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Developments in Laser Techniques and Fluid Mechanics pp 361–380Cite as

LDV-Measurements on the Chaotic Behaviour in Wide Gap Spherical Couette Flow

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Abstract

We report on a concurrent study of LDV-measurements on bifurcation scenario in rotating spherical Couette flow. As an example for a bifurcation scenario a complex route into chaos can be observed in the wide gap spherical Couette flow experimentally. By increasing the Reynolds number with the angular velocity of the driving inner sphere the flow bifurcates from laminar axisymmetric basic flow to the periodic motion of non-axisymmetric secondary spiral waves for relative large aspect ratios (Egbers, 1994). In the present study the relative wide gap width of ß = 0.50 is chosen. The spiral waves exist over a wide range of the Reynolds number. In this range a change in shape and periodicity can be detected by visualization with small aluminum flakes and also measured by Laser Doppler velocime- try (LDV-technique). At high Reynolds numbers, the flow undergoes a bifurcation to low-dimensional chaotic motion before it eventually becomes turbulent. The dynamic behaviour is discussed by spectral bifurcation diagrams, reconstructed attractors and their Lyapunov exponents as a quantitative parameter. These quantities are calculated from the measured LDV time series.

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References

  • Andereck, C.D., Liu, S.S. and Swinney, H.L. (1986): Flow regimes in a circular Couette system with independently rotating cylinders. J. Fluid Mech., vol. 164, 155–183

    Article  ADS  Google Scholar 

  • Belyaev, Yu.N., Monakhov, A.A., Scherbakov, S.A. and Yavorskaya, I.M. (1984): Some routes to turbulence in spherical Couette Flow, in: Kozlov, V.V. (ed.): Laminar-Turbulent Transition. IUTAM-Symp. Novosibirsk/USSR, Springer

    Google Scholar 

  • Broomhead, D.S. & King, G.P. (1986): Physica D 20, 217

    ADS  MathSciNet  Google Scholar 

  • Bühler, K. (1985): Strömungsmechanische Instabilitäten zäher Medien im Kugelspalt. VDI-Berichte, Reihe7: Strömungstechnik Nr. 96

    Google Scholar 

  • Bühler, K. and Zierep, J. (1984): New secondary instabilities for high Re-number flow between two rotating spheres, in: Kozlov, V. V. (ed.): Laminar-Turbulent Transition. IUTAM-Symp. Novosibirsk/USSR, Springer, Berlin, Heidelberg, New York, Tokyo

    Google Scholar 

  • Bühler, K. and Zierep, J. (1986): Dynamical instabilities and transition to turbulence in spherical gap flows, in: Comte-Bellot, G. and Mathieu, J.: Advances in turbulence. Proc. 1st Europ. Turb. Conf., Lyon, France, 1–4 July, Springer, Berlin, Heidelberg, NewYork, London, Paris, Tokyo

    Google Scholar 

  • Buzug, Th.& Pfister, G (1992): Physical Review A 45, 10

    Article  Google Scholar 

  • Buzug, Th., V. Stamm, J. and Pfister, G. (1992): Fractal dimensions of strange attractors obtained from the Taylor-Couette experiment. Phys. A, 191, 559

    Article  Google Scholar 

  • Buzug, Th., v. Stamm, J. and Pfister, G. (1993): Characterization of period-doubling scenarios in Taylor- Couette flow. Physical Review E, 47, no. 2, 1054–1065

    Article  ADS  Google Scholar 

  • Egbers, C. (1994): Zur Stabilität der Strömung im konzentrischen Kugelspalt. Dissertation, Universität Bremen

    Google Scholar 

  • Egbers, C. and Rath, H.J. (1995): The existence of Taylor vortices and wide-gap instabilities in spherical Couette flow. Acta Mech. 111, 3–4, 125–140

    Article  Google Scholar 

  • Egbers, C. and Rath, H.J. (1996): Developments in Laser Techniques and Applications to Fluid Mechanics (Eds.: R.J. Adrian, D.F.G. Durao, F. Durst, M.V. Heitor, M. Maeda, J.H. Whitelaw), Springer,45–66

    Chapter  Google Scholar 

  • Fechtmann, C., Wulf, P., Egbers, C. & Rath, H.J.; 1996; LDA-Messungen zum chaotischen Verhalten der Strömung im konzentrischen Kugelspalt; Lasermethoden in der Strömungsmeßtechnik, 5. Fachtagung der GALA, 11.–13. Sept. Berlin, vol. V, pp 17.1–17.7

    Google Scholar 

  • Fenstermacher, P.R., Swinney, H.L. and Gollub, J.P. (1979): Dynamic instabilities and the transition to chaotic Taylor vortex flow. J. Fluid Mech., 94, part 1, 103–128

    Article  ADS  Google Scholar 

  • Holzfuss, J. (1987): Doctoral thesis, Universität Göttingen

    Google Scholar 

  • Landau, L.D. (1944): On the problem of turbulence. C. R. Acad. Sci. USSR 44, 311

    MATH  Google Scholar 

  • Liu, M., Blohm, C., Egbers, C., Wulf, P. & Rath, H. J.; 1996; Taylor vortices in wide spherical shells.; Phys. Rev. Lett., vol. 77, No. 2, pp 286–289

    Article  ADS  Google Scholar 

  • Mullin, T. (1993): The nature of chaos, Oxford Science Publications

    MATH  Google Scholar 

  • Munson, B.R. and Menguturk, M. (1975): Viscous incompressible flow between concentric rotating spheres. Part 3: Linear stability and experiments. J. Fluid Mech., vol. 69, 705–719

    Article  ADS  MATH  Google Scholar 

  • Nakabayashi, K. and Tsuchida, Y. (1988): Spectral study of the laminar-turbulent transition in spherical Couette flow. J. Fluid Mech., vol. 194, 101–132

    Article  ADS  Google Scholar 

  • Sawatzki, O. und Zierep, J. (1970): Das Stromfeld im Spaltzwischen zwei konzentrischenKugelflächen, von denen die innere rotiert. Acta Mech. 9, 13–35

    Article  Google Scholar 

  • v. Stamm, J., Buzug, Th. and Pfister, G. (1993): Frequency locking in axisymmetric Taylor Couette flow. Physical Review E., submitted

    Google Scholar 

  • Takens, F. (1980): Lecture Notes in Mathematics, 898, Springer

    Google Scholar 

  • Taylor, G.J. (1923): Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. A223,289–293

    ADS  Google Scholar 

  • Wimmer, M. (1981): Experiments on the stability of viscous flow between two concentric rotating spheres. J. Fluid Mech., vol.103, 117–131

    Article  ADS  Google Scholar 

  • Yavorskaya, I.M., Belyaev, Yu.N. and Monakhov, A.A. (1975): Experimental study of a spherical Couette flow. Sov. Phys. Dokl., vol. 20, 4, 256–258

    ADS  Google Scholar 

  • Yavorskaya, I.M., Belyaev, Yu.N., Monakhov, A.A., Astafeva, N.M, Scherbakov, S.A. and Vvedenskaya, N.D. (1980): Stability, non-uniqueness and transition to turbulence in the flow between two rotating spheres. IUTAM-Symposium, Toronto

    Google Scholar 

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Author information

Authors and Affiliations

  1. Center of Applied Space Technology and Microgravity (ZARM), University of Bremen, 28359, Bremen, Germany

    P. Wulf, C. Fechtmann, C. Egbers & H. J. Rath

Authors
  1. P. Wulf
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  2. C. Fechtmann
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  3. C. Egbers
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  4. H. J. Rath
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Editor information

Editors and Affiliations

  1. Dept. of Theoretical and Applied Mechanics, University of Illinois at Urbana — Champaign, 61801, Urbana, Illinois, USA

    R. J. Adrian

  2. Dept. of Mechanical Engineering, Instituto Superior Técnico, Av. Rovisco Pais, 1096, Lisboa Codex, Portugal

    D. F. G. Durão

  3. Lehrstuhl für Strömungsmechanik, University of Erlangen — Nuremberg, Cauerstraße 4, 91058, Erlangen, Germany

    F. Durst

  4. Dept. of Mechanical Engineering, Instituto Superior Técnico, Av. Rovisco Pais, 1096, Lisboa Codex, Portugal

    M. V. Heitor

  5. Dept. of Mechanical Engineering, Keio University, 1-14-1 Hiyoshi, 223, Kohuku Yokohama, Japan

    M. Maeda

  6. Imperial College of Science, Technology and Medicine, Dept. of Mechanical Engineering, Exhibition Road, SW 7 2BX, London, England

    J. H. Whitelaw

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© 1997 Springer-Verlag Berlin Heidelberg

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Wulf, P., Fechtmann, C., Egbers, C., Rath, H.J. (1997). LDV-Measurements on the Chaotic Behaviour in Wide Gap Spherical Couette Flow. In: Adrian, R.J., Durão, D.F.G., Durst, F., Heitor, M.V., Maeda, M., Whitelaw, J.H. (eds) Developments in Laser Techniques and Fluid Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60911-4_23

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  • DOI: https://doi.org/10.1007/978-3-642-60911-4_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64604-1

  • Online ISBN: 978-3-642-60911-4

  • eBook Packages: Springer Book Archive

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