Detailed investigations of the spanwise coherence that accompanies lock-on were made recently by 

 Ramberg and Griffin at NRL (22,23). These experiments were conducted to investigate the wakes of 

 vibrating cables as part of the overall program to develop the semi-empirical "wake-oscillator" model for 

 predicting the cross flow response of flexible cables (see Appendix D). The spanwise correlation 

 coefficient p ^^ measured between two hot-wire probes in the wake of a vibrating cable is plotted in Fig. 

 2.11. There the normalized cross correlation function (correlation coefficient) for two periodic signals, 

 measured at the spatial displacement Az, is given by 



^JJu^(z,t)uB(z+Az.t)dt 



Pab(^^) = I = -j=== (2.6) 



^jSJ^n^>^)dt ^\S^ ui{z+Az,)dt 



where u^ and Wg are the fluctuating velocity signals at probes A and B in the near wake of the cable 

 (22,23). The correlation coefficient p^g can also be defined in terms of the pressure fluctuations meas- 

 ured at two locations at varying displacements along a cylinder (19). Both probes were positioned 

 above the cable, so as to measure vortices of like sign, and one probe was moved in a direction parallel 

 to the cable which was vibrated at several displacement amplitudes. The results shown in the figure 

 correspond to vibration frequencies equal to 90 percent of the Strouhal frequency f^. 



There are three distinguishing characteristics of the correlation in vortex shedding along the cable 

 (22). The shedding is in phase along the cable's half- wavelength as shown by the constant sign of the 

 correlation coefficient p^g. When the moveable probe was traversed past the node of the cable, a 

 change in sign of p^g was observed. The degree of the correlation was determined by the maximum 

 value of p^B (relative to unity) along the cable and the extent of the correlation was defined as the 

 length along the cable that p^g was equal to its maximum constant value. Typically it was observed 

 that the Pabmax ~ 0-90 to 0.96 for the frequencies that correspond to vortex-excited oscillations, f^fs 

 as shown in Table 2.5. The vortex shedding was fully correlated in degree and extent over most of the 

 half-wavelength of the cable (L = 12 to 14 Z)) where the displacement amplitude was greater than a 

 threshold of ? = 0.05 to O.ID. 



15 



