Ordered and chaotic vortex streets behind circular cylinders at low Reynolds numbers

Abstract

We report some experiments undertaken to investigate the origin of ordered and chaotic laminar vortex streets behind circular cylinders at low Reynolds numbers. We made simultaneous measurements of near wake longitudinal velocity and cylinder lateral vibration amplitude spectra for cylinder Reynolds numbers in the range from 40 to 160. For a non-vibrating cylinder the velocity energy spectra contained only a single peak, at the Strouhal frequency. When the cylinder was observed to vibrate in response to forcing by the vortex wake, additional dominant spectral peaks appeared in the resulting ‘ordered’ velocity spectra. Cylinder vibrations too small to be noticed with the naked eye or from audible Aeolian tones produced a coupled wake-cylinder response with dramatic effects in hot-wire and cylinder vibration detector signals. The velocity spectra associated with these coupled motions had dominant peaks at the Strouhal frequency f_s, at a frequency f_c proportional to the fundamental cylinder vibration frequency, and at sum and difference combinations of multiples of f_s and f_c. In windows of chaos the velocity spectra were broadened by switching between different competing coupling modes. The velocity spectra were very sensitive to the nature of the boundary conditions at the ends of the cylinder. Our measurements strongly suggest that the very similar regions of ‘order’ and ‘chaos’ observed by Sreenivasan and interpreted by him as transition through quasi-periodic states in the sense of the Ruelle, Takens, and Newhouse theory were also due to aeroelastic coupling of the vortex wake with cylinder vibration modes.