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Mechanism of determination of the shedding frequency of vortices behind a cylinder at low Reynolds numbers

Published online by Cambridge University Press:  19 April 2006

Michio Nishioka  and
Hiroshi Sato
Michio Nishioka
Affiliation:
College of Engineering, University of Osaka Prefecture, Japan
Hiroshi Sato
Affiliation:
Institute of Space and Aeronautical Science, University of Tokyo, Japan
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Abstract

Two kinds of experiment were made in the wake of a cylinder at Reynolds numbers ranging between 20 and 150. One was a close look at the structure of the vortex street with a stationary cylinder at Reynolds numbers greater than 48. The other experiment was made at lower Reynolds numbers with a cylinder vibrating normal to the flow direction. In this case an artificially induced small-amplitude fluctuation grows exponentially with the rate predicted by the stability theory. Because of the similarity between the two kinds of wake, we postulate that the shedding of the vortex at low Reynolds numbers is initiated by the linear growth, namely, the fluctuation with the frequency of maximum linear growth rate develops into vortex streets. By using the measured width of the wake at the stagnation point in the wake and the result of the stability theory, we could calculate the Strouhal number for Reynolds numbers ranging from 48 to 120. The predicted Strouhal numbers agree well with the values from direct measurements.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 89 , Issue 1 , 14 November 1978 , pp. 49 - 60
Copyright
© 1978 Cambridge University Press

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References

Acrivos, A., Leal, L. G., Snowden, D. D. & Pan, F. 1968 Further experiments on steady separated flows past bluff objects. J. Fluid Mech. 34, 25.Google Scholar
Berger, E. & Wille, R. 1972 Periodic flow phenomena. Ann. Rev. Fluid Mech. 4, 313.Google Scholar
Dennis, S. C. R. & Chang, G.-Z. 1970 Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100. J. Fluid Mech. 42, 471.Google Scholar
Mattingly, G. E. & Criminale, W. O. 1972 The stability of an incompressible two-dimensional wake. J. Fluid Mech. 51, 233.Google Scholar
Nakaya, C. 1976 Instability of the near wake behind a circular cylinder. J. Phys. Soc. Japan 41, 1087.Google Scholar
Nishioka, M. 1973 Hot-wire technique for measuring velocities at extremely low wind-speed. Bull. Japan Soc. Mech. Engrs 16, 1887.Google Scholar
Nishioka, M. & Sato, H. 1974 Measurements of velocity distributions in the wake of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 65, 97.Google Scholar
Roshko, A. 1954 On the development of turbulent wakes from vortex streets. N.A.C.A. Rep. no. 1191.Google Scholar
Sato, H. & Kuriki, K. 1961 The mechanism of transition in the wake of a thin flat plate placed parallel to a uniform flow. J. Fluid Mech. 11, 321.Google Scholar
Takami, H. & Keller, H. B. 1969 Steady two-dimensional viscous flow of an incompressible fluid past a circular cylinder. Phys. Fluids Suppl. 12, II 51.Google Scholar
Taneda, S. 1956 Experimental investigation of the wakes behind cylinders and plates at low Reynolds numbers. J. Phys. Soc. Japan 11, 1284.Google Scholar
Tritton, D. J. 1959 Experiments on the flow past a circular cylinder at low Reynolds numbers. J. Fluid Mech. 6, 547.Google Scholar