Hostname: page-component-7479d7b7d-m9pkr Total loading time: 0 Render date: 2024-07-12T22:32:28.694Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear Taylor vortices and their stability

Published online by Cambridge University Press:  20 April 2006

C. A. Jones
C. A. Jones
Affiliation:
School of Mathematics, University of Newcastle upon Tyne
Get access Rights & Permissions [Opens in a new window]

Abstract

Axisymmetric numerical solutions of the Navier–Stokes equations for flow between rotating cylinders are obtained. The stability of these solutions to non-axisymmetric perturbations is considered and the results of these calculations are compared with recent experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 102 , January 1981 , pp. 249 - 261
Copyright
© 1981 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

Barcilon, A., Brindley, J., Lessen, M. & Mobbs, F. R. 1979 Marginal instability in Taylor-Couette flows at a very high Taylor number. J. Fluid Mech. 94, 453–463.Google Scholar
Batchelor, G. K. 1956 On steady laminar flow with closed streamlines. J. Fluid Mech. 1, 177–190.Google Scholar
Batchelor, G. K. 1960 Appendix to An empirical torque relation for supercritical flow between rotating cylinders (by R. J. Donnelly & N. J. Simon). J. Fluid Mech. 7, 416–418.Google Scholar
Benjamin, T. B. 1977 Bifurcation phenomena in steady viscous flows of a viscous fluid. I. Theory; II. Experiments. Proc. Roy. Soc. A 359, 1–26; 27–43.Google Scholar
Clever, R. M. & Busse, F. H. 1974 Transition to time-dependent convection. J. Fluid Mech. 65, 625–645.Google Scholar
Cole, J. A. 1976 Taylor vortex instability and annulus-length effects. J. Fluid Mech. 75, 1–15.Google Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385–425.Google Scholar
Davey, A. 1962 The growth of Taylor vortices in flow between rotating cylinders. J. Fluid Mech. 14, 336–368.Google Scholar
Davey, A., DiPrima, R. C. & Stuart, J. T. 1968 On the instability of Taylor vortices. J. Fluid Mech. 31, 17–52.Google Scholar
DiPrima, R. C. 1961 Stability of nonrotationally symmetric disturbances for viscous flow between rotating cylinders. Phys. Fluids 4, 751–755.Google Scholar
DiPrima, R. C. & Eagles, P. M. 1977 Amplification rates and torque for Taylor-vortex flows between rotating cylinders. Phys. Fluids 20, 171–175.Google Scholar
Donnelly, R. J. & Simon, N. J. 1960 An empirical torque relation for supercritical flow between rotating cylinders. J. Fluid Mech. 7, 401–418.Google Scholar
Donnelly, R. J. & Schwarz, K. W. 1965 Experiments on the stability of viscous flow between rotating cylinders. Proc. Roy. Soc. A 283, 531–546.Google Scholar
Donnelly, R. J., Park, K., Shaw, R. & Walden, R. W. 1979 Early non-periodic transitions in Couette flow. (In Press.)
Eagles, P. M. 1971 On stability of Taylor vortices by fifth-order amplitude expansions. J. Fluid Mech. 49, 529–550.Google Scholar
Eagles, P. M. 1974 On the torque of wavy vortices. J. Fluid Mech. 62, 1–9.Google Scholar
Fenstermacher, P. R., Swinney, H. L. & Gollub, J. P. 1979 The transition to chaotic Taylor vortex flow. J. Fluid Mech. 94, 103–127.Google Scholar
Fox, L. & Parker, I. B. 1968 Chebyshev Polynomials in Numerical Analysis. Oxford University Press.
Gorman, M. & Swinney, H. L. 1979 Visual observation of the second characteristic mode in a quasi-periodic flow. Phys. Rev. Lett. 43.Google Scholar
Jones, C. A., Moore, D. R. & Weiss, N. O. 1976 Axisymmetric convection in a cylinder. J. Fluid Mech. 73, 353–388.Google Scholar
Jones, C. A. & Moore, D. R. 1979 Stability of axisymmetric convection. Geophys. Astrophys. Fluid Dyn. 11, 245–270.Google Scholar
Krueger, E. R., Gross, A. & DiPrima, R. C. 1966 On the relative importance of Taylor-vortex and non-axisymmetric modes in flow between rotating cylinders. J. Fluid Mech. 24, 521–538.Google Scholar
Meyer, K. A. 1969 Three-dimensional study of flow between concentric rotating cylinders. In High Speed Computing in Fluid Dynamics. Phys. Fluids Suppl. II12, 165–170.Google Scholar
Moore, D. R. & Weiss, N. O. 1973 Two-dimensional Rayleigh–-Bénard convection. J. Fluid Mech. 58, 289–312.Google Scholar
Rabinowitz, M. I. 1978 Stochastic self-oscillations and turbulence. Sov. Phys. Uspecki 21 (5), 443–469.Google Scholar
Roberts, P. H. 1965 Appendix to Experiments on the stability of viscous flow between rotating cylinders. VI. Finite amplitude experiments. Proc. Roy. Soc. A 283, 531–556.Google Scholar
Rogers, E. H. & Beard, D. W. 1969 A numerical study of wide gap Taylor vortices. J. Comp. Phys. 4, 1–18.Google Scholar
Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. Roy. Soc. A 223, 289–343.Google Scholar
Wright, K. 1964 Chebyshev collocation methods for ordinary differential equations. Computer J. 6, 358–365.Google Scholar
Yahata, H. 1978 Temporal development of the Taylor vortices in a rotating fluid. Prog. Theor. Phys. Suppl. 64, 165–185.Google Scholar
Zarti, A. S. & Mobbs, F. R. 1979 Wavy Taylor vortex flow between eccentric rotating cylinders. Energy conservation through fluid film lubrication technology: Frontiers in Research and Design. A.S.M.E.