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



transverse forces. Examples of waves, "lift" forces and longitudinal 

 forces are shown in Figure 6 for three different values of Nj^q 

 (3.2, 6.2 and 10.2). The terms "top" and "bottom" associated 

 with the lift and longitudinal forces refer to the forces measured by 

 the top and bottom strain gages on the transducer ; the total "lift" 

 and total longitudinal forces are the sums of the outputs of the top and 

 bottom gages. 



There is agreement between the visual observations described 

 previously and the force measurements. Figure 6a shows a set of 

 records for a Nj^q of 3. 2. The "lift" force has just begun to be non- 

 zero. For this value of Nj^q the first eddies develop and shed. The 

 eddy strength is probably very small so that the "lift" force recorded 

 is negligible. The "lift" forces for this case have a frequency which 

 is about the same as the wave frequency. This might be due to the 

 fact that the flow is not perfectly symmetrical. The horizontal com- 

 ponent of velocity in one direction (wave crest) are slightly larger 

 than those in the opposite direction (wave trough), and for the thres- 

 hold condition the eddies only shed for one direction of the flow. The 

 Keulegan-Carpenter number is 6. 2 for the run shown in Figure 6b. 

 The eddy is distinct, and the frequency of "lift" forces is approxi- 

 mately twice the frequency of waves. This shows that there is time 

 only for two eddies to shed in each direction. The "lift" forces are 

 about 25% of the longitudinal force. The wake is not yet completely 

 turbulent, and the lift force records show a more or less regular pat- 

 tern. The Keulegan-Carpenter number for the run shown in Figure 6c 

 is 10.2. The wake is fully turbulent. The transvers ("lift") force 

 record appears to be random. The ratio of maximum "lift" to maxi- 

 mum longitudinal force is about 40%. 



An equation for "lift" forces is given by Equation (7). Use of 

 this equation leads to difficulties as the time history of the force does 

 not necessarily vanish when u goes through zero owing in part to the 

 inertial force. Thus, very large values of Ct can be calculated from 

 the laboratory measurements. This difficulty can be overcome par- 

 tially by defining the relationship only for maximum values of the force 

 as 



^ F Lh^ max 2 P C L 



max 



u) D. (8) 



max 



Chang (1964) found values of Cl between 1. and 1. 5 for value 



NkC g reater than about 10. 



771 



