Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-12T19:55:05.857Z Has data issue: false hasContentIssue false
  • English
  • Français

A numerical and experimental investigation of a new solution in the Taylor vortex problem

Published online by Cambridge University Press:  26 April 2006

D. K. Anson ,
T. Mullin  and
K. A. Cliffe
D. K. Anson
Affiliation:
Mathematical Institute, Oxford University, Oxford OX1 3LB, UK Present address: ICI Corporate Management Services, Brunner Business Centre, Brunner House, PO Box 7, Winnington, Northwich, Cheshire CW8 4DJ, UK.
T. Mullin
Affiliation:
Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
K. A. Cliffe
Affiliation:
Theoretical Physics Division, UKAEA, Harwell Laboratory, Oxon OX11 ORA, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

We present the results of a numerical and experimental study of the five-cell flow in the Taylor vortex problem. There is evidence for a new five-cell solution which is different in nature to the previously recorded solution. We find that there is an exchange in stability between the two solutions which we explain in terms of bifurcation theory. Streamline plots of the numerical results are compared with photographs of the observed flow. The agreement between the calculations and experiments is good. We use the Schaeffer homotopy to study the new solution in the periodic model. The results show that the new solution is not connected in any continuous manner to the trivial Couette flow solution.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 207 , October 1989 , pp. 475 - 487
Copyright
© 1989 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

Benjamin, T. B. 1978 Bifurcation phenomena in steady flows of a viscous liquid. I. Theory. Proc. R. Soc. Lond. A 359, 1–26.Google Scholar
Benjamin, T. B. 1978b Bifurcation phenomena in steady flows of a viscous liquid. II. Experiments. Proc. R. Soc. Lond. A 359, 27–43.Google Scholar
Benjamin, T. B. & Mullin, T. 1981 Anomalous modes in the Taylor experiment. Proc. R. Soc. Lond. A 377, 221–249.Google Scholar
Bolstad, J. H. & Keller, H. B. 1987 Computation of anomalous modes in the Taylor experiment. J. Comput. Phys. 69, 230–251.Google Scholar
Cliffe, K. A. 1983 Numerical calculations of two-cell and single-cell Taylor flows J. Fluid Mech. 135, 219–233.Google Scholar
Cliffe, K. A. & Mullin, T. 1985 A numerical and experimental study of anomalous modes in the Taylor experiment. J. Fluid Mech. 153, 243–258.Google Scholar
Cliffe, K. A. & Spence, A. 1984 The calclation of high order singularities in the finite Taylor problem. In Numerical Methods for Bifurcation Problems (ed. T. Küpper, H. D. Mittelman & H. Weber), pp. 129–144. ISNM, Birkhäuser.
Griewank, A. & Reddien, G. 1983 The calculation of Hopf points by a direct method. IMA J. Numer. Anal. 3, 295–303.Google Scholar
Guckenheimer, J. & Holmes, P. J. 1986 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer.
Jepson, A. D. & Spence, A. 1985 Folds in solutions of two parameter systems and their calculation Part I. SIAM J. Numer. Anal. 22, 347–368.Google Scholar
Jepson, A. D., Spence, A. & Cliffe, K. A. 1988 Hopf along a fold. Harwell Rep. AERE-Tp. 1264.
Keller, H. B. 1977 Numerical solutions of bifurcation and nonlinear eigenvalue problems. In Applications of Bifurcation Theory (ed. P. H. Rabinowitz), pp. 359–384. Academic.
Moore, G. & Spence, A. 1980 The calculation of turning points of nonlinear equations. SIAM J. Numer. Anal. 17, 567–576.Google Scholar
Pfister, G., Schmidt, H., Cliffe, K. A. & Mullin, T. 1988 Bifurcation phenomena in Taylor-Couette flow in a very short annulus. J. Fluid Mech. 191, 1–18.Google Scholar
Schaeffer, D. G. 1980 Analysis of a model in the Taylor problem. Math. Proc. Camb. Phil. Soc. 87, 307–337.Google Scholar
Werner, B. & Spence, A. 1984 The computation of symmetry-breaking bifurcation points. SIAM J. Numer. Anal. 21, 388–399.Google Scholar