as relative runup, R/H^, but is also given as a ratio of rough-slope 

 runup to smooth-slope runup for a particular structure type and slope. 

 Scale effects are reviewed using Reynolds numbers, but only a limited 

 number of large-scale tests are available. Consequently, a single 

 scale- correction curve is given for smooth slopes; scale-effect correc- 

 tions for rough slopes are discussed, and correction values are given. 



II. PROBLEM DEFINITION 



Extensive theoretical and laboratory work has been reported for 

 regular waves--waves which are long crested and periodic in time. 

 Figure 2 is a definition sketch of the important dimensions for de- 

 scribing runup tests. 



The wave is defined by its height, H, and length, L, in water 

 of given depth, d. Wavelength is a function of period, T, and depth, 

 where 



L = 



L tanh 



(¥) - (S 



g?) 



tanhfel 



CD 



Lq is the deepwater wavelength, where deep water is defined as d > 0.5L 

 (Table 1; Fig. 2). Deep water may or may not exist for a given experi- 

 ment or field problem; however, deepwater values can be calculated. 

 Deepwater variables are preferred because of the general applicability 

 of results and because the deepwater wavelength is then only a function 

 of period. The use of deepwater variables is particularly applicable 

 to problems involving sloping beaches, because the difficulty in des- 

 cribing varying wavelengths on sloping bottoms is avoided. 



Table 1. Relative water depths. 





Shallow water 



Transitional water 



Deep water 



d/L 

 d/gT 2 



<0.04 

 <0. 00155 



0.04 to 0.5 

 0.00155 to 0.0793 



>0.5 

 >0.0793 



Wave height is also a function of water depth, and in a given depth 

 is related to the deepwater wave height by a shoaling coefficient, K g ; 

 linear theory gives the expression 



h = \ 



tanh(27rd/L) 



[l + { (47Td/L Vsinh(4,d/L)0' 



(2) 



where H£ is the unrefracted equivalent deepwater wave height of a 

 wave approaching the shoreline, and d, L, and H are the shallow- 

 water values at the depth of interest. The shoaling coefficient is 

 derived from theory for waves in water of constant depth, d, but the 

 relationship is commonly applied to coastal areas with variable depths. 



