however, except in the case of in-Hne oscillations. These results are discussed by King (2). It was 

 found from the experiments conducted by King that full-scale results at high Reynolds numbers could 

 be modelled in small scale laboratory experiments when the reduced velocity V,. and the reduced damp- 

 ing /Cj of the two systems were the same. This point is discussed at greater length in Section 4.3. The 

 limited results that are available suggest that Reynolds number effects are of secondary importance if 

 the critical reduced velocity is exceeded and the structural damping is small enough to allow excitation 

 of a flexible cylinder or cable into resonant cross flow oscillations. 



The inverse of the reduced velocity V,. or the Strouhal number corresponding to the peak vortex- 

 excited displacement is plotted as the solid line in Fig. 2.15, adapted from the results of Wootton (24). 

 The conditions span the critical regime near Re = 10^ to 10^, and little influence of the critical Rey- 

 nolds number is shown. For the results in the figure, the shedding frequency fs was locked onto the 

 natural frequency /„ of the cylinder; the dashed line represents the value of St corresponding to the ini- 

 tiation of lock-on. It is likely that conditions such as shear gradients, surface roughness, and inclination 

 to the flow are of greater importance than the Reynolds number. 



In order to consider the effects of Reynolds number on vortex-excited oscillations, a universal 

 Strouhal number — Reynolds number correlation was developed for the case of cross flow lock-on 

 (25,26) which had not been considered in previous studies of wake similarity (27). This universal 

 Strouhal number (or non-dimensional frequency scale) is valid at subcritical and supercritical Reynolds 

 numbers (or non-dimensional flow velocities). The formulation has been verified for stationary two- 

 dimensional bluff bodies with fixed and free separation points, vibrating bluff structures, and bluff 

 cylinders in confined flow passages and at large yaw angles to the incident flow. The Strouhal number 

 St* = fsd'/Vj, is based upon the characteristic frequency of the wake, fs', the wake width d' ai the end 

 of the vortex formation region; and the mean velocity V/, in the region where flow separation takes 

 place. The usual pressure drag coefficient Cd, the vortex shedding frequency, and the base pressure 

 coefficient Cpi, are also related by means of an inverse dependence between St* and a wake drag 

 coefficient C^ = C[)/{d'ld)K^, where A^ = (1 - C^^)'^^. Here d' is the width of the separated vortex 



wake and </ is a characteristic lateral dimension of the structure. 



18 



