obtained (19) when the cross correlation p^g was measured between the signals from pressure taps at 

 various spacings along a circular cylinder. When the complications of various types of turbulence and 

 boundary layer profiles were added to the case of a low-turbulence uniform flow, Howell and Novak 

 found that the displacement response of the cylinder was largely independent of the flow characteristics 

 if the structural damping was sufficiently small to allow lock-on. 



As the damping ratio i^ was increased, the displacement response of the flexibly-mounted 

 cylinders became susceptible to the characteristics of the flow incident to the cylinder. The correlation 

 coefficient at the pressures measured between two taps on the cylinder is plotted in Fig. 2.13. The 

 cylinder employed during the experiments was a pivoted rigid rod of aspect ratio L/D = 10 in a deep 

 boundary layer, but the results are very similar to those plotted in Figs. 2.11. In addition to the correla- 

 tion profiles, Howell and Novak measured the cross flow displacement amplitudes as a function of 

 structural damping {t,^ = 0.01 to 0.11) and obtained results in various types of boundary layer (shear 

 flow) environments. The measured amplitudes compare very well with those plotted in Fig. 2.2, and 

 full lock-on was observed for the cylinder with {j = 0.01 and YE^fuf^x ~ 0-5- This case is plotted in 

 Fig. 2.14. These findings further confirm that flexible cylindrical structures and cables with small 

 reduced damping iJn will be vulnerable to resonant vortex-excited oscillations even if the incident 

 flow is nonuniform (as discussed in Section 2.7). 



A number of computer codes, prediction models and design procedures have been developed on 

 the basis of the results just discussed. It has been found that local displacement amplitudes and forces 

 can be predicted for flexible structures and cables from empirical data that are measured in experiments 

 conducted with rigid cylinders, so long as the condition of lock-on is met and the frequency ratios ///j 

 (or reduced velocities V^) and displacement amplitudes are matched appropriately in the two cases. 



2.4 Reynolds number effects. The overall pattern of cable and cylinder response described else- 

 where in this section of the report is typical of measurements in water, air and similar fluids at all Rey- 

 nolds number where vortex shedding takes place. Few results at large Reynolds numbers are available, 



17 



