Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-25T17:53:48.764Z Has data issue: false hasContentIssue false
  • English
  • Français

A novel subcritical transition to turbulence in Taylor–Couette flow with counter-rotating cylinders

Published online by Cambridge University Press:  02 April 2020

Christopher J. Crowley Open the ORCID record for Christopher J. Crowley [Opens in a new window] ,
Michael C. Krygier Open the ORCID record for Michael C. Krygier [Opens in a new window] ,
Daniel Borrero-Echeverry Open the ORCID record for Daniel Borrero-Echeverry [Opens in a new window] ,
Roman O. Grigoriev Open the ORCID record for Roman O. Grigoriev [Opens in a new window]  and
Michael F. Schatz Open the ORCID record for Michael F. Schatz [Opens in a new window]
Christopher J. Crowley*
Affiliation:
Center for Nonlinear Science and School of Physics, Georgia Institute of Technology, Atlanta, GA30332, USA
Michael C. Krygier
Affiliation:
Center for Nonlinear Science and School of Physics, Georgia Institute of Technology, Atlanta, GA30332, USA
Daniel Borrero-Echeverry
Affiliation:
Department of Physics, Willamette University, Salem, OR97301, USA
Roman O. Grigoriev
Affiliation:
Center for Nonlinear Science and School of Physics, Georgia Institute of Technology, Atlanta, GA30332, USA
Michael F. Schatz
Affiliation:
Center for Nonlinear Science and School of Physics, Georgia Institute of Technology, Atlanta, GA30332, USA
*
†Email address for correspondence: chris.crowley@gatech.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

The transition to turbulence in Taylor–Couette flow often occurs via a sequence of supercritical bifurcations to progressively more complex, yet stable, flows. We describe a subcritical laminar–turbulent transition in the counter-rotating regime mediated by a transient intermediate state in a system with an axial aspect ratio of $\unicode[STIX]{x1D6E4}=5.26$ and a radius ratio of $\unicode[STIX]{x1D702}=0.905$. In this regime, flow visualization experiments and numerical simulations indicate the intermediate state corresponds to an aperiodic flow featuring interpenetrating spirals. Furthermore, the reverse transition out of turbulence leads first to the same intermediate state, which is now stable, before returning to an azimuthally symmetric laminar flow. Time-resolved tomographic particle image velocimetry is used to characterize the experimental flows; these measurements compare favourably to direct numerical simulations with axial boundary conditions matching those of the experiments.

JFM classification

Instability: Transition to turbulence Nonlinear Dynamical Systems: Bifurcation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 892 , 10 June 2020 , A12
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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
Avila, K. & Hof, B. 2013 High-precision Taylor–Couette experiment to study subcritical transitions and the role of boundary conditions and size effects. Rev. Sci. Instrum. 84, 065106.Google ScholarPubMed
Avila, K., Moxey, D., de Lozar, A., Avila, M., Barkley, D. & Hof, B. 2011 The onset of turbulence in pipe flow. Science 333, 192–196.CrossRefGoogle ScholarPubMed
Avila, M. 2012 Stability and angular-momentum transport of fluid flows between corotating cylinders. Phys. Rev. Lett. 108, 124501.CrossRefGoogle ScholarPubMed
Avila, M., Grimes, M., Lopez, J. M. & Marques, F. 2008 Global endwall effects on centrifugally stable flows. Phys. Fluids 20, 104104.CrossRefGoogle Scholar
Borrero-Echeverry, D.2014 Subcritical transition to turbulence in Taylor–Couette flow. PhD thesis, Georgia Institute of Technology.Google Scholar
Borrero-Echeverry, D., Crowley, C. J. & Riddick, T. P. 2018 Rheoscopic fluids in a post-Kalliroscope world. Phys. Fluids 30, 087103.CrossRefGoogle Scholar
Borrero-Echeverry, D. & Morrison, B. C. A. 2016 Aqueous ammonium thiocyanate solutions as refractive index-matching fluids with low density and viscosity. Exp. Fluids 57, 123.CrossRefGoogle Scholar
Borrero-Echeverry, D., Schatz, M. F. & Tagg, R. 2010 Transient turbulence in Taylor–Couette flow. Phys. Rev. E 81, 025301(R).Google ScholarPubMed
Bottin, S. & Chaté, H. 1998 Statistical analysis of the transition to turbulence in plane Couette flow. Eur. Phys. J. B 6, 143–155.CrossRefGoogle Scholar
Burin, M. J. & Czarnocki, C. J. 2012 Subcritical transition and spiral turbulence in circular Couette flow. J. Fluid Mech. 709, 106–122.CrossRefGoogle Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385–425.CrossRefGoogle Scholar
Coles, D. 1967 A note on Taylor instability in circular Couette flow. Trans. ASME J. Appl. Mech. 34, 529–534.CrossRefGoogle Scholar
Couette, M. M. 1890 Études sur le frottement des liquides. Ann. Chim. Phys. 20, 433–510.Google Scholar
Coughlin, K. & Marcus, P. S. 1996 Turbulent bursts in Couette–Taylor flow. Phys. Rev. Lett. 77, 2214.CrossRefGoogle ScholarPubMed
Do, Y. & Lai, Y.-C. 2005 Scaling laws for noise-induced superpersistent chaotic transients. Phys. Rev. E 71, 046208.Google Scholar
Eckhardt, B. & Yao, D. 1995 Local stability analysis along Lagrangian paths. Chaos, Solitons and Fractals 5, 2073–2088.CrossRefGoogle Scholar
Edlund, E. M. & Ji, H. 2014 Nonlinear stability of laboratory quasi-Keplerian flows. Phys. Rev. E 89, 021004(R).Google ScholarPubMed
Elsinga, G. E., Scarano, F., Wieneke, B. & van Oudheusden, B. W. 2006 Tomographic particle image velocimetry. Exp. Fluids 41, 933–947.CrossRefGoogle Scholar
Esser, A. & Grossmann, S. 1996 Analytic expression for Taylor–Couette stability boundary. Phys. Fluids 8, 1814–1819.CrossRefGoogle Scholar
Faisst, H. & Eckhardt, B. 2004 Sensitive dependence on initial conditions in transition to turbulence in pipe flow. J. Fluid Mech. 504, 343–352.CrossRefGoogle Scholar
Goharzadeh, A. & Mutabazi, I. 2001 Experimental characterization of intermittency regimes in the Couette–Taylor system. Eur. Phys. J. B 19, 157–162.CrossRefGoogle Scholar
Hamill, C. F.1995 Turbulent bursting in the Couette–Taylor system. Master’s thesis, University of Texas at Austin.Google Scholar
Hof, B., van Doorne, C. W. H., Westerweel, J., Nieuwstadt, F. T. M., Faisst, H., Eckhardt, B., Wedin, H., Kerswell, R. R. & Waleffe, F. 2004 Experimental observation of nonlinear traveling waves in turbulent pipe flow. Science 305, 1594–1598.CrossRefGoogle ScholarPubMed
Ji, H., Burin, M., Schartman, E. & Goodman, J. 2006 Hydrodynamic turbulence cannot transport angular momentum effectively in astrophysical disks. Nature 444, 343–346.CrossRefGoogle ScholarPubMed
Kadanoff, L. P. & Tang, C. 1984 Escape from strange repellers. Proc. Natl Acad. Sci. USA 81, 1276–1279.CrossRefGoogle ScholarPubMed
Kantz, H. & Grassberger, P. 1985 Repellers, semi-attractors, and long-lived chaotic transients. Physica D 17, 75–86.Google Scholar
Lopez, J. M. 2016 Subcritical instability of finite circular Couette flow with stationary inner cylinder. J. Fluid Mech. 793, 589–611.CrossRefGoogle Scholar
Lopez, J. M. & Marques, F. 2003 Small aspect ratio Taylor–Couette flow: Onset of a very-low-frequency three-torus state. Phys. Rev. E 68, 036302.Google ScholarPubMed
Mallock, A. 1896 Experiments on fluid viscosity. Phil. Trans. R. Soc. Lond. A 1897, 41–56.Google Scholar
Maretzke, S., Hof, B. & Avila, M. 2014 Transient growth in linearly stable Taylor–Couette flows. J. Fluid Mech. 742, 254–290.CrossRefGoogle Scholar
Matisse, P. & Gorman, M. 1984 Neutrally buoyant anisotropic particles for flow visualization. Phys. Fluids 27, 759.CrossRefGoogle Scholar
Mercader, I., Batiste, O. & Alonso, A. 2010 An efficient spectral code for incompressible flows in cylindrical geometries. Comput. Fluids 39, 215–224.CrossRefGoogle Scholar
Meseguer, A., Mellibovsky, F., Avila, M. & Marques, F. 2009a Families of subcritical spirals in highly counter-rotating Taylor–Couette flow. Phys. Rev. E 79, 036309.Google Scholar
Meseguer, A., Mellibovsky, F., Avila, M. & Marques, F. 2009b Instability mechanisms and transition scenarios of spiral turbulence in Taylor–Couette flow. Phys. Rev. E 80, 046315.Google Scholar
Moore, D. & McCabe, P. G. 1998 Introduction to the Practice of Statistics, 3rd edn. W. H. Freeman.Google Scholar
Morkovin, M. V. 1985 Bypass transition to turbulence and research desiderata. In Transition in Turbines (ed. Graham, R.), NASA Conference Publications, vol. 2386, pp. 161–204. NASA Scientific and Technical Information Office.Google Scholar
Nishioka, M., Iida, S. & Ichikawa, Y. 1975 An experimental investigation of the stability of plane Poiseuille flow. J. Fluid Mech. 72, 731–751.CrossRefGoogle Scholar
Paoletti, M. S. & Lathrop, D. P. 2011 Angular momentum transport in turbulent flow between independently rotating cylinders. Phys. Rev. Lett. 106, 024501.CrossRefGoogle ScholarPubMed
Peixinho, J. & Mullin, T. 2006 Decay of turbulence in pipe flow. Phys. Rev. Lett. 96, 094501.CrossRefGoogle ScholarPubMed
Pfister, G., Schmidt, H., Cliffe, K. A. & Mullin, T. 1988 Bifurcation phenomena in Taylor–Couette flow in a very short annulus. J. Fluid Mech. 191, 1–18.CrossRefGoogle Scholar
Prigent, A. & Dauchot, O. 2005 Transition to versus from turbulence in subcritical Couette flows. In IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions (ed. Mullin, T. & Kerswell, R.), pp. 195–219. Springer.CrossRefGoogle Scholar
Reshotko, E. 1976 Boundary-layer stability and transition. Annu. Rev. Fluid Mech. 8, 311–349.CrossRefGoogle Scholar
Richard, D. & Zahn, J. P. 1999 Turbulence in differentially rotating flows: What can be learned from the Couette–Taylor experiment. Astronom. Astrophys. 347, 734–738.Google Scholar
Schneider, T. M., Gibson, J. F., Lagha, M., De Lillo, F. & Eckhardt, B. 2008 Laminar-turbulent boundary in plane Couette flow. Phys. Rev. E 78 (3), 037301.Google ScholarPubMed
Schultz-Grunow, F. 1959 Zur Stabilität der Couette–Strömung. Z. Angew. Math. Mech. 39, 101–110.CrossRefGoogle Scholar
Sommeria, J., Meyers, S. D. & Swinney, H. L. 1991 Experiments on vortices and Rossby waves in eastward and westward jets. In Nonlinear Topics in Ocean Physics (ed. Osborne, A. R.), Enrico Fermi International School of Physics, vol. 109, pp. 227–269. North-Holland.Google Scholar
Suri, B., Tithof, J., Grigoriev, R. O. & Schatz, M. F. 2017 Forecasting fluid flows using the geometry of turbulence. Phys. Rev. Lett. 118, 114501.CrossRefGoogle ScholarPubMed
Tagg, R. 1994 The Couette–Taylor problem. Nonlinear Sci. Today 4, 1–25.Google Scholar
Tavener, S. J., Mullin, T. & Cliffe, K. A. 1991 Novel bifurcation phenomena in rotating annulus. J. Fluid Mech. 229, 483–497.CrossRefGoogle Scholar
Taylor, G. I. 1936a Fluid friction between rotating cylinders. I. Torque measurements. Proc. R. Soc. Lond. A 157, 546–564.Google Scholar
Taylor, G. I. 1936b Fluid friction between rotating cylinders. II. Distribution of velocity between concentric cylinders when outer one is rotating and inner one is at rest. Proc. R. Soc. Lond. A 157, 565–578.Google Scholar
Van Atta, C. 1966 Exploratory measurements in spiral turbulence. J. Fluid Mech. 25, 495–512.CrossRefGoogle Scholar
Wendt, F. 1933 Turbulente Strömungen zwischen zwei rotierenden konaxialen Zylindern. Ing.-Arch. 4, 577–595.CrossRefGoogle Scholar