Davidson, a critical IL 



is found at R e * 3 x 10 3 . Scale effects cease 



to be important for R e values larger than this critical value. 



In evaluating scale effects in runup, a Reynolds number may again be 

 defined and used for plotting R/H^ versus R e , but only if the remain- 

 ing dimensionless variables are equal between models. This would allow 

 comparison for one set of conditions (i.e., waves with H„ „) , as was 

 done by Hudson and Davidson, or for a whole range of conditions, lead- 

 ing possibly to differing scale effects for different wave conditions; 

 e.g., different wave steepnesses, relative depths, etc. 



The Reynolds number used in this study is a "depth" Reynolds number 

 (defined in Sec. II) : 



( R e^d 



LEU 



112 



(ID 



The depth, d, is arbitrary but must be considered in the dimensional 

 analysis. Here, d g , the depth at the toe of the structure slope, is 

 the depth variable. The Reynolds number then is 



Re = (R e )d c 



(gd g ) 



1/2 



(12) 



This definition is particularly useful because the terms are easily 

 defined. The term (gdg) 1 ' 2 may be recognized as the shallow-water wave 

 celerity; however, it is not synonymous with the actual wave speed tested 

 because nearly all runup tests were conducted in transitional or deep 

 water. 



As examples, the three scales of Dai and Kamel (1969) have Rg 

 values for the specific depths as given in Table 19. The value of v 

 is that for freshwater at 16° Celsius: v =« 1.21 x 10" 5 feet squared per 

 second = 1.124 * 10~ 6 meters squared per second. A family of curves might 

 be drawn as shown schematically in Figure 47. If the scale effects are 

 the same, over a range of R g values for each set of specified wave 

 conditions, then the curves should all have the same shape. However, 

 runup data obtained at different scales but with comparable test condi- 

 tions are insufficient to adequately define scale effects. Therefore, 

 it has not been clearly established that scale effects follow the trends 

 as suggested in Figure 47; i.e., scale effects are the same for varying 

 wave con di t i ons . 



Table 19. 



Reynolds numbers 



for three different depths . 



dg, m 

 (ft) 





4.57 

 (15) 



0.61 

 (2) 



0.30 

 CD 



R e 



2.72 x 10 7 



1.33 x lo 5 



4.69 x 10 5 



105 



