, 1963, 1964), Bowen, 

 Inman, and Simmons (1968), and Hwang and Divoky (1970). Theoretical devel- 

 opments can account for many of the principal processes, but contain 

 factors that are often difficult to specify in practical problems. 



R.O. Reid (personal communication) has suggested the following approach 

 for estimating the wave setup at shore, using Longuet-Higgins and Stewart 

 (1963) theory for the setdown at the breaking zone and solitary wave theory. 

 The theory for setdown at the breaking zone indicates that 



gi/2 Hj T 



in which Sj^ is the setdown at the breaking zone, T is the wave period, 

 Hq is the deepwater significant wave height, dj^ is the depth of water 



at the breaker point and g is gravity. The laboratory data of Saville 

 (1961) gives somewhat larger values than those obtained by use of Equation 

 3-46. 



By using relations derived from solitary wave theory relating dh 

 to the breaker height of the significant wave, H^j, and d^/H^ to Ho/Lo, 

 the above relation can be converted to 



3/2 



0.536 H, 

 Su = — -^— . (3-47) 



'b 



g 



1/2 J 



Longuet-Higgins and Stewart (1963) show from an analysis of Saville's 

 data that the wave setup AS between the breaker zone and shore is given 

 approximately by AS = 0.15 dj. Assuming that djy = 1.28 Hj,, this becomes 

 AS = 0.19 Hfe. 



The net wave setup at the shore is 



Sj^, = AS + Sj, , (3-48) 



or 



Sh; = 0.19 



1 - 2.82 



3-81 



gT^ 



Hy . (3-49) 



