Hostname: page-component-7dd5485656-zklqj Total loading time: 0 Render date: 2025-10-29T20:16:14.381Z Has data issue: false hasContentIssue false
  • English
  • Français

Axisymmetric propagating vortices in centrifugally stable Taylor–Couette flow

Published online by Cambridge University Press:  11 July 2013

C. Hoffmann ,
S. Altmeyer ,
M. Heise ,
J. Abshagen  and
G. Pfister
C. Hoffmann
Affiliation:
Institut für Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
S. Altmeyer
Affiliation:
Institut für Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany Department of Mathematics, Kyungpook National University, Deagu, 702-701, Korea
M. Heise*
Affiliation:
Institut für Experimentelle und Angewandte Physik, Universität Kiel, D-24098 Kiel, Germany
J. Abshagen
Affiliation:
Institut für Experimentelle und Angewandte Physik, Universität Kiel, D-24098 Kiel, Germany
G. Pfister
Affiliation:
Institut für Experimentelle und Angewandte Physik, Universität Kiel, D-24098 Kiel, Germany
*
†Email address for correspondence: heise@physik.uni-kiel.de
Get access Rights & Permissions [Opens in a new window]

Abstract

We present numerical as well as experimental results of axisymmetric, axially propagating vortices appearing in counter-rotating Taylor–Couette flow below the centrifugal instability threshold of circular Couette flow without additional externally imposed forces. These propagating vortices are periodically generated by the shear flow near the Ekman cells that are induced by the non-rotating end walls. These axisymmetric vortices propagate into the bulk towards mid-height, where they get annihilated by rotating, non-propagating defects. These propagating structures appear via a supercritical Hopf bifurcation from axisymmetric, steady vortices, which have been discovered recently in centrifugally stable counter-rotating Taylor–Couette flow (Abshagen et al., Phys. Fluids, vol. 22, 2010, 021702). In the nonlinear regime of the Hopf bifurcation, contributions of non-axisymmetric modes also appear.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Convection: Convection Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Nonlinear Dynamical Systems: Pattern formation

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 728 , 10 August 2013 , pp. 458 - 470
Copyright
©2013 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.)

Article purchase

Temporarily unavailable

References

Abshagen, J., Heise, M., Pfister, G. & Mullin, T. 2010 Multiple localized states in centrifugally stable rotating flow. Phys. Fluids 22, 021702.Google Scholar
Altmeyer, S. & Hoffmann, C. 2010 Secondary bifurcation of mixed-cross-spirals connecting travelling wave solutions. New J. Phys. 12 (11), 113035.Google Scholar
Altmeyer, S., Hoffmann, C., Heise, M., Abshagen, J., Pinter, A., Lücke, M. & Pfister, G. 2010 End wall effects on the transitions between Taylor vortices and spiral vortices. Phys. Rev. E 81 (6), 066313.Google Scholar
Altmeyer, S., Hoffmann, C. & Lücke, M. 2011 Islands of instability for growth of spiral vortices in the Taylor–Couette system with and without axial through flow. Phys. Rev. E 84 (4), 046308.Google Scholar
Andereck, C. D., Liu, S. S. & Swinney, H. L. 1986 Flow regimes in a circular Couette system with independently rotating cylinders. J. Fluid Mech. 164, 155–183.CrossRefGoogle Scholar
Avila, M., Grimes, M., Lopez, J. M. & Marques, F. 2008 Global endwall effects on centrifugally stable flows. Phys. Fluids 20, 104104.CrossRefGoogle Scholar
Benjamin, T. B. 1978 Bifurcation phenomena in steady flows of a viscous fluid. I. Theory. – II. Experiments. Proc. R. Soc. Lond. A 359, 1–26 and 27–43.Google Scholar
Bodenschatz, E., Pesch, W. & Ahlers, G. 2000 Recent developments in Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 32 (1), 709–778.CrossRefGoogle Scholar
Borrero-Echeverry, D., Schatz, M. F. & Tagg, R. 2010 Transient turbulence in Taylor–Couette flow. Phys. Rev. E 81, 025301.Google Scholar
Cliffe, K. A., Mullin, T. & Schaeffer, D. 2012 The onset of steady vortices in Taylor–Couette flow: the role of approximate symmetry. Phys. Fluids 24 (6), 064102.Google Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21 (3), 385–425.CrossRefGoogle Scholar
Cross, M. C. & Hohenberg, P. C. 1993 Pattern formation outside of equilibrium. Rev. Mod. Phys. 65 (3), 851–1112.Google Scholar
Czarny, O., Serre, E., Bontoux, P. & Lueptow, R. M. 2003 Interaction between Ekman pumping and the centrifugal instability in Taylor–Couette flow. Phys. Fluids 15, 467–477.Google Scholar
Di Prima, R. C. & Swinney, H. L. 1981 Instabilities and transition in flow between concentric rotating cylinders. In Hydrodynamic Instabilities and the Transition to Turbulence, Topics in Applied Physics, vol. 45, pp. 139–180. Springer.Google Scholar
Edwards, W. S., Beane, S. R. & Varma, S. 1991 Onset of wavy vortices in the finite-length Couette–Taylor problem. Phys. Fluids 3 (6), 1510–1518.CrossRefGoogle Scholar
Golubitsky, M., Stewart, I. & Schaeffer, D. G. 1988 Singularities and Groups in Bifurcation Theory, vol. I, Applied Mathematical Sciences, vol. 51. Springer.Google Scholar
Guckenheimer, J. & Holmes, P. 1983 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Applied Mathematical Sciences, vol. 42. Springer.Google Scholar
Heise, M., Abshagen, J., Hochstrate, K., Küter, D., Pfister, G. & Hoffmann, C. 2008 Localized spirals in Taylor–Couette flow. Phys. Rev. E 77, 026202.Google Scholar
Heise, M., Hoffmann, C., Will, C., Altmeyer, S., Abshagen, J. & Pfister, G. 2013 Co-rotating Taylor–Couette flow enclosed by stationary disks. J. Fluid Mech. 716, R4 (12pp).CrossRefGoogle Scholar
Hoffmann, C., Altmeyer, S., Pinter, A. & Lücke, M. 2009 Transitions between Taylor vortices and spirals via wavy Taylor vortices and wavy spirals. New J. Phys. 11, 053002.Google Scholar
Hoffmann, C. & Lücke, M. 2000 Spiral vortices and Taylor vortices in the annulus between counter-rotating cylinders. In Physics of Rotating Fluids, Lecture Notes in Physics, vol. 549, pp. 55–66. Springer.CrossRefGoogle Scholar
Hoffmann, C., Lücke, M. & Pinter, A. 2004 Spiral vortices and Taylor vortices in the annulus between rotating cylinders and the effect of an axial flow. Phys. Rev. E 69 (5), 056309.Google Scholar
Hoffmann, C., Lücke, M. & Pinter, A. 2005 Spiral vortices travelling between two rotating defects in the Taylor–Couette system. Phys. Rev. E 72 (5), 056311.CrossRefGoogle ScholarPubMed
Langford, W. F., Tagg, R., Kostelich, E. J., Swinney, H. L. & Golubitsky, M. 1988 Primary instabilities and bicriticality in flow between counter rotating cylinders. Phys. Fluids 31, 776–785.Google Scholar
Lopez, J. M. & Marques, F. 2002 Modulated Taylor–Couette flow: onset of spiral modes. Theor. Comput. Fluid Dyn. 16, 59–69.Google Scholar
Lopez, J. M., Marquez, F. & Shen, J. 2000 Endwall effects in a periodically forced centrifugally unstable flow. Fluid Dyn. Res. 27 (2), 91.Google Scholar
Lorenzen, A., Pfister, G. & Mullin, T. 1983 End effects on the transition to time-dependent motion in the Taylor experiment. Phys. Fluids 26 (1), 10–13.CrossRefGoogle Scholar
Marques, F. & Lopez, J. M. 2000 Spacial and temporal resonances in a periodically forced hydrodynamic system. Physica D 136, 340–352.CrossRefGoogle Scholar
Tagg, R. 1994 The Couette–Taylor problem. Nonlinear Sci. Today 4 (3), 1–25.Google Scholar