cylinder diameter was Re = 5 x lO'*, the largest value reached by Sarpkaya. This corresponded to a 

 roughness Reynolds number of Reg = 500, where the relationship between Reg and Re is 



Rqs= Rei8/D). (2.7) 



Here 8 is the average roughness height. Sarpkaya (30) employed a uniform sand roughness on the 



cylinder and discusses some of the complexities that arise when the roughness is nonuniform and irreg- 

 ular. 



Peltzer and Rooney (31) have conducted one of the most complete and up-to-date studies of the 

 effects of shear and roughness on vortex shedding from stationary circular cylinders. The Reynolds 

 numbers for their experiments spanned the range from Re = 1.6 x 10' to 3.6 x 10^, for smooth and 

 roughened cylinders (roughness 8/D = 1 x 10~^), and steepness parameters (see Section 2.7) from /3 

 = (uniform flow) to /8 = 0.041. This range of parameters was sufficient to provide both subcritical, 

 critical (or transcritical), and supercritical vortex shedding conditions. Some of the uniform flow base- 

 line conditions for the smooth and rough cylinders are plotted in Fig. 2.22, along with some recent 

 measurements by Buresti and Lanciotti (32) and by Alemdaroglu, Rebillat and Goethals (33). The 

 Strouhal number St versus roughness Reynolds number Res plot illustrates the three Reynolds number 

 ranges just mentioned. Szechenyi (34) introduced the idea of roughness scaling to achieve high 

 Reynolds number flows, and found that critical and supercritical flows were reached for Reg > 200. 

 The results in Fig. 2.22 are in good agreement with this finding. These results are in good overall 

 agreement with the original supercritical roughness Reynolds number simulation of Szechenyi although 

 the supercritical Strouhal numbers measured by Szechenyi were somewhat higher {St ~ 0.26) than 

 those plotted in Fig. 2.22. Sarpkaya's experiments with vibrating cylinders spanned the three regimes 

 and the results at Reg = 500 in Fig. 2.21 approach close to, or are in, the supercritical range of Reg. 



Nakamura (35) has measured the steady drag forces and Strouhal frequencies on rough circular 

 cylinders at supercritical Reynolds numbers, and has observed strong regular vortex shedding at Re ~ 

 4(10^) and above. In this Reynolds number range the vortex-excited cross flow displacement amplitude 

 of a rough cylinder increased substantially from the corresponding smooth cylinder experiment. This 



22 



