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Flow regimes in a plane Couette flow with system rotation

Published online by Cambridge University Press:  07 April 2010

T. TSUKAHARA ,
N. TILLMARK  and
P. H. ALFREDSSON
T. TSUKAHARA*
Affiliation:
Linné Flow Centre, KTH Mechanics, Royal Institute of Technology, S-100 44, Stockholm, Sweden
N. TILLMARK
Affiliation:
Linné Flow Centre, KTH Mechanics, Royal Institute of Technology, S-100 44, Stockholm, Sweden
P. H. ALFREDSSON
Affiliation:
Linné Flow Centre, KTH Mechanics, Royal Institute of Technology, S-100 44, Stockholm, Sweden
*
†Present address: Department of Mechanical Engineering, Faculty of Science and Technology, Tokyo University of Science, Yamazaki 2641, Noda-shi, Chiba, 278-8510, Japan. Email address for correspondence: [email protected]
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Abstract

Flow states in plane Couette flow in a spanwise rotating frame of reference have been mapped experimentally in the parameter space spanned by the Reynolds number and rotation rate. Depending on the direction of rotation, the flow is either stabilized or destabilized. The experiments were made through flow visualization in a Couette flow apparatus mounted on a rotating table, where reflected flakes are mixed with the water to visualize the flow. Both short- and long-time exposures have been used: the short-time exposure gives an instantaneous picture of the turbulent flow field, whereas the long-time exposure averages the small, rapidly varying scales and gives a clearer representation of the large scales. A correlation technique involving the light intensity of the photographs made it possible to obtain, in an objective manner, both the spanwise and streamwise wavelengths of the flow structures. During these experiments 17 different flow regimes have been identified, both laminar and turbulent with and without roll cells, as well as states that can be described as transitional, i.e. states that contain both laminar and turbulent regions at the same time. Many of these flow states seem to be similar to those observed in Taylor–Couette flow.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 648 , 10 April 2010 , pp. 5 - 33
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Alfredsson, P. H. & Persson, H. 1989 Instabilities in channel flow with system rotation. J. Fluid Mech. 202, 543–557.CrossRefGoogle Scholar
Alfredsson, P. H. & Tillmark, N. 2005 Instability, transition and turbulence in plane Couette flow with system rotation. In IUTAM Symposium on Laminar Turbulent Transition and Finite Amplitude Solutions (ed. Mullin, T. & Kerswell, R. R.), Fluid Mechanics and Its Applications, vol. 77, pp. 173–193. Springer.CrossRefGoogle 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
Barkley, D. & Tuckerman, L. S. 2005 Computational study of turbulent laminar patterns in Couette flow. Phys. Rev. Lett. 94, 014502.CrossRefGoogle ScholarPubMed
Barkley, D. & Tuckerman, L. S. 2007 Mean flow of turbulent–laminar patterns in plane Couette flow. J. Fluid Mech. 576, 109–137.CrossRefGoogle Scholar
Barth, W. L. & Burns, C. A. 2007 Virtual rheoscopic fluids for flow visualization. IEEE Trans. Visual. Comp. Graphics 13, 1751–1758.CrossRefGoogle ScholarPubMed
Bech, K. H. & Andersson, H. I. 1996 Secondary flow in weakly rotating turbulent plane Couette flow. J. Fluid Mech. 317, 195–214.CrossRefGoogle Scholar
Bech, K. H. & Andersson, H. I. 1997 Turbulent plane Couette flow subject to strong system rotation. J. Fluid Mech. 347, 289–314.CrossRefGoogle Scholar
Bech, K. H., Tillmark, N., Alfredsson, P. H. & Andersson, H. I. 1995 An investigation of turbulent plane Couette flow at low Reynolds numbers. J. Fluid Mech. 286, 291–325.CrossRefGoogle Scholar
Carey, C. S., Schlender, A. B. & Andereck, C. D. 2007 Localized intermittent short-wavelength bursts in the high-radius ratio limit of the Taylor–Couette system. Phys. Rev. E 75, 016303.CrossRefGoogle ScholarPubMed
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.Google Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385–425.CrossRefGoogle Scholar
Dauchot, O. & Daviaud, F. 1995 Finite amplitude perturbation and spots growth mechanism in plane Couette flow. Phys. Fluids 7, 335–343.CrossRefGoogle Scholar
Daviaud, F., Hegseth, J. & Bergé, P. 1992 Subcritical transition to turbulence in plane Couette flow. Phys. Rev. Lett. 69, 2511–2514.CrossRefGoogle ScholarPubMed
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Faisst, H. & Eckhardt, B. 2000 Transition from the Couette–Taylor system to the plane Couette system. Phys. Rev. E 61, 7227–7230.CrossRefGoogle Scholar
Hegseth, J. J., Anderech, C. D., Hayot, F. & Pomeau, Y. 1989 Spiral turbulence and phase dynamics. Phys. Rev. Lett. 62, 257–260.CrossRefGoogle ScholarPubMed
Hiwatashi, K., Alfredsson, P. H., Tillmark, N. & Nagata, M. 2007 Experimental observations of instabilities in rotating plane Couette flow. Phys. Fluids 19, 048103.CrossRefGoogle Scholar
Johnston, J. P., Halleent, R. M. & Lezius, D. K. 1972 Effects of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow. J. Fluid Mech. 56, 533–557.CrossRefGoogle Scholar
Kitoh, O., Nakabayashi, K. & Nishimura, F. 2005 Experimental study on mean velocity and turbulence characteristics of plane Couette flow: low-Reynolds-number effects and large longitudinal vortical structure. J. Fluid Mech. 539, 199–227.CrossRefGoogle Scholar
Komminaho, J., Lundblad, A. & Johansson, A. V. 1996 Very large structures in plane turbulent Couette flow. J. Fluid Mech. 320, 259–285.CrossRefGoogle Scholar
Koschmieder, E. L. 1993 Bénard Cells and Taylor Vortices. Cambridge University Press.Google Scholar
Lee, M. J. & Kim, J. 1991 The structure of turbulence in a simulated plane Couette flow. In Proceedings of Eighth Symposium on Turbulent Shear Flows (ed. Durst, F. et al. ), Munich, Germany, paper 5-3, 6 pp.Google Scholar
Lezius, D. K. & Johnston, J. P. 1976 Roll-cell instabilities in rotating laminar and turbulent channel flows. J. Fluid Mech. 77, 153–175.CrossRefGoogle Scholar
Lundbladh, A. & Johansson, A. V. 1991 Direct simulation of turbulent spots in plane Couette flow. J. Fluid Mech. 229, 499–516.CrossRefGoogle Scholar
Nagata, M. 1998 Tertiary solutions and their stability in rotating plane Couette flow. J. Fluid Mech. 358, 357–378.CrossRefGoogle Scholar
Nagata, M. & Kawahara, G. 2004 Three-dimensional periodic solutions in rotating/non-rotating plane Couette flow. In Advances in Turbulence X, Proceedings of the Tenth European Turbulence Conference (ed. Andersson, H. I. & Krogstad, P. Å.), pp. 391–394. CIMNE.Google Scholar
Prigent, A. & Dauchot, O. 2005 Transitional to versus from turbulence in subcritical Couette flows. In IUTAM Symposium on Laminar Turbulent Transition and Finite Amplitude Solutions (ed. Mullin, T. & Kerswell, R. R.), Fluid Mechanics and Its Applications, vol. 77, pp. 195–219. Springer.CrossRefGoogle Scholar
Prigent, A., Grégoire, G., Chaté, H., Dauchot, O. & van Saarloos, W. 2002 Large-scale finite-wavelength modulation within turbulent shear flows. Phys. Rev. Lett. 89, 014501.CrossRefGoogle ScholarPubMed
Rayleigh, L. 1880 On the stability, or instability, of certain fluid motions. Proc. Lond. Math. Soc. 174, 57–70.Google Scholar
Reynolds, O. 1883 An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Phil. Trans. R. Soc. Lond. A 174, 935–982.Google Scholar
Savaş, Ö. 1985 On flow visualization using reflective flakes. J. Fluid Mech. 152, 235–248.CrossRefGoogle Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows, Applied Mathematical Sciences, vol. 142. Springer.CrossRefGoogle Scholar
Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lond. 223, 289–343.Google Scholar
Tillmark, N. & Alfredsson, P. H. 1990 An experimental study of transition in plane Couette flow. In Advances in Turbulence III, Proceedings of the Third European Turbulence Conference (ed. Johansson, A. V. & Alfredsson, P. H.), pp. 235–242. Springer.Google Scholar
Tillmark, N. & Alfredsson, P. H. 1992 Experiments on transition in plane Couette flow. J. Fluid Mech. 235, 89–102.CrossRefGoogle Scholar
Tillmark, N. & Alfredsson, P. H. 1996 Experiments on rotating plane Couette flow. In Advances in Turbulence VI, Proceedings of the Sixth European Turbulence Conference (ed. Gavrilakis, S., Machiels, L. & Monkewitz, P. A.), pp. 391–394. Kluwer Academic.CrossRefGoogle Scholar
Tsukahara, T., Kawamura, H. & Shingai, K. 2006 DNS of turbulent Couette flow with emphasis on the large-scale structure in the core region. J. Turbul. 7 (19), 16 pp.CrossRefGoogle Scholar
Tsukahara, T., Seki, Y., Kawamura, H. & Tochio, D. 2005 DNS of turbulent channel flow at very low Reynolds numbers. In Proceedings of Fourth International Symposium on Turbulence and Shear Flow Phenomena (ed. Humphrey, J. A. C. et al. ), pp. 935–940.Google Scholar