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
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
Broomhead, D.S. & King, G.P. (1986): Physica D 20, 217
Bühler, K. (1985): Strömungsmechanische Instabilitäten zäher Medien im Kugelspalt. VDI-Berichte, Reihe7: Strömungstechnik Nr. 96
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
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
Buzug, Th.& Pfister, G (1992): Physical Review A 45, 10
Buzug, Th., V. Stamm, J. and Pfister, G. (1992): Fractal dimensions of strange attractors obtained from the Taylor-Couette experiment. Phys. A, 191, 559
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
Egbers, C. (1994): Zur Stabilität der Strömung im konzentrischen Kugelspalt. Dissertation, Universität Bremen
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
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
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
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
Holzfuss, J. (1987): Doctoral thesis, Universität Göttingen
Landau, L.D. (1944): On the problem of turbulence. C. R. Acad. Sci. USSR 44, 311
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
Mullin, T. (1993): The nature of chaos, Oxford Science Publications
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
Nakabayashi, K. and Tsuchida, Y. (1988): Spectral study of the laminar-turbulent transition in spherical Couette flow. J. Fluid Mech., vol. 194, 101–132
Sawatzki, O. und Zierep, J. (1970): Das Stromfeld im Spaltzwischen zwei konzentrischenKugelflächen, von denen die innere rotiert. Acta Mech. 9, 13–35
v. Stamm, J., Buzug, Th. and Pfister, G. (1993): Frequency locking in axisymmetric Taylor Couette flow. Physical Review E., submitted
Takens, F. (1980): Lecture Notes in Mathematics, 898, Springer
Taylor, G.J. (1923): Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. A223,289–293
Wimmer, M. (1981): Experiments on the stability of viscous flow between two concentric rotating spheres. J. Fluid Mech., vol.103, 117–131
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
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
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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
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