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On the formation of vortex streets behind stationary cylinders

Published online by Cambridge University Press:  21 April 2006

George S. Triantafyllou ,
Michael S. Triantafyllou  and
C. Chryssostomidis
George S. Triantafyllou
Affiliation:
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Michael S. Triantafyllou
Affiliation:
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
C. Chryssostomidis
Affiliation:
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

The formation of vortex streets behind stationary cylinders is found to be caused by an absolute instability in the wake immediately behind the cylinder. The inviscid Orr–Sommerfeld equation is used together with measured profiles at Reynolds numbers of (a) Re = 56 when the absolute instability provides a Strouhal number of 0.13; and (b) Re = 140000 providing a Strouhal number of 0.21, both in agreement with experimental values. At the subcritical Re = 34 the instability is of the convective type; i.e. the disturbance decays, being convected away once the external disturbance is removed, in agreement with experimental observations. Finally, the instability of the mode which causes a symmetric array of vortices is shown to be always of the convective type.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 170 , September 1986 , pp. 461 - 477
Copyright
© 1986 Cambridge University Press

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References

Abernathy, F. H. & Kronauer R. E.1962 The Formation of vortex streets. J. Fluid Mech. 13, 1–20.Google Scholar
Ahlfors L. V.1966 Complex Analysis, 2nd edn. McGraw-Hill.
Bers A.1983 Basic Plasma Physics I. In Handbook of Plasma Physics (ed. M. N. Rosenbluth & R. Z. Sagdeev), vol. 1, chap. 3.2. North Holland.
Cantwell B. J.1976 ‘A flying hot wire study of the turbulent near wake of a circular cylinder at a Reynolds number of 140000’. Ph.D. thesis, California Institute of Technology, Pasadena, California.
Faltinsen, O. M. & Pettersen B.1982 Vortex shedding around two-dimensional bodies at high Reynolds number Fourteenth Symp. on Naval Hydrodynamics, Ann Arbor, Michigan, pp. 1171–1213.
Fromm, J. E. & Harlow F. H.1963 Numerical solution of the problem of vortex street development. Phys. Fluids 6, 975–982.Google Scholar
Gaster M.1965 The role of spatially growing waves in the theory of hydrodynamic stability, Prog. Aeron. Sci. 6, 251–270.Google Scholar
Ho, C. M. & Huerre P.1984 Perturbed free shear layers. Ann. Rev. Fluid Mech. 16, 365–424.Google Scholar
Jordan, S. K. & Fromm J. E.1972 Oscillatory drag, lift and torque on a circular cylinder in a uniform flow. Phys. Fluids 15, 371–376.Google Scholar
Koch W.1985 Local instability characteristics and frequency determination of self-excited wake flows. J. Sound Vib. 99, 53–83.Google Scholar
Kovasznay L. S. G.1949 Hot-wire investigation of the wake behind cylinders at low Reynolds numbers. Proc. R. Soc. A, Lond. 198, 174–190.Google Scholar
Mattingly, G. E. & Criminale W. O.1972 The stability of an incompressible two-dimensional wake. J. Fluid Mech. 51, 233–272.Google Scholar
Rayleigh Lord1945 Theory of Sound, vol. ii. Dover.
Rosenhead L.1931 The formation of vortices from a surface of discontinuity Proc. R. Soc. Lond. A 134, 170–192.Google Scholar
Roshko A.1953 On the development of turbulent wakes from vortex streets. National advisory Comm. Aeronaut., Tech. Note 2913.Google Scholar
Roshko A.1961 Experiments on the flow past a circular cylinder at very high Reynolds number. J. Fluid Mech. 10, 345–356.Google Scholar
Sarpkaya T.1979 Vortex-induced oscillations. Trans. ASME E: J. Appl. Mech. 46, 241–258.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, 321–352.Google Scholar
Tyler E.1931 Vortex formation behind obstacles of various sections. Phil. Mag. 11, 849–890.Google Scholar