WAVE SETUP ON A SLOPING BEACH 



hy 

 John R. Lesni-k 



I. INTRODUCTION 



Design of coastal structures requires consideration of abnormally 

 high water levels produced by storms. An important component of the 

 storm surge can be the rise in water level produced by wave action. 



The wave train approaching the coast and breaking offshore causes the 

 water to pile up on the beach. Depending upon the wave characteristics 

 (height and period) and beach slope, this accumulation of water will 

 continue until the slope of the water surface in the onshore-offshore 

 direction results in a head which balances the forces tending to drive 

 the water onto the beach. This rise in water level is commonly called 

 wave setup. 



Two conditions that could produce wave setup will be examined in this 

 report. The simplest case is illustrated in Figure 1(a), where the dash- 

 line represents the normal Stillwater level CSWL) ; i.e., the water level 

 that would exist if no wave action were present. The solid line represents 

 the average water level when wave shoaling and breaking occur. A series of 

 waves is shown at an instant in time, illustrating the actual wave breaking 

 and the resultant runup. As the waves approach the shore, the average 

 water level decreases to a minimum at the breaking point, d^,. The differ- 

 ence in elevation between the mean water level (MWL) and the normal SWL 

 at this point is called the wave setdown, S^. Beyond this point, d^, 

 the MWL rises until it intersects the shoreline. The total rise between 

 these points is the wave setup between the breaking zone and the shore, 

 denoted AS. The net wave setup, ^ Sy, is the difference between AS and 

 S^, and is the rise in the water surface at the shore above the normal SWL. 

 In this case, the wave runup, R, is equal to the greatest height above 

 normal (SWL) which is reached by the uprush of the waves breaking on the 

 shore. For this type of problem, the runup, R, includes the setup 

 component and a separate computation for Sy is not needed. The reason 

 for this is that laboratory measurements of wave runup are taken in refer- 

 ence to the SWL and already include the wave setup component. 



Figure 1(b) illustrates a more complete situation involving wave setup 

 on a beach fronted by a wide shelf. At some distance offshore the shelf 

 abruptly drops off to deep water. As waves approach the beach, the larger 

 waves in the spectrum begin to break at the seaward edge of the shelf and 

 a setup is produced. The increase in water level produced by this setup 

 allows larger waves to travel toward shore until they break on the beach. 

 Runup calculations performed at that point would include setup effects 

 from the breaking of these waves. 



Calculation of the precise value of the wave setup for all conditions 

 is a formidable problem for which a satisfactory solution is not yet 



