estimated to be as large as Co = 2.12, an amplification of 230 perceni from the drag measured when 

 the cylinder was restrained. This is comparable to the drag amplification measurements that are plotted 

 in Fig. 2.9. 



2.3 Coherence of Shedding due to Lock-on. An important consequence of lock-on between the vor- 

 tex and vibration frequencies is the greatly increased coherence or correlation of the vortex shedding 

 along the length of the structure or cable. Above a threshold cross flow displacement amplitude (typi- 

 cally Y/D = 0.05 to 0.1) the shedding is in phase along the length of the cylinder or cable and the wake 

 is nearly two-dimensional even at large Reynolds numbers. Koopmann (17) and Toebes (18) in experi- 

 ments at low and high Reynolds numbers, respectively, were among the first to investigate the 

 increased coherence of the shedding that accompanies lock-on. Koopmann's experiments were limited 

 to Reynolds numbers below 300 but his flow-visualization photographs clearly showed that the vortex 

 shedding was in phase along the vibrating cylinder when the cross flow displacement amplitude was 

 above 2Y/D = 0.1. Toebes' experiments were conducted at much larger Reynolds numbers (Re ~ 

 68,000), but detailed wake and pressure correlation measurements showed clearly that lock-on was 

 accompanied by increased coherence of the shedding along the cylinder. The magnitude of the cross 

 correlation function was reduced to values below unity only by the eff'ects of turbulent fluctuations in 

 the wake, and the sign of the cross correlation measured along the cylinder indicated that the shedding 

 was in phase for distances up to seven and one-half diameters when the displacement amplitude was 

 above 2Y/D = 0.16. The results of these studies were limited by the relatively small length/diameter 

 ratios, L/D = 7.5 to 12, in the experiments. Novak and Tanaka (19) and Howell and Novak (20) also 

 have investigated the effects of turbulence in the incident stream on the correlation eff'ects that accom- 

 pany lock-on. Smooth flow (low turbulence) experiments were conducted by them to provide a base- 

 line for comparison with the eff'ects of various kinds of turbulence introduced into the incident flow. 

 Blevins and Burton (21) have developed an empirical model for predicting the vortex-excited reso- 

 nance, and this mode! takes account of the variation in correlation length at small displacement ampli- 

 tudes. 



14 



