Skip to main content Accessibility help

Elastically induced turbulence in Taylor–Couette flow: direct numerical simulation and mechanistic insight

  • Nansheng Liu (a1) (a2) and Bamin Khomami (a1)


Direct numerical simulation (DNS) of elastically induced turbulent flows has posed great challenges to researchers engaged in developing first-principle models and simulations that can predict faithfully the complex spatio-temporal dynamics of polymeric flows. To this end, DNS of elastically induced turbulent flow states in the Taylor–Couette (TC) flow are reported here with the aim of paving the way for a mechanistic understanding of this new class of flows. Specifically, the DNS not only faithfully reproduce the key feature of elastically induced turbulent flows, namely, substantial excitation of fluid motion at the smallest temporal and spatial scales, but also for the first time demonstrate the existence of three distinct flow regions in the gap for the inertio-elastic turbulence state: (i) a fluid-inertia (or outflow-) dominated inner-wall region; (ii) a fluid-elasticity (or inflow-) dominated outer-wall region; and (iii) an inflow/outflow core region. Based on this observation, a simple mechanism for the inertio-elastic turbulence in the TC flow has been postulated.


Corresponding author

Email address for correspondence:


Hide All
Al-Mubaiyedh, U. A., Sureshkumar, R. & Khomami, B. 1999 Influence of energetics on the stability of viscoelastic Taylor–Couette flow. Phys. Fluids 11, 32173226.
Al-Mubaiyedh, U. A., Sureshkumar, R. & Khomami, B. 2000 Linear stability of Taylor–Couette flow: influence of fluid rheology and energetics. J. Rheol. 44, 11211138.
Avgousti, M. & Beris, A. N. 1993 Viscoelastic Taylor–Couette flow: Bifurcation analysis in the presence of symmetries. Proc. R. Soc. Lond. A 443, 1737.
Baumert, B. M. & Muller, S. J. 1997 Flow regimes in model viscoelastic fluids in a circular Couette system with independently rotating cylinders. Phys. Fluids 9, 566586.
Baumert, B. M. & Muller, S. J. 1999 Axisymmetric and non-axisymmetric elastic and inertio-elastic instabilities in Taylor–Couette flow. J. Non-Newtonian Fluid Mech. 83, 3369.
Berti, S., Bistagnino, A., Boffetta, G., Celani, A. & Musacchio, S. 2008 Two-dimensional elastic turbulence. Phys. Rev. E 77, 055306(R).
Berti, S. & Boffetta, G. 2010 Elastic waves and transition to elastic turbulence in a two-dimensional viscoelastic kolmogorov flow. Phys. Rev. E 82, 036314.
Bonn, D., Ingremeau, F., Amarouchene, Y. & Kellay, H. 2011 Large velocity fluctuations in small-Reynolds-number pipe flow of polymer solutions. Phys. Rev. E 84, 045301.
Burghelea, T., Segre, E. & Steinberg, V. 2007 Elastic turbulence in von Kármán swirling flow between two disks. Phys. Fluids 19, 053104.
Dutcher, C. S. & Muller, S. J. 2009 The effects of drag reducing polymers on flow stability insights from the Taylor–Couette problem. Korea-Australia Rheol. J. 21, 213223.
Dutcher, C. S. & Muller, S. J. 2011 Effects of weak elasticity on the stability of high Reynolds number co- and counter-rotating Taylor–Couette flows. J. Rheol. 55, 12711295.
Dutcher, C. S. & Muller, S. J. 2013 Effects of moderate elasticity on the stability of co- and counter-rotating Taylor–Couette flows. J. Rheol. 57, 791812.
Groisman, A. & Steinberg, V. 1996 Couette–Taylor flow in a dilute polymer solution. Phys. Rev. Lett. 77, 14801483.
Groisman, A. & Steinberg, V. 1997 Solitary vortex pairs in viscoelastic Couette flow. Phys. Rev. Lett. 78, 14601463.
Groisman, A. & Steinberg, V. 1998 Mechanism of elastic instability in Couette flow of polymer solutions: experiment. Phys. Fluids 10, 24512463.
Groisman, A. & Steinberg, V. 2004 Elastic turbulence in curvilinear flows of polymer solutions. New J. Phys. 6, 29.
Jun, Y. G. & Steinberg, V. 2011 Elastic turbulence in a curvilinear channel flow. Phys. Rev. E 84, 056325.
Kumar, K. A. & Graham, M. D. 2000 Solitary coherent structures in viscoelastic shear flow: Computation and mechanism. Phys. Rev. Lett. 85, 40564059.
Larson, R. G. 1992 Instabilities in viscoelastic flows. Rheol. Acta 31, 213263.
Larson, R. G., Shaqfeh, E. S. G. & Muller, S. J. 1990 A purely elastic transition in Taylor–Couette flow. J. Fluid Mech. 218, 573600.
Latrache, N., Crumeyrolle, O. & Mutabazi, I. 2012 Transition to turbulence in a flow of a shear-thinning viscoelastic solution in a Taylor–Couette cell. Phys. Rev. E 86, 056305.
Li, C. F., Sureshkumar, R. & Khomami, B. 2006 Influence of rheological parameters on polymer induced turbulent drag reduction. J. Non-Newtonian Fluid Mech. 140, 2340.
Shaqfeh, E. S. G. 1996 Purely elastic instabilities in viscometric flows. Annu. Rev. Fluid Mech. 28, 129185.
Su, Y. Y. & Khomami, B. 1992 Numerical solution of eigenvalue problems using spectral techniques. J. Comput. Phys. 100, 297305.
Sureshkumar, R. & Beris, A. N. 1995 Effect of artificial stress diffusivity on the stability of numerical calculations and the dynamics of time-dependent viscoelastic flows. J. Non-Newtonian Fluid Mech. 60, 5380.
Sureshkumar, R., Beris, A. N. & Avgousti, M. 1994 Non-axisymmetric subcritical bifurcations in viscoelastic Taylor–Couette flow. Proc. R. Soc. Lond. A 447, 135153.
Thomas, D. G., Al-Mubaiyedh, U. A., Sureshkumar, R. & Khomami, B. 2006a Time-dependent simulations of non-axisymmetric patterns in Taylor–Couette flow of dilute polymer solutions. J. Non-Newtonian Fluid Mech. 138, 111133.
Thomas, D. G., Khomami, B. & Sureshkumar, R. 2009 Nonlinear dynamics of viscoelastic Taylor–Couette flow: effect of elasticity on pattern selection, molecular conformation and drag. J. Fluid Mech. 620, 353382.
Thomas, D. G., Sureshkumar, R. & Khomami, B. 2006b Pattern formation in Taylor–Couette flow of dilute polymer solutions: dynamical simulations and mechanism. Phys. Rev. Lett. 97, 054501.
White, J. M. & Muller, S. J. 2000 Viscous heating and the stability of Newtonian and viscoelastic Taylor–Couette flows. Phys. Rev. Lett. 84, 51305133.
White, J. M. & Muller, S. J. 2002a Experimental studies on the stability of Newtonian Taylor–Couette flow in the presence of viscous heating. J. Fluid Mech. 462, 133159.
White, J. M. & Muller, S. J. 2002b The role of thermal sensitivity of fluid properties, centrifugal destabilization, and nonlinear disturbances on the viscous heating instability in Newtonian Taylor–Couette flow. Phys. Fluids 14, 38803890.
Zhang, H. N., Li, F. C., Cao, Y., Tomoaki, K. & Yu, B. 2013 Direct numerical simulation of elastic turbulence and its mixing-enhancement effect in a straight channel flow. Chin. Phys. B 22, 024703.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Elastically induced turbulence in Taylor–Couette flow: direct numerical simulation and mechanistic insight

  • Nansheng Liu (a1) (a2) and Bamin Khomami (a1)


Full text views

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

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed