Disappearance Phenomena of Velocity Fluctuation in the Transition of Spherical Couette Flow
In order to study on disappearance phenomena of velocity fluctuation in the laminar-turbulent transition of spherical Couette flow with only an inner sphere rotating, we measured azimuthal component of velocity fluctuation at the equator for various clearance ratios β=0.06∼0.206, and considered the...
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| Published in | Nihon Kikai Gakkai rombunshuu. B hen Vol. 68; no. 668; pp. 972 - 978 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | Japanese |
| Published |
The Japan Society of Mechanical Engineers
2002
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0387-5016 1884-8346 |
| DOI | 10.1299/kikaib.68.972 |
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| Abstract | In order to study on disappearance phenomena of velocity fluctuation in the laminar-turbulent transition of spherical Couette flow with only an inner sphere rotating, we measured azimuthal component of velocity fluctuation at the equator for various clearance ratios β=0.06∼0.206, and considered the evolution of correlation dimension d, maximum Lyapunov exponent λ and power spectra of the azimuthal velocity component with an increase of the rotating Reynolds number Re for each β. Consequently, the following conclusions were obtained. The disappearance phenomena occur only for β≒0.13∼0.17. Even though d≒2, no T2 torus appears in the case of λ>0. The kinetic energy of disturbance increases with Re in the range of higher frequencies in the case of β where the disappearance phenomena do not occur, but decreases to almost zero in the case where they occur. |
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| AbstractList | In order to study on disappearance phenomena of velocity fluctuation in the laminar-turbulent transition of spherical Couette flow with only an inner sphere rotating, we measured azimuthal component of velocity fluctuation at the equator for various clearance ratios β=0.06∼0.206, and considered the evolution of correlation dimension d, maximum Lyapunov exponent λ and power spectra of the azimuthal velocity component with an increase of the rotating Reynolds number Re for each β. Consequently, the following conclusions were obtained. The disappearance phenomena occur only for β≒0.13∼0.17. Even though d≒2, no T2 torus appears in the case of λ>0. The kinetic energy of disturbance increases with Re in the range of higher frequencies in the case of β where the disappearance phenomena do not occur, but decreases to almost zero in the case where they occur. |
| Author | ADACHI, Naofumi SHA, Weiming TSUCHIDA, Yoichi NAKABAYASHI, Koichi |
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| References | (3) Buhler, K. and Zierep, J. (Comte-Bellot, G. and Mathieu, J., eds.), Dynamical Instabilities and Transition to Turbulence in Spherical Gap Flows, Advances in Turbulence, Proceeding 1st European Turbulence Conference, (1987), 16-26, Springer. (12) Brandstater, A. and Swinney, H.L., Strange Attractors in Weakly Turbulent Couette-Taylor Flow, (13) Belyaev, Yu. N. and Yavorskaya, I.M., Spherical Couette Flow: Transitions and Onset of Chaos, Fluid Dyn., 26-1 (1991), 7-15. (9) 中林功一•鄭志明,回転2球間クエット流におけるかく乱の基本周波数のすきま比依存性,機論,55-517,B(1989),2574-2580. (5) Buhler, K. and Zierep, J. (Kozlov, V.V., ed.), New Secondary Instabilities for High-Re number Flow between Two Rotating Spheres, Laminar- Turbulent Transition, (1984), 677-685, Springer. (4) Yavorskaya, I.M., ほか5名, Stability, Non-uniqueness and Transition to Turbulence in the Flow between Two Rotating Spheres, (1980), 1, Space Research Institute, Academy of Science, USSR. (6) Nakabayashi, K. and Tsuchida, Y., Flow-History Effect on Higher Modes in the Spherical Couette System, J. Fluid Mech., 295 (1995), 43-60. (11) 中林功一•森西洋平•小林政弘,すきま比β=0.14での回転2球間クエット流れの層流一乱流遷移のカオス,機論,63-615,B(1997),3499-3504. (1) Nakabayashi, K., Transition of Taylor-Gortler Vortex Flow in Spherical Couette Flow, J. Fluid Mech., 132 (1983), 209-230. (14) Wolf, A., Swift, J.B., Swinney, H.L. and Vastano, J.A., Determining Lyapunov Exponents from a Time Series, Physic, 16D (1985), 285-317. (8) Egbers, C. and Rath, H.J., Existence of Taylor Vortices and Wide-Gap Instabilities in Spherical Couette Flow, Acta Mech., 111 (1995), 125-140. (2) Nakabayashi, K. and Tsuchida, Y., Spectral Study of the Laminar-Turbulent Transition in Spherical Couette Flow, J. Fluid Mech., 194 (1988), 101-132. (10) 中林功一•鄭志明,2球間クエット超臨界流のかく乱の構造と渦運動,機論,57-541,B(1991),2924-2930. (15) Fraser, A.M. and Swinney, H.L., Independent Coordinates for Strange Attractors from Mutual Information, Phys. Rev., A33 (1986), 1134-1140. (16) Buhler, K., Symmetric and Asymmetric Taylor Vortex Flow in Spherical Gaps, Acto Mech., 81 (1990), 3-38. (7) Araki, K., Mizushima, J. and Yanase, S., The Nonaxisymmetric Instability of the Wide-Gap Spherical Couette Flow, Phys Fluids, 9 (1997), 1197-1199. |
| References_xml | – reference: (2) Nakabayashi, K. and Tsuchida, Y., Spectral Study of the Laminar-Turbulent Transition in Spherical Couette Flow, J. Fluid Mech., 194 (1988), 101-132. – reference: (15) Fraser, A.M. and Swinney, H.L., Independent Coordinates for Strange Attractors from Mutual Information, Phys. Rev., A33 (1986), 1134-1140. – reference: (7) Araki, K., Mizushima, J. and Yanase, S., The Nonaxisymmetric Instability of the Wide-Gap Spherical Couette Flow, Phys Fluids, 9 (1997), 1197-1199. – reference: (14) Wolf, A., Swift, J.B., Swinney, H.L. and Vastano, J.A., Determining Lyapunov Exponents from a Time Series, Physic, 16D (1985), 285-317. – reference: (1) Nakabayashi, K., Transition of Taylor-Gortler Vortex Flow in Spherical Couette Flow, J. Fluid Mech., 132 (1983), 209-230. – reference: (5) Buhler, K. and Zierep, J. (Kozlov, V.V., ed.), New Secondary Instabilities for High-Re number Flow between Two Rotating Spheres, Laminar- Turbulent Transition, (1984), 677-685, Springer. – reference: (6) Nakabayashi, K. and Tsuchida, Y., Flow-History Effect on Higher Modes in the Spherical Couette System, J. Fluid Mech., 295 (1995), 43-60. – reference: (11) 中林功一•森西洋平•小林政弘,すきま比β=0.14での回転2球間クエット流れの層流一乱流遷移のカオス,機論,63-615,B(1997),3499-3504. – reference: (4) Yavorskaya, I.M., ほか5名, Stability, Non-uniqueness and Transition to Turbulence in the Flow between Two Rotating Spheres, (1980), 1, Space Research Institute, Academy of Science, USSR. – reference: (10) 中林功一•鄭志明,2球間クエット超臨界流のかく乱の構造と渦運動,機論,57-541,B(1991),2924-2930. – reference: (16) Buhler, K., Symmetric and Asymmetric Taylor Vortex Flow in Spherical Gaps, Acto Mech., 81 (1990), 3-38. – reference: (9) 中林功一•鄭志明,回転2球間クエット流におけるかく乱の基本周波数のすきま比依存性,機論,55-517,B(1989),2574-2580. – reference: (12) Brandstater, A. and Swinney, H.L., Strange Attractors in Weakly Turbulent Couette-Taylor Flow, (13) Belyaev, Yu. N. and Yavorskaya, I.M., Spherical Couette Flow: Transitions and Onset of Chaos, Fluid Dyn., 26-1 (1991), 7-15. – reference: (3) Buhler, K. and Zierep, J. (Comte-Bellot, G. and Mathieu, J., eds.), Dynamical Instabilities and Transition to Turbulence in Spherical Gap Flows, Advances in Turbulence, Proceeding 1st European Turbulence Conference, (1987), 16-26, Springer. – reference: (8) Egbers, C. and Rath, H.J., Existence of Taylor Vortices and Wide-Gap Instabilities in Spherical Couette Flow, Acta Mech., 111 (1995), 125-140. |
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| Title | Disappearance Phenomena of Velocity Fluctuation in the Transition of Spherical Couette Flow |
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