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Subcritical transition and spiral turbulence in circular Couette flow

Published online by Cambridge University Press:  21 August 2012

M. J. Burin  and
C. J. Czarnocki
M. J. Burin*
Affiliation:
Department of Physics, California State University San Marcos, CA 92096, USA
C. J. Czarnocki
Affiliation:
Department of Physics, California State University San Marcos, CA 92096, USA
*
†Email address for correspondence: [email protected]
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Abstract

We present new observations of a controlled transition to turbulence in a fundamental but little-studied regime: circular Couette flow with only the outer cylinder rotating. Our apparatus consists of an outer cylinder of fixed radius and three inner cylinders having different radii that are used interchangeably to study the effect of flow curvature. With the smallest inner cylinder the end-cap configuration (vertical boundary conditions) may also be varied. The turbulent transition is found to be sensitive to both gap width and end-cap configuration, with wider gaps transitioning at higher rotation rates. All configurations are observed to transition with hysteresis and intermittency. A laser Doppler velocimetry (LDV)-based study of the azimuthal velocity profile as a function of gap width and rotation rate reveals that turbulence, once initiated, is confined to regions of significant shear. For wider gap widths, the radial location of these shear layers is determined by the chosen end-cap configuration. This, in turn, affects the transition Reynolds number, which we posit to be radially dependent. The narrow-gap case in particular features spiral turbulence, whose properties are found to be similar to observations of the phenomenon in related shear flows. The velocity profile in this case is correlated with overlapping boundary layers, suggesting a coupling mechanism for the origin of laminar-turbulent banding phenomena.

JFM classification

Turbulent Flows: Shear layer turbulence Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 709 , 25 October 2012 , pp. 106 - 122
Copyright
Copyright © Cambridge University Press 2012

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References

1. Andereck, C. D., Liu, S. S. & Swinney, H. 1986 Flow regimes in a circular Couette system with independently rotating cylinders. J. Fluid Mech. 164, 155–183.CrossRefGoogle Scholar
2. van Atta, C. 1966 Exploratory measurements in spiral turbulence. J. Fluid Mech. 25, 495–512.CrossRefGoogle Scholar
3. Barkley, D. & Tuckerman, L. S. 2007 Mean flow of turbulent-laminar patterns in plane Couette flow. J. Fluid Mech. 576, 109–137.CrossRefGoogle Scholar
4. Borrero-Echeverry, D., Schatz, M. F. & Tagg, R. 2010 Transient turbulence in Taylor–Couette flow. Phys. Rev. E 81, 025301.CrossRefGoogle ScholarPubMed
5. Bottin, S. & Chaté, H. 1998 Statistical analysis of the transition to turbulence in plane Couette flow. Eur. Phys. J. B 6, 144–155.CrossRefGoogle Scholar
6. Burin, M. J., Ji, H., Schartman, E., Cutler, R., Heitzenroeder, P., Liu, W., Morris, L. & Raftopolous, S. 2006 Reduction of Ekman circulation within Taylor–Couette flow. Exp. Fluids 40, 962–966.CrossRefGoogle Scholar
7. Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385–425.CrossRefGoogle Scholar
8. Coles, D. & van Atta, C. 1966 Measured distortion of a laminar circular Couette flow by end effects. J. Fluid Mech. 25, 513–521.CrossRefGoogle Scholar
9. Colovas, P. W. & Andereck, C. D. 1997 Turbulent bursting and spatiotemporal intermittency in the counterrotating Taylor–Couette system. Phys. Rev. E 55, 2736–2741.CrossRefGoogle Scholar
10. Couette, M. M. 1890 Etudes sur le frottement des liquides. Ann. Chim. Phys. 6, 433–510.Google Scholar
11. Coughlin, K. & Marcus, P. S. 1996 Turbulent bursts in Couette–Taylor flow. Phys. Rev. Lett. 77, 2214–2217.CrossRefGoogle ScholarPubMed
12. Cros, A. & Le Gal, P. 2002 Spatiotemporal intermittency in the torsional Couette flow between a rotating and a stationary disk. Phys. Fluids 14, 3755–3765.CrossRefGoogle Scholar
13. Czarny, O. & Lueptow, R. 2007 Time scales for transition in Taylor–Couette flow. Phys. Fluids 19, 054103.CrossRefGoogle Scholar
14. Dahm, W. J. A., Frieler, C. E. & Tryggvason, G. 1992 Vortex structure and dynamics in the near field of a coaxial jet. J. Fluid Mech. 241, 371–402.CrossRefGoogle Scholar
15. Daviaud, F., Hegseth, J. & Bergé, P. 1992 Subcritical transition to turbulence in plane Couette flow. Phys. Rev. Lett. 69, 054103.CrossRefGoogle ScholarPubMed
16. Dong, S. 2009 Evidence for internal structures of spiral turbulence. Phys. Rev. E 80, 067301.CrossRefGoogle ScholarPubMed
17. Dong, S. & Zheng, X. 2011 Direct numerical simulation of spiral turbulence. J. Fluid Mech. 668, 150–173.CrossRefGoogle Scholar
18. Dubrulle, B., Dauchot, O., Daviaud, F., Longretti, P.-Y, Richard, D. & Zahn, J.-P. 2005 Stability and turbulent transport in Taylor–Couette flow from analysis of experimental data. Phys. Fluids 17, 095103.CrossRefGoogle Scholar
19. Duguet, Y., Schlatter, P. & Henningson, D. S. 2010 Formation of turbulent patterns near the onset of transition in plane Couette flow. J. Fluid Mech. 650, 119–129.CrossRefGoogle Scholar
20. Dunst, M. 1972 An experimental and analytical investigation of angular momentum exchange in a rotating fluid. J. Fluid Mech. 55, 301–310.CrossRefGoogle Scholar
21. Eckhardt, B., Grossmann, S. & Lohse, D. 2007 Torque scaling in turbulent Taylor–Couette flow between independently rotating cylinders. J. Fluid Mech. 581, 221–250.CrossRefGoogle Scholar
22. Elder, J. W. 1960 An experimental investigation of turbulent spots and breakdown to turbulence. J. Fluid Mech. 9, 235–246.CrossRefGoogle Scholar
23. van Gils, D. P. M., Huisman, S., Bruggert, G.-W., Sun, C. & Lohse, D. 2011 Torque scaling in turbulent Taylor–Couette flow with co- and counter-rotating cylinders. Phys. Rev. Lett. 106, 024502.CrossRefGoogle Scholar
24. Goharzadeh, A. & Mutabazi, I. 2001 Experimental characterization of intermittency regimes in the Couette-Taylor system. Eur. Phys. J. B 19, 157–162.CrossRefGoogle Scholar
25. Hashimoto, S., Hasobe, A., Tsukahara, T., Kawaguchi, Y. & Kawamura, H. 2009 An experimental study on turbulent-stripe structure in transitional channel flow. In Proceedings of the Sixth International Symposium on Turbulence, Heat and Mass Transfer, Rome, Italy, pp. 193–196.Google Scholar
26. Hegseth, J. J., Andereck, C. D., Hayot, F. & Pomeau, Y. 1989 Spiral turbulence and phase dynamics. Phys. Rev. Lett. 62, 257–260.CrossRefGoogle ScholarPubMed
27. van Hout, R. & Katz, J. 2011 Measurements of mean flow and turbulence characteristics in high-Reynolds number counter-rotating Taylor–Couette flow. Phys. Fluids 23, 105102.CrossRefGoogle Scholar
28. Hunt, M. L., Zenit, R., Campbell, C. S. & Brennen, C. E. 2002 Revisiting the 1954 suspension experiments of R. A. Bagnold. J. Fluid Mech. 452, 1–24.CrossRefGoogle Scholar
29. Ji, H., Burin, M. J., Schartman, E. & Goodman, J. 2006 Hydrodynamic turbulence cannot transport angular momentum effectively in astrophysical disks. Nature 444, 343.CrossRefGoogle ScholarPubMed
30. Joseph, D. D. 1976 Stability of Fluid Motions. Springer-Verlag.Google Scholar
31. Lesur, G. & Longaretti, P.-Y. 2005 On the relevance of subcritical hydrodynamic turbulence to accretion disk transport. Astron. Astrophys. 444, 25–44.CrossRefGoogle Scholar
32. Mallock, A. 1896 Experiments on fluid viscosity. Proc. R. Soc. Lond. 45, 126–132.Google Scholar
33. Manneville, P. 2004 Spots and turbulent domains in a model of transitional plane Couette flow. Theor. Comput. Fluid Dyn. 18, 169–181.CrossRefGoogle Scholar
34. Meseguer, A., Mellibovsky, F., Avila, M. & Marques, F. 2009 Instability mechanisms and transition scenarios of spiral turbulence in Taylor–Couette flow. Phys. Rev. E 80, 046315.CrossRefGoogle ScholarPubMed
35. Paoletti, M. S. & Lathrop, D. P. 2011 Angular momentum transport in turbulent flow between independently rotating cylinders. Phys. Rev. Lett. 106, 024501.CrossRefGoogle ScholarPubMed
36. Pfenniger, W. 1961 Transition in the inlet length of tubes at high Reynolds numbers.. In Boundary Layer and Flow Control (ed. Lachman, G. V. ). pp. 970–980. Pergamon.Google Scholar
37. Prigent, A. 2001La spirale turbulente : motif de grande longueur donde dans les écoulements cisaillés turbulents. PhD thesis, Univ. Paris Sud, Orsay, France.Google Scholar
38. Prigent, A., Grégoire, G., Chaté, H. & Dauchot, O. 2003 Long-wavelength modulation of turbulent shear flows. Physica D 174, 100–113.CrossRefGoogle Scholar
39. Prigent, A., Grégoire, G., Chaté, H., Dauchot, O. & Saarloos, W. V. 2002 Large-scale finite-wavelength modulation within turbulent shear flows. Phys. Rev. Lett. 89, 014501.CrossRefGoogle ScholarPubMed
40. Richard, D. 2001Instabilités hydrodynamiques dans les écoulements en rotation différentielle. PhD thesis, Univ. Paris 7 Denis Diderot, Paris, France.Google Scholar
41. Richard, D. & Zahn, J.-P. 1999 Turbulence in differentially rotating flows. Astron. Astrophys. 347, 734–738.Google Scholar
42. Rolland, J. & Manneville, P. 2011 Ginzburg–Landau description of laminar-turbulent oblique band formation in transitional plane Couette flow. Eur. Phys. J. B 80, 529–544.CrossRefGoogle Scholar
43. Schartman, E., Ji, H. & Burin, M. J. 2009 Development of a Couette–Taylor flow device with active minimization of secondary circulation. Rev. Sci. Instrum. 80, 024501.CrossRefGoogle ScholarPubMed
44. Schultz-Grunow, F. 1959 Zur Stabilität der Couette–Strömung. Z. Angew. Math. Mech. 39, 101–110.CrossRefGoogle Scholar
45. So, R. M. C. & Mellor, G. 1973 Experiment on convex curvature effects in turbulent boundary layers. J. Fluid Mech. 60, 43–62.CrossRefGoogle Scholar
46. Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lon. A 223, 289–343.Google Scholar
47. Taylor, G. I. 1936 Fluid friction between rotating cylinders. I. Torque measurements. Proc. Roy. Soc. Lond. A 157, 546–564.Google Scholar
48. Tsukahara, T., Tillmark, N. & Alfredsson, P. H. 2010 Flow regimes in a plane Couette flow with system rotation. J. Fluid Mech. 648, 5–33.CrossRefGoogle Scholar
49. Tuckerman, L. & Barkley, D. 2011 Patterns and dynamics in transitional plane Couette flow. Phys. Fluids 23, 041301.CrossRefGoogle Scholar
50. Wendt, F. 1933 Turbulente Strömungen zwischen zwei rotierenden konaxialen Zylindern. Ing.-Arch. 4, 577–595.CrossRefGoogle Scholar
51. Yamada, Y. & Imao, S. 1986 Flow of a fluid contained between concentric cylinders both rotating. Bull. Japan Soc. Mech. Eng. 29, 1691–1697.CrossRefGoogle Scholar
52. Zeldovich, Y. B. 1981 On the friction of fluids between rotating cylinders. Proc. R. Soc. Lond. A 374, 299–312.Google Scholar