Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-18T16:02:54.891Z Has data issue: false hasContentIssue false

The formation of vortex streets

Published online by Cambridge University Press:  28 March 2006

Frederick H. Abernathy
Affiliation:
Division of Engineering and Applied Physics, Harvard University, Cambridge, Massachusetts
Richard E. Kronauer
Affiliation:
Division of Engineering and Applied Physics, Harvard University, Cambridge, Massachusetts

Abstract

The formation of vortex streets in the wake of two-dimensional bluff bodies can be explained by considering the non-linear interaction of two infinite vortex sheets, initially a fixed distance, h, apart, in an inviscid incompressible fluid. The interaction of such sheets (represented in the calculation by rows of point-vortices) is examined in detail for various ratios of h to the wavelength, a, of the initial disturbance. The number and strength of the concentrated regions of vorticity formed in the interaction depend very strongly on h/a. The non-linear interaction of the two vortex sheets explains both the cancellation of vorticity and vortex-street broadening observed in the wakes of bluff bodies.

Type
Research Article
Copyright
© 1962 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Birkhoff, G. & Zarantonello, E. H. 1957 Jets, Wakes, and Cavities. New York: Academic Press.
Birkhoff, G. & Fisher, J. 1959 Do vortex sheets roll up? Rendi. Circ. Mat. Palermo, Ser. 2, 8, 7790.Google Scholar
Fage, A. & Johansen, F. C. 1927 On the flow of air behind an inclined flat plate of infinite span. Proc. Roy. Soc. A, 116, 17097.Google Scholar
Fage, A. & Johansen, F. C. 1928 The structure of the vortex sheet. Phil. Mag. 5, 41741.Google Scholar
Goldstein, S. (ed.) 1938 Modern Developments in Fluid Dynamics. Oxford: The Clarendon Press.
Hama, F. R. & Burke, E. R. 1960 On the rolling-up of a vortex sheet. Univ. of Maryland, Tech. Note no. BN-220.Google Scholar
Homann, F. 1936 Einfluss grosser Zähigheit bei Strömung um Zylinder. Forschung auf dem Gebiete des Ingenieurwesens, 7, 110.Google Scholar
Karman, Th. von 1911 Über den Mechanismus des Widerstandes, den ein bewegter Körper in einer FlÜssigkeit erfährt. Gottinger Nachrichten, math.-phys. Kl. pp. 50917.Google Scholar
Kovasznay, L. S. G. 1949 Hot-wire investigation of the wake behind cylinders at low Reynolds numbers. Proc. Roy. Soc. A, 198, 17490.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th ed. Cambridge University Press.
Lippisch, A. M. 1958 Flow visualization. Aero. Eng. Rev., 17, 2432.Google Scholar
Rayleigh, Lord 1894 The Theory of Sound, vol. II. Cambridge University Press. (Reprinted 1945, New York: Dover).
Rosenhead, L. 1931 The formation of vortices from a surface of discontinuity. Proc. Roy. Soc. A, 134, 17092.Google Scholar
Roshko, A. 1954a On the development of turbulent wakes from vortex streets. Nat. Adv. Comm. Aero., Wash., Rep. no. 1191.Google Scholar
Roshko, A. 1954b On the drag and shedding frequency of bluff cylinders. Nat. Adv. Comm. Aero., Wash., Tech. Note no. 3169.Google Scholar