Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-12T19:59:46.710Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-dimensional finite-amplitude solutions in plane Couette flow: bifurcation from infinity

Published online by Cambridge University Press:  26 April 2006

M. Nagata
M. Nagata
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK and Department of Mathematical Sciences, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK Present address: Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

Finite-amplitude solutions of plane Couette flow are discovered. They take a steady three-dimensional form. The solutions are obtained numerically by extending the bifurcation problem of a circular Couette system between co-rotating cylinders with a narrow gap to the case with zero average rotation rate.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 217 , August 1990 , pp. 519 - 527
Copyright
© 1990 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

Andereck, C. D., Dickman, R. & Swinney, H. L. 1983 New flows in a circular Couette system with co-rotating cylinders. Phys. Fluids 26, 1395–1401.Google Scholar
Andereck, C. C., Liu, S. S. & Swinney, H. L. 1986 Flow regimes in a circular Couette system with independently rotating cylinders. J. Fluid Mech. 164, 155–183.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Cowley, S. J. & Smith, F. T. 1985 On the stability of Poiseuille—Couette flow: a bifurcation from infinity. J. Fluid Mech. 156, 83–100.Google Scholar
Craik, A. D. D. 1985 Wave Interactions and Fluid Flows. Cambridge University Press.
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Nagata, M. 1986 Bifurcations in Couette flow between almost co-rotating cylinders. J. Fluid Mech. 169, 229–250.Google Scholar
Nagata, M. 1988 On wavy instabilities of the Taylor-vortex flow between co-rotating cylinders. J. Fluid Mech. 188, 585–598.Google Scholar
Orszag, S. A. & Kells, L. C. 1980 Transition to turbulence in plane Poiseuille and plane Couette flow. J. Fluid Mech. 96, 159–206.Google Scholar
Reichardt, H. 1959 Über die Geschwindigkeitsverteilung in einer geradlinigen turbulenten Couetteströmung. Z. Angew. Math. Mech. 36, S26–29.Google Scholar
Rosenblat, S. & Davis, S. H. 1978 Bifurcation from infinity. SIAM J. Appl. Maths 37, 1–19.Google Scholar