available. The problem can be greatly simplified through an idealization 

 which leads to a satisfactory estimate of the upper limit of this effect 

 for many practical problems. Fortunately, the upper limit of the wave 

 setup is of greatest importance in most design problems. 



When waves, coming from deep water, are dissipated on the beach with- 

 out refraction, the kinetic energy of the waves is converted to the 

 potential energy of wave setup, and the kinetic energy of longshore cur- 

 rents and turbulence. The wave setup component is maximized by neglecting 

 the longshore currents and turbulence. This situation exists in many 

 laboratory wave tanks and on beaches where the bottom contours are approx- 

 imately parallel to the beach and the waves approach along a line normal 

 to the shore. At most locations, it is also possible for the extreme 

 waves to approach along a line normal to the shore. Where this is not 

 true, a conservative upper limit can generally be obtained by multiplying 

 the value obtained by the procedure given in Section II by the cosine of 

 the angle between the wave crest outside the breaker zone and the shoreline. 



Where bottom contours are not approximately parallel to the shore, 

 the estimates (Sec. II) will tend to be too large for regions of diverg- 

 ing wave rays and too small for regions of converging wave rays. 



A more complex analysis involving refraction analysis and a solution 

 of the radiation stress equations is expected to provide essentially the 

 same answer as the procedures given in Section II where bottom contours 

 are nearly parallel to the shore and the waves approach along a line 

 nearly normal to the shore. When the waves undergo significant refraction 

 over parallel bottom contours, the more detailed calculations are expected 

 to yield lower values. Additional development is needed to provide satis- 

 factory procedures for computing wave setup in regions with complex 

 bathymetry. 



This report provides the designer with a simplified method of estimat- 

 ing wave setup on a sloping beach. Section 3.85 of the Shore Protection 

 Manual (SPM) (U.S. Army, Corps of Engineers, Coastal Engineering Research 

 Center, 1975) provides a method for estimating wave setup assuming dr^ = 

 1.28 H^j. This assumption best applies to relatively flat beaches 

 (m < 0.01) with breaker steepness (H/j/gT^) values less than 0.01. 



A method for relating dr, to H^j for sloping beaches is given in 

 the SPM (Sec. 2.62). By applying these relationships to the method for 

 estimating wave setup, a family of curves is developed that defines the 

 net wave setup for the breaker height, H^, and the period, T, for 

 any breaker steepness or beach slope. 



The computation of wave setup can be an important part of a thorough 

 design effort requiring water level estimation. For major engineering 

 structures such as nuclear powerplants, it is quite important to consider 

 all possible causes of water level rise. Wave runup computations alone 

 will usually be sufficient, but in cases similar to that shown in Figure 

 1(b), where large waves break offshore, an initial adjustment to the SWL 



