Skip to main content
×
Home
    • Aa
    • Aa

Optimal Taylor–Couette turbulence

  • Dennis P. M. van Gils (a1), Sander G. Huisman (a1), Siegfried Grossmann (a2), Chao Sun (a1) and Detlef Lohse (a1)...
Abstract
Abstract

Strongly turbulent Taylor–Couette flow with independently rotating inner and outer cylinders with a radius ratio of is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux as a function of the Taylor number and the angular velocity ratio in the large-Taylor-number regime and well off the inviscid stability borders (Rayleigh lines) for co-rotation and for counter-rotation. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux , with an amplitude and an exponent . The data are consistent with one effective exponent for all , but we discuss a possible dependence in the co- and weakly counter-rotating regimes. The amplitude of the angular velocity flux is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of , i.e. along the line . This value is theoretically interpreted as the result of a competition between the destabilizing inner cylinder rotation and the stabilizing but shear-enhancing outer cylinder counter-rotation. With the help of laser Doppler anemometry, we provide angular velocity profiles and in particular identify the radial position of the neutral line, defined by for fixed height . For these large values, the ratio , which is close to , is distinguished by a zero angular velocity gradient in the bulk. While for moderate counter-rotation , the neutral line still remains close to the outer cylinder and the probability distribution function of the bulk angular velocity is observed to be monomodal. For stronger counter-rotation the neutral line is pushed inwards towards the inner cylinder; in this regime the probability distribution function of the bulk angular velocity becomes bimodal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating outer cylinder. Finally, a hypothesis is offered allowing a unifying view and consistent interpretation for all these various results.

Copyright
Corresponding author
Email address for correspondence: d.lohse@utwente.nl.
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1. G. Ahlers , D. Funfschilling & E. Bodenschatz 2011 Addendum to Transitions in heat transport by turbulent convection at Rayleigh numbers up to $1{0}^{15} $. New J. Phys. 13, 049401.

2. G. Ahlers , S. Grossmann & D. Lohse 2009 Heat transfer and large-scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503.

4. T. H. van den Berg , C. Doering , D. Lohse & D. Lathrop 2003 Smooth and rough boundaries in turbulent Taylor–Couette flow. Phys. Rev. E 68, 036307.

5. D. Borrero-Echeverry , M. F. Schatz & R. Tagg 2010 Transient turbulence in Taylor–Couette flow. Phys. Rev. E 81, 025301.

7. P. Buchel , M. Lucke , D. Roth & R. Schmitz 1996 Pattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow. Phys. Rev. E 53 (5), 47644777.

8. M. J. Burin , E. Schartman & H. Ji 2010 Local measurements of turbulent angular momentum transport in circular Couette flow. Exp. Fluids 48, 763769.

9. F. H. Busse 1972 The bounding theory of turbulence and its physical significance in the case of turbulent Couette flow. In Statistical Models and Turbulence, Lecture Notes in Physics , vol. 12, p. 103Springer.

10. E. Calzavarini , D. Lohse , F. Toschi & R. Tripiccione 2005 Rayleigh and Prandtl number scaling in the bulk of Rayleigh–Bénard turbulence. Phys. Fluids 17, 055107.

13. K. Coughlin & P. S. Marcus 1996 Turbulent bursts in Couette–Taylor flow. Phys. Rev. Lett. 77 (11), 22142217.

14. R. C. DiPrima & H. L. Swinney 1981 Instabilities and transition in flow between concentric rotating cylinders. In Hydrodynamic Instabilities and the Transition to Turbulence (ed. H. L. Swinney & J. P. Gollub ), pp. 139180. Springer.

15. C. Doering & P. Constantin 1994 Variational bounds on energy-dissipation in incompressible flow: shear flow. Phys. Rev. E 49, 40874099.

16. M. A. Dominguez-Lerma , G. Ahlers & D. S. Cannell 1984 Marginal stability curve and linear growth rate for rotating Couette–Taylor flow and Rayleigh–Bénard convection. Phys. Fluids 27, 856.

17. M. A. Dominguez-Lerma , D. S. Cannell & G. Ahlers 1986 Eckhaus boundary and wavenumber selection in rotating Couette–Taylor flow. Phys. Rev. A 34, 4956.

18. B. Dubrulle , O. Dauchot , F. Daviaud , P. Y. Longgaretti , D. Richard & J. P. Zahn 2005 Stability and turbulent transport in Taylor–Couette flow from analysis of experimental data. Phys. Fluids 17, 095103.

19. B. Dubrulle & F. Hersant 2002 Momentum transport and torque scaling in Taylor–Couette flow from an analogy with turbulent convection. Eur. Phys. J. B 26, 379386.

20. C. S. Dutcher & S. J. Muller 2007 Explicit analytic formulas for Newtonian Taylor–Couette primary instabilities. Phys. Rev. E 75, 04730.

22. H. Effinger & S. Grossmann 1987 Static structure function of turbulent flow from the Navier–Stokes equation. Z. Phys. B 66, 289.

23. A. Esser & S. Grossmann 1996 Analytic expression for Taylor–Couette stability boundary. Phys. Fluids 8, 18141819.

24. D. P. M. van Gils , G. W. Bruggert , D. P. Lathrop , C. Sun & D. Lohse 2011a The Twente turbulent Taylor–Couette $({T}^{3} C)$ facility: strongly turbulent (multi-phase) flow between independently rotating cylinders. Rev. Sci. Instrum. 82, 025105.

25. D. P. M. van Gils , S. G. Huisman , G. W. Bruggert , C. Sun & D. Lohse 2011b Torque scaling in turbulent Taylor–Couette flow with co- and counter-rotating cylinders. Phys. Rev. Lett. 106, 024502.

27. S. Grossmann 2000 The onset of shear flow turbulence. Rev. Mod. Phys. 72, 603618.

29. S. Grossmann & D. Lohse 2001 Thermal convection for large Prandtl number. Phys. Rev. Lett. 86, 33163319.

30. S. Grossmann & D. Lohse 2002 Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection. Phys. Rev. E 66, 016305.

31. S. Grossmann & D. Lohse 2004 Fluctuations in turbulent Rayleigh–Bénard convection: the role of plumes. Phys. Fluids 16, 44624472.

32. S. Grossmann & D. Lohse 2011 Multiple scaling in the ultimate regime of thermal convection. Phys. Fluids 23, 045108.

33. X. He , D. Funfschilling , H. Nobach , E. Bodenschatz & G. Ahlers 2012 Transition to the ultimate state of turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 108, 024502.

35. R. van Hout & J. Katz 2011 Measurements of mean flow and turbulence characteristics in high-Reynolds number counter-rotating Taylor–Couette flow. Phys. Fluids 23 (10), 105102.

36. S. G. Huisman , D. P. M. van Gils , S. Grossmann , C. Sun & D. Lohse 2012a Ultimate turbulent Taylor–Couette flow. Phys. Rev. Lett. 108, 024501.

38. H. Ji , M. Burin , E. Schartman & J. Goodman 2006 Hydrodynamic turbulence cannot transport angular momentum effectively in astrophysical disks. Nature 444, 343346.

39. R. H. Kraichnan 1962 Turbulent thermal convection at arbritrary Prandtl number. Phys. Fluids 5, 13741389.

40. L. D. Landau & E. M. Lifshitz 1987 Fluid Mechanics. Pergamon.

41. D. P. Lathrop , J. Fineberg & H. S. Swinney 1992a Transition to shear-driven turbulence in Couette–Taylor flow. Phys. Rev. A 46, 63906405.

42. D. P. Lathrop , J. Fineberg & H. S. Swinney 1992b Turbulent flow between concentric rotating cylinders at large Reynolds numbers. Phys. Rev. Lett. 68, 15151518.

43. G. S. Lewis & H. L. Swinney 1999 Velocity structure functions, scaling, and transitions in high-Reynolds-number Couette–Taylor flow. Phys. Rev. E 59, 54575467.

44. D. Lohse & F. Toschi 2003 The ultimate state of thermal convection. Phys. Rev. Lett. 90, 034502.

46. T. Mullin , K. A. Cliffe & G. Pfister 1987 Unusual time-dependent phenomena in Taylor–Couette flow at moderately low Reynolds numbers. Phys. Rev. Lett. 58 (21), 22122215.

47. T. Mullin , G. Pfister & A. Lorenzen 1982 New observations on hysteresis effects in Taylor–Couette flow. Phys. Fluids 25 (7), 11341136.

49. M. S. Paoletti & D. P. Lathrop 2011 Angular momentum transport in turbulent flow between independently rotating cylinders. Phys. Rev. Lett. 106, 024501.

50. G. Pfister & I. Rehberg 1981 Space dependent order parameter in circular Couette flow transitions. Phys. Lett. 83, 1922.

52. F. Ravelet , R. Delfos & J. Westerweel 2010 Influence of global rotation and Reynolds number on the large-scale features of a turbulent Taylor–Couette flow. Phys. Fluids 22 (5), 055103.

54. P. E. Roche , B. Castaing , B. Chabaud & B. Hebral 2001 Observation of the $1/ 2$ power law in Rayleigh–Bénard convection. Phys. Rev. E 63, 045303.

59. K. Sugiyama , E. Calzavarini , S. Grossmann & D. Lohse 2007 Non-Oberbeck–Boussinesq effects in Rayleigh–Bénard convection: beyond boundary-layer theory. Europhys. Lett. 80, 34002.

62. G. I. Taylor 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lond. A 223, 289.

63. F. Wendt 1933 Turbulente Strömungen zwischen zwei rotierenden Zylindern. Ingenieurs-Archiv 4, 577595.

64. J. Werne 1994 Plume model for boundary layer dynamics in hard turbulence. Phys. Rev. E 49, 4072.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 43 *
Loading metrics...

Abstract views

Total abstract views: 147 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 29th March 2017. This data will be updated every 24 hours.