Wave-Induced Eddies and "Lift" Forces on Circular Cylinders 



appears to be as good a parameter for correlation purposes as Nt^q. 

 However, No fails to correlate well with the ratio of "lift" to longi- 

 tudinal force when the values of the larger pile are compared with 

 those of the smaller pile. For the smaller pile the minimum value of 

 Nr> at which eddies form is about 0. 5 x 10*+ , whereas it is 2. 5 x 

 104- for the larger pile. For the same conditions the value of Nt^q 

 is 3 to 5 for both the piles. The UCB(1972) and BEB(l972 

 analysis) data reported herein seem to show an effect of Np^. 



When the oscillating flow is such that the Nj^c becomes large, 

 one might expect the ratio fo "lift" to longitudinal forces would ap- 

 proach the values obtained for steady rectilinear flows. The writers 

 were not able to find many data in the technical literature, however. 

 The results they found have been plotted in Figure 8 (Bishop and 

 Hassan, 1964 ; Humphrey, I960 ; the two sets of curves labeled Fung 

 and Macovsky were drawn from data attributed to them as they ap- 

 peared in Humphrey's paper). These points were obtained by calculat- 

 ing the ratios of C^ to Cj) from the values of the two coefficients 

 given by the investigators. 



Although it is evident that much work remains to be done before 

 the problem is solved, it is clear that an engineer must consider a 

 rather large "lift" force as well as a longitudinal force in his design. 



If tests are made with piles of two different sizes, and com- 

 plete geometric similarity conditions are met, and the Froude model 

 law is adhered to, it can be shown that the "prototype" and "model" 

 Keulegan- Carpenter numbers will be equal, but that the Reynolds 

 numbers will not be equal. All geometric scale ratios must be the 

 same, however. For example, in Figure 10 records obtained by Bidde 

 of waves and forces for the 1. 63 inch (0 . 14 ft. ) and the 0. 5 ft. 

 diameter piles are reproduced. The wave height ratio is the same as 

 the pile diameter ratio, and the wave period ratio is the square root 

 of the pile diameter ratio. However, the water depth was the same in 

 both cases, so that complete geometric similarity was not obtained. 

 Note how different are the two sets of waves and forces. The records 

 in this figure, and in Figure 11 show another interesting feature. 

 There is not a "one to one" correlation of the wave to the "lift" force 

 time series. Rather, the "lift" forces occur in bursts, with intervals 

 of very small forces in between. 



Comparative records are given in Figures 12-14 for the UCB 

 1972 and the BEB experiments. Froude modeling was used and com- 

 plete geometric similarity was maintained. Owing to difficulties with 

 the equipment, the ratio of wave heights was not quite correct for the 



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