Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-20T05:14:07.405Z Has data issue: false hasContentIssue false
  • English
  • Français

The transition to wavy Taylor vortices

Published online by Cambridge University Press:  20 April 2006

C. A. Jones
C. A. Jones
Affiliation:
School of Mathematics, University of Newcastle-upon-Tyne. NE1 7RU
Get access Rights & Permissions [Opens in a new window]

Abstract

The transition from steady axisymmetric Taylor vortices to time-dependent wavy vortices is examined. The critical Taylor number and frequency at the transition point are determined in the infinite-cylinder approximation for a wide range of parameters. The results are compared with long-aspect-ratio experiments. The variation with axial wavelength is examined, and is found to be important when the radius ratio η < 0.75. A new spatially subharmonic mode is found to be the most unstable mode in some parameter regimes. This mode is identified with the jet mode recently discovered experimentally by Lorenzen, Pfister & Mullin and by Cole.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 157 , August 1985 , pp. 135 - 162
Copyright
© 1985 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

Ahlers G., Cannell, D. S. & Dominguez Lerma 1983 Possible mechanism for transitions in wavy Taylor-vortex flow Phys. Rev. A 27, 1225–1227.Google Scholar
Andereck C. D., Liu, S. S. & Swinney H. L.1984 Flow Regimes in a Circular Couette System with Independently Rotating Cylinders. Univ. of Texas Preprint.
Barcilon A., Brindley J., Lessen, M. & Mobbs F. R.1979 Marginal stability in Taylor—Couette flows at very high Taylor number. J. Fluid Mech. 94, 453–463.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
Cole J. A.1976 Taylor vortex instability and annulus length effects. J. Fluid Mech. 75, 1–15.Google Scholar
Cole J. A.1981 Wavy vortex onset and cylinder radius ratio. Proc. 2nd Taylor vortex flow working party, Tufts University, pp. 11–12. Tufts University, Medford. Mass.
Cole J. A.1983 The effect of cylinder radius ratio on wavy vortex onset. Proc. 3rd Taylor vortex flow working party (Nancy) pp. 1–4.
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, Eagles, P. M. & Ng B. S.1984 The effect of radius ratio on the stability of Couette flow and Taylor vortex flow. To appear in Phys. Fluids.Google Scholar
Donnelly R. J., Park K., Shaw, R. & Walden R. W.1979 Early non-periodic transitions in Couette flow. Phys. Rev. Lett. 44, 987–989.Google Scholar
Eagles P. M.1971 On stability of Taylor vortices by fifth-order amplitude expansions. J. Fluid Mech. 49, 529–550.Google Scholar
Fasel, H. & Booz O.1984 Numerical investigation of supercritical Taylor-vortex flow for a wide gap. J. Fluid Mech. 138, 21–52.Google Scholar
Jones C. A.1981 Nonlinear Taylor vortices and their stability. J. Fluid Mech. 102, 249–261.Google Scholar
Jones C. A.1982 On flow between counter-rotating cylinders. J. Fluid Mech. 120, 433–450.Google Scholar
Jones C. A.1984 Numerical methods for the transition to wavy Taylor vortices. To appear in J. Comp. Phys.Google Scholar
King G. P., Li Y., Lee W., Swinney, H. L. & Marcus P. S.1982 Wave speeds in wavy Taylor vortex flow. J. Fluid Mech. 141, 365–390.Google Scholar
King, G. P. & Swinney H. L.1983 Limits of stability and irregular flow patterns in wavy vortex flow Phys. Rev. A 27, 1240–1243.Google Scholar
Kogelman, S. & DiPrima R. C.1970 Stability of spatially periodic supercritical flows in hydrodynamics. Phys. Fluids 13, 1–11.Google Scholar
Lorenzen A., Pfister, G. & Mullin T.1982 End effects on the transition to time-dependent motion in the Taylor experiment. Phys. Fluids 26, 10–13.Google Scholar
Meyer K.1966 A two-dimensional time-dependent numerical study of rotational Couette flow. Los Alamos rep. LA-3497, Los Alamos, New Mexico.Google Scholar
Meyer K.1969 Three-dimensional study of flow between concentric rotating cylinders. In High Speed Computing in Fluid-Dynamics Phys. Fluid Suppl. II 12, 165–170.Google Scholar
Mullin, T. & Benjamin T. B.1980 Transition to oscillatory motion in the Taylor experiment. Nature 288, 567–569.Google Scholar
Park K.1984 Unusual transition in Taylor wavy vortex flow Phys. Rev. A 29, 3458–3460.Google Scholar
Park, K. & Crawford G. L.1983 Deterministic transitions in Taylor wavy-vortex flow. Phys. Rev. Lett. 50, 343–346.Google Scholar
Park, K. & Donnelly R. J.1981 Study of the transition to Taylor vortex flow Phys. Rev. A 24, 2277–2279.Google Scholar
Park, K. & Jeong K.1984 Stability boundary of Taylor vortex flow. Submitted to Phys Fluids.Google Scholar
Rayleigh Lord1880 On the stability, or instability, of certain fluid motions. Proc. Lond. Math. Soc. 11, 57–70.Google Scholar
Roberts P. H.1965 Appendix to ‘Experiments on the stability of viscous flow between rotating cylinders’ (by R. J. Donnelly & K. W. Schwarz). Proc. R. Soc. Lond. A 283, 531–556.Google Scholar
Taylor G. I.1923 Stability of a viscous liquid contained between two rotating cylinders Phil. Trans. R. Soc. Lond. A 223, 289–343.Google Scholar
Walgraef D., Borckmans, P. & Dewel G.1983 Onset of wavy Taylor vortex flow in finite geometries Phys Rev. A 28.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. ASME publications.