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On the stability of viscous plane Couette flow

Published online by Cambridge University Press:  28 March 2006

J. W. Deardorff
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado

Abstract

The problem of the stability of plane Couette flow to infinitesimal disturbances is carried numerically to larger Reynolds numbers than heretofore. The flow is definitely stable up to R = 1430, although at Reynolds numbers in this vicinity plane Couette flow has been observed experimentally to be turbulent. Observations on boundary-layer instability suggest this to be the source of turbulence in plane Couette flow channels.

Type
Research Article
Copyright
© 1963 Cambridge University Press

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References

Dryden, H. L. 1947 Some recent contributions to the study of transitions and turbulent boundary layers. Nat. Adv. Comm. Aero. T. N. no. 1168.Google Scholar
Gallagher, A. P. & Mercer, A. McD. 1962 On the behaviour of small disturbances in plane Couette flow. J. Fluid Mech. 13, 91100.Google Scholar
Hinze, J. O. 1959 Turbulence. New York: McGraw-Hill.
Hopf, L. 1914 Der Verlauf kleiner Schwingungen aufeiner Strömung reibender Flüssigkeit. Ann. Phys., Lpz., 44, 160.Google Scholar
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Reichardt, H. 1959 Gesetzmässigkeiten der geradlinigen turbulenten Couetteströmung. Mitteilungen aus dem Max-Planck Institut für Stromungsforschung und der Aerodynamischen Versuchsanstalt, no. 22.Google Scholar
Robertson, J. M. 1959 On turbulent plane-Couette flow. Proc. 6th Midwestern Conference on Fluid Mechanics, University of Texas, 16982.
Schlichting, H. 1932 Über die Enstehung der Turbulenz in einem rotierenden Zylinder. Nachr. Ges. Wiss. Göttingen, 16098.Google Scholar
Squire, H. B. 1933 On the stability of the three-dimensional disturbances of viscous flow between parallel walls. Proc. Roy. Soc. A, 142, 6218.Google Scholar
Stuart, J. T. 1958 On the non-linear mechanics of hydrodynamical stability. J. Fluid Mech., 4, 121.Google Scholar
Wasow, W. 1953 On small disturbances of plane Couette flow. J. Res. Nat. Bur. Stand., 51, 195202.Google Scholar
Watson, J. 1960 On the non-linear mechanics of wave disturbances in stable and unstable parallel flows. J. Fluid Mech., 9, 37189.Google Scholar
Zondek, B. & Thomas, L. H. 1953 Stability of limiting case of plane Couette flow. Phys. Rev. 90, 73843.Google Scholar