IRREGULAR WAVE RUNUP ON SMOOTH SLOPES 



by 

 John P. Ahrens 



I . INTRODUCTION 



This report provides guidance on the magnitude and distribution of wave 

 runup and rundown elevations caused by irregular wave conditions similar to 

 those occurring in nature. The results presented are for plane, smooth struc- 

 tures with relatively deep water at the toe of the structure. For these con- 

 ditions this report supersedes earlier guidance in Section 7.212 of the Shore 

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

 Research Center, 1977) and Ahrens (1977) which indicate that irregular wave 

 runup has a Rayleigh distribution. Within the range of test conditions this 

 report also supersedes Stoa (1978a) and the parts of Stoa (1979) which esti- 

 mate wave runup on rough and porous slopes by adjusting the runup on a smooth 

 slope by a correction factor. The range of test conditions covered in this 

 report is discussed in the next section. 



II. IRREGULAR WAVE RUNUP ON PLANE, SMOOTH SLOPES 



Three sources of data were used in establishing the methods presented in 

 this report: van Oorschot and d'Angremond (1968), Kamphuis and Mohamed (1978), 

 and Ahrens (1979) which discussed data recently collected at the Coastal Engi- 

 neering Research Center (CERC) . The conditions considered are a structure 

 with a plane, smooth slope fronted by a horizontal bottom offshore. The water 

 depth at the toe of the structure is relatively deep, i.e., 3 < d s /H g < 12, 

 where d s is the water depth and H s the significant wave height at the toe 

 of the structure. When there is relatively deep water at the toe of the struc- 

 ture the offshore slope of the bottom has little influence on the wave condi- 

 tions and therefore little influence on the wave runups. This lack of influence 

 indicates that the runup results presented can be applied to situations where 

 there is an offshore slope. Since the water depth also has little influence on 

 wave runup for conditions when d s /Ho > 8 (Stoa, 1978a), where Hq is the deep- 

 water, unrefracted wave height, Stoa's finding suggests that the results of this 

 study should be good for d s /H s > 12. 



Three runup parameters were chosen to characterize the runup distribution 

 caused by irregular wave conditions, i.e., the mean runup, R, the significant 

 runup, R s , and the 2-percent runup, R2 . The significant runup is the aver- 

 age runup of the highest one-third of wave runups and the 2-percent runup is 

 the elevation exceeded by 2 percent of the wave runups. 



Figure 1 shows trend-line curves for R2/H s , R s /H s , and R/H s for a plane, 

 smooth slope of 1 on 1. These parameters are plotted as a function of the 

 irregular wave steepness parameter, H s /gTp 2 , where T is the period of peak 

 energy density of the wave spectrum and g the acceleration of gravity. The 

 approximate relationship between Tp and the average period of the significant 

 waves, Ts, is given by Goda (1974) as 



T n ■ 1.05 T (1) 



