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Direct numerical simulation of inertio-elastic turbulent Taylor–Couette flow

Published online by Cambridge University Press:  15 September 2021

Jiaxing Song Open the ORCID record for Jiaxing Song [Opens in a new window] ,
Fenghui Lin Open the ORCID record for Fenghui Lin [Opens in a new window] ,
Nansheng Liu Open the ORCID record for Nansheng Liu [Opens in a new window] ,
Xi-Yun Lu Open the ORCID record for Xi-Yun Lu [Opens in a new window]  and
Bamin Khomami Open the ORCID record for Bamin Khomami [Opens in a new window]
Jiaxing Song
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Fenghui Lin
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Nansheng Liu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Xi-Yun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Bamin Khomami*
Affiliation:
Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, TN 37996, USA
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

The flow physics of inertio-elastic turbulent Taylor–Couette flow for a radius ratio of $0.5$ in the Reynolds number ($Re$) range of $500$ to $8000$ is investigated via direct numerical simulation. It is shown that as $Re$ is increased the turbulence dynamics can be subdivided into two distinct regimes: (i) a low $Re \leqslant 1000$ regime where the flow physics is essentially dominated by nonlinear elastic forces and the main contribution to transport and mixing of momentum, stress and energy comes from large-scale flow structures in the bulk region and (ii) a high $Re \geqslant 5000$ regime where inertial forces govern the flow physics and the flow dynamics is mainly governed by small-scale flow structures in the near-wall region. Flow–microstructure coupling analysis reveals that the elastic Görtler instability in the near-wall region is triggered via significant polymer extension and commensurately high hoop stresses. This instability gives rise to small-scale elastic vortical structures identified as elastic Görtler vortices which are present at all $Re$ considered. In fact, these vortices develop herringbone streaks near the inner wall that have a longer average life span than their Newtonian counterparts due to their elastic origin. Examination of the budgets of mean streamwise enstrophy, mean kinetic energy, turbulent kinetic energy and Reynolds shear stress demonstrates that increasing fluid inertia hinders the generation of elastic stresses, leading to a monotonic reduction of the elastic-related effects on the flow physics.

JFM classification

Turbulent Flows: Turbulence simulation Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 926 , 10 November 2021 , A37
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© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Al-Mubaiyedh, U.A., Sureshkumar, R. & Khomami, B. 1999 Influence of energetics on the stability of viscoelastic Taylor–Couette flow. Phys. Fluids 11, 3217–3226.CrossRefGoogle Scholar
Al-Mubaiyedh, U.A., Sureshkumar, R. & Khomami, B. 2000 Linear stability of Taylor–Couette flow: influence of fluid rheology and energetics. J. Rheol. 44, 1121–1138.CrossRefGoogle Scholar
Al-Mubaiyedh, U.A., Sureshkumar, R. & Khomami, B. 2002 The effect of viscous heating on the stability of Taylor–Couette flow. J. Fluid Mech. 462, 111–132.CrossRefGoogle Scholar
Alves, M.A., Oliveira, P.J. & Pinho, F.T. 2021 Numerical methods for viscoelastic fluid flows. Annu. Rev. Fluid Mech. 53, 509–541.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
Avgousti, M. & Beris, A.N. 1993 Viscoelastic Taylor–Couette flow: bifurcation analysis in the presence of symmetries. Proc. R. Soc. Lond. A 443, 17–37.Google Scholar
Barcilon, A. & Brindley, J. 1984 Organized structures in turbulent Taylor–Couette flow. J. Fluid Mech. 143, 429–68.CrossRefGoogle Scholar
Barcilon, A., Brindley, J., Lessen, M. & Mobbs, P.R. 1979 Marginal instability in Taylor–Couette flows at a very high Taylor number. J. Fluid Mech. 94, 453–68.CrossRefGoogle Scholar
Baumert, B.M. & Muller, S.J. 1995 Flow visualization of the elastic Taylor–Couette instability in Boger fluids. Rheol. Acta 34, 147–159.CrossRefGoogle Scholar
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, 566–586.CrossRefGoogle Scholar
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, 33–69.CrossRefGoogle Scholar
Bilson, M. & Bremhorst, K. 2007 Direct numerical simulation of turbulent Taylor–Couette flow. J. Fluid Mech. 579, 227–270.CrossRefGoogle Scholar
Bird, R.B., Curtiss, C.F., Armstrong, R.C. & Hassager, O. 1987 Kinetic theory. In Dynamics of Polymeric Fluids, pp. 1397–1398. Wiley.Google Scholar
Chossat, P. & Iooss, G. 1994 Taylor vortices, spirals and ribbons. In The Couette–Taylor Problem, pp. 35–58. Springer.CrossRefGoogle Scholar
Choueiri, G.H., Lopez, J.M. & Hof, B. 2018 Exceeding the asymptotic limit of polymer drag reduction. Phys. Rev. Lett. 120, 124501.CrossRefGoogle ScholarPubMed
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385–425.CrossRefGoogle Scholar
Crumeyrolle, O. & Mutabazi, I. 2002 Experimental study of inertio-elastic Couette–Taylor instability modes in dilute and semidilute polymer solutions. Phys. Fluids 14, 1681–1688.CrossRefGoogle Scholar
Dallas, V. & Vassilicos, J.C. 2010 Strong polymer-turbulence interactions in viscoelastic turbulent channel flow. Phys. Rev. E 82, 066303.CrossRefGoogle ScholarPubMed
Dimitropoulos, C.D., Sureshkumar, R., Beris, A.N. & Handler, R.A. 2001 Budgets of Reynolds stress, kinetic energy and streamwise enstrophy in viscoelastic turbulent channel flow. Phys. Fluids 13, 1016–1027.CrossRefGoogle Scholar
Dong, S. 2007 Direct numerical simulation of turbulent Taylor–Couette flow. J. Fluid Mech. 587, 373–393.CrossRefGoogle Scholar
Dong, S. 2008 Turbulent flow between counter–rotating concentric cylinders: a direct numerical simulation study. J. Fluid Mech. 615, 371–399.CrossRefGoogle Scholar
Dubief, Y., Terrapon, V.E. & Soria, J. 2013 On the mechanism of elasto-inertial turbulence. Phys. Fluids 25, 110817.CrossRefGoogle ScholarPubMed
Dubief, Y., Terrapon, V.E., White, C.M., Shaqfeh, E.S.G., Moin, P. & Lele, S.K. 2005 New answers on the interaction between polymers and vortices in turbulent flows. Flow Turbul. Combust. 74, 311–329.CrossRefGoogle Scholar
Dutcher, C.S. & Muller, S.J. 2009 a The effects of drag reducing polymers on flow stability: insights from the Taylor–Couette problem. Korea-Aust. Rheol. J. 21, 223–233.Google Scholar
Dutcher, C.S. & Muller, S.J. 2009 b Spatio-temporal mode dynamics and higher order transitions in high aspect ratio Newtonian Taylor–Couette flows. J. Fluid Mech. 641, 85–113.CrossRefGoogle Scholar
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, 1271–1295.CrossRefGoogle Scholar
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, 791–812.CrossRefGoogle Scholar
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
Fardin, M.A., Perge, C. & Taberlet, N. 2014 ‘The hydrogen atom of fluid dynamics’ – introduction to the Taylor–Couette flow for soft matter scientists. Soft Matt. 10, 3523–3535.CrossRefGoogle Scholar
Fernstermatcher, P.R., Swinney, H.L. & Gollub, J.P. 1979 Dynamical instabilities and the transition to chaotic Taylor vortex flow. J. Fluid Mech. 94, 103–128.CrossRefGoogle Scholar
Fouxon, A. & Lebedev, V. 2003 Spectra of turbulence in dilute polymer solutions. Phys. Fluids 15, 2060–2072.CrossRefGoogle Scholar
Ghanbari, R. & Khomami, B. 2014 The onset of purely elastic and thermo-elastic instabilities in Taylor–Couette flow: influence of gap ratio and fluid thermal sensitivity. J. Non-Newtonian Fluid Mech. 208–209, 108–117.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 1996 Couette–Taylor flow in a dilute polymer solution. Phys. Rev. Lett. 77, 1480–1483.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 1997 Solitary vortex pairs in viscoelastic Couette flow. Phys. Rev. Lett. 78, 1460–1463.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 1998 a Elastic vs inertial instability in a polymer solution flow. Europhys. Lett. 43, 165–170.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 1998 b Mechanism of elastic instability in Couette flow of polymer solutions: experiment. Phys. Fluids 10, 2451–2463.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 2000 Elastic turbulence in a polymer solution flow. Nature 405, 53–55.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 2004 Elastic turbulence in curvilinear flows of polymer solutions. New J. Phys. 6, 29.CrossRefGoogle Scholar
Grossmann, S., Lohse, D. & Sun, C. 2016 High-Reynolds number Taylor–Couette turbulence. Annu. Rev. Fluid Mech. 48, 53–80.CrossRefGoogle Scholar
Gupta, A. & Vincenzi, D. 2019 Effect of polymer-stress diffusion in the numerical simulation of elastic turbulence. J. Fluid Mech. 870, 405–418.CrossRefGoogle Scholar
Housiadas, K.D. & Beris, A.N. 2004 An efficient fully implicit spectral scheme for DNS of turbulent viscoelastic channel flow. J. Non-Newtonian Fluid Mech. 122, 243–262.CrossRefGoogle Scholar
Housiadas, K.D., Wang, L. & Beris, A.N. 2010 A new method preserving the positive definiteness of a second order tensor variable in flow simulations with application to viscoelastic turbulence. Comput. Fluids 39, 225–241.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Kim, K., Li, C.F., Sureshkumar, R., Balachandar, S. & Adrian, R.J. 2007 Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow. J. Fluid Mech. 584, 281–299.CrossRefGoogle Scholar
Kumar, K.A. & Graham, M.D. 2000 Solitary coherent structures in viscoelastic shear flow: computation and mechanism. Phys. Rev. Lett. 85, 4056–4059.CrossRefGoogle ScholarPubMed
Larson, R.G. 1992 Instabilities in viscoelastic flows. Rheol. Acta 31, 213–263.CrossRefGoogle Scholar
Larson, R.G. & Desai, P.S. 2015 Modeling the rheology of polymer melts and solutions. Annu. Rev. Fluid Mech. 47, 47–65.CrossRefGoogle Scholar
Larson, R.G., Shaqfeh, E.S.G. & Muller, S.J. 1990 A purely elastic transition in Taylor–Couette flow. J. Fluid Mech. 218, 573–600.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Lee, S.H.K., Sengupta, S. & Wei, T. 1995 Effect of polymer additives on Görtler vortices in Taylor–Couette flow. J. Fluid Mech. 282, 115–129.CrossRefGoogle Scholar
Li, C.F., Sureshkumar, R. & Khomami, B. 2006 Influence of rheological parameters on polymer induced turbulent drag reduction. J. Non-Newtonian Fluid Mech. 140, 23–40.CrossRefGoogle Scholar
Li, C.F., Sureshkumar, R. & Khomami, B. 2015 Simple framework for understanding the universality of the maximum drag reduction asymptote in turbulent flow of polymer solutions. Phys. Rev. E 92, 043014.CrossRefGoogle ScholarPubMed
Liu, N.S. & Khomami, B. 2013 a Elastically induced turbulence in Taylor–Couette flow: direct numerical simulation and mechanistic insight. J. Fluid Mech. 737, R4.CrossRefGoogle Scholar
Liu, N.S. & Khomami, B. 2013 b Polymer-induced drag enhancement in turbulent Taylor–Couette flows: direct numerical simulations and mechanistic insight. Phys. Rev. Lett. 111, 114501.CrossRefGoogle ScholarPubMed
Lopez, J.M., Choueiri, G.H. & Hof, B. 2019 Dynamics of viscoelastic pipe flow at low Reynolds numbers in the maximum drag reduction limit. J. Fluid Mech. 874, 699–719.CrossRefGoogle Scholar
Lumley, J.L. 1969 Drag reduction by additives. Annu. Rev. Fluid Mech. 1, 367–384.CrossRefGoogle Scholar
Lumley, J.L. 1977 Drag reduction in two phase and polymer flows. Phys. Fluids 20, S64.CrossRefGoogle Scholar
Marchioli, C. & Campolo, M. 2021 Drag reduction in turbulent flows by polymer and fiber additives. KONA Powder Part J. 38, 64–81.CrossRefGoogle Scholar
Metzner, A.B. 1977 Polymer solution and fiber suspension rheology and their relationship to turbulent drag reduction. Phys. Fluids 20, S145.CrossRefGoogle Scholar
Mohammadigoushki, H. & Muller, S.J. 2017 Inertio-elastic instability in Taylor–Couette flow of a model wormlike micellar system. J. Rheol. 61, 683–696.CrossRefGoogle Scholar
Muller, S.J. 2008 Elastically-influenced instabilities in Taylor–Couette and other flows with curved streamlines: a review. Korea-Aust. Rheol. J. 20, 117–125.Google Scholar
Ostilla-Mónico, R., Verzicco, R. & Lohse, D. 2015 Effects of the computational domain size on direct numerical simulations of Taylor–Couette turbulence with stationary outer cylinder. Phys. Fluids 27, 025110.CrossRefGoogle Scholar
Samanta, D., Dubief, Y., Holzner, M., Schafer, C., Morozov, A.N., Wagner, C. & Hof, B. 2013 Elasto-inertial turbulence. Proc. Natl Acad. Sci. USA 110, 12498.CrossRefGoogle ScholarPubMed
Saric, W.S. 1994 Görtler vortices. Annu. Rev. Fluid Mech. 26, 379–409.CrossRefGoogle Scholar
Shaqfeh, E.S.G. 1996 Purely elastic instabilities in viscometric flows. Annu. Rev. Fluid Mech. 28, 129–185.CrossRefGoogle Scholar
Shekar, A., McMullen, R.M., McKeon, B.J. & Graham, M.D. 2020 Self-sustained elastoinertial Tollmien–Schlichting waves. J. Fluid Mech. 897, A3.CrossRefGoogle Scholar
Shekar, A., McMullen, R.M., Wang, S., McKeon, B.J. & Graham, M.D. 2019 Critical-layer structures and mechanisms in elastoinertial turbulence. Phys. Rev. Lett. 122, 124503.CrossRefGoogle ScholarPubMed
Sid, S., Terrapon, V.E. & Dubief, Y. 2018 Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction. Phys. Rev. Fluids 3 (1), 011301.CrossRefGoogle Scholar
Song, J., Teng, H., Liu, N., Ding, H., Lu, X.-Y. & Khomami, B. 2019 The correspondence between drag enhancement and vortical structures in turbulent Taylor–Couette flows with polymer additives: a study of curvature dependence. J. Fluid Mech. 881, 602–616.CrossRefGoogle Scholar
Steinberg, V. 2019 Scaling relations in elastic turbulence. Phys. Rev. Lett. 123, 234501–234505.CrossRefGoogle ScholarPubMed
Steinberg, V. 2021 Elastic turbulence: an experimental view on inertialess random flow. Annu. Rev. Fluid Mech. 53, 27–58.CrossRefGoogle Scholar
Stone, P.A., Waleffe, F. & Graham, M.D. 2002 Toward a structural understanding of turbulent drag reduction: nonlinear coherent states in viscoelastic shear flows. Phys. Rev. Lett. 89, 208301.CrossRefGoogle Scholar
Sureshkumar, R., Beris, A.N. & Avgousti, M. 1994 Non-axisymmetric subcritical bifurcations in viscoelastic Taylor–Couette flow. Proc. R. Soc. Lond. A 447, 135–153.Google Scholar
Sureshkumar, R., Beris, A.N. & Avgousti, M. 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, 53–80.CrossRefGoogle Scholar
Sureshkumar, R., Beris, A.N. & Avgousti, M. 1997 Direct numerical simulation of the turbulent channel flow of a polymer solution. Phys. Fluids 9, 743–755.CrossRefGoogle Scholar
Swinney, H.L. & Gollub, J.P. 1985 Instabilities and transition in flow between concentric rotating cylinders. In Hydrodynamic Instabilities and the Transition to Turbulence, pp. 139–180. Springer.Google Scholar
Takeda, Y. 1999 Quasi-periodic state and transition to turbulence in a rotating Couette system. J. Fluid Mech. 389, 81–99.CrossRefGoogle Scholar
Talwar, K.K., Ganpule, H.K. & Khomami, B. 1994 A note on selection of spaces in computation of viscoelastic flows using the hp-finite element method. J. Non-Newtonian Fluid Mech. 52, 293–307.CrossRefGoogle Scholar
Taylor, G.I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lond. A 223, 289.Google Scholar
Teng, H., Liu, N.S., Lu, X.Y. & Khomami, B. 2018 Turbulent drag reduction in plane Couette flow with polymer additives: a direct numerical simulation study. J. Fluid Mech. 846, 482–507.CrossRefGoogle Scholar
Thais, L., Gatski, T.B. & Mompean, G. 2012 Some dynamical features of the turbulent flow of a viscoelastic fluid for reduced drag. J. Turbul. 13, N19.CrossRefGoogle Scholar
Thais, L., Gatski, T.B. & Mompean, G. 2013 Analysis of polymer drag reduction mechanisms from energy budgets. Intl J. Heat Fluid Flow 43, 52–61.CrossRefGoogle Scholar
Thomas, D.G. 2006 Flow instabilities and pattern formation in complex fluids: effect of elasticity and thermal gradients. PhD thesis, Washington University.Google Scholar
Thomas, D.G., Al-Mubaiyedh, U.A., Sureshkumar, R. & Khomami, B. 2006 a Time dependent simulations of non-axisymmetric patterns in Taylor–Couette flow of dilute polymer solutions. J. Non-Newtonian Fluid Mech. 138, 111–133.CrossRefGoogle Scholar
Thomas, D.G., Khomami, B. & Sureshkumar, R. 2006 b Pattern formation in Taylor–Couette flow of dilute polymer solutions: dynamical simulations and mechanism. Phys. Rev. Lett. 97, 054501.CrossRefGoogle ScholarPubMed
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, 353–382.CrossRefGoogle Scholar
Thomas, D.G., Sureshkumar, R. & Khomami, B. 2003 Influence of fluid thermal sensitivity on the thermo-mechanical stability of the Taylor–Couette flow. Phys. Fluids 15, 3308–3317.CrossRefGoogle Scholar
Toms, B.A. 1948 Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. In Proceedings of the First International Congress on Rheology (ed. J.M. Burgers), pp. 135–141. North Holland.Google Scholar
Tsukahara, T., Ishigamia, T., Yub, B. & Kawaguchia, Y. 2011 DNS study on viscoelastic effect in drag-reduced turbulent channel flow. J. Turbul. 12, 1–25.CrossRefGoogle Scholar
Vaithianathan, T. & Collins, L.R. 2003 Numerical approach to simulating turbulent flow of a viscoelastic polymer solution. J. Comput. Phys. 187, 1–21.CrossRefGoogle Scholar
Vaithianathan, T., Robert, A., Brasseur, J.G. & Collins, L.R. 2006 An improved algorithm for simulating three-dimensional, viscoelastic turbulence. J. Non-Newtonian Fluid Mech. 140, 3–22.CrossRefGoogle Scholar
Van Gils, D.P.M., Huisman, S.G., Bruggert, G.W., Sun, C. & Lohse, D. 2011 Torque scaling in turbulent Taylor–Couette flow with co- and counterrotating cylinders. Phys. Rev. Lett. 106, 024502.CrossRefGoogle ScholarPubMed
Virk, P.S. 1975 Drag reduction fundamentals. AIChE J. 21, 625–656.CrossRefGoogle Scholar
Watanabea, T. & Gotoh, T. 2013 Hybrid Eulerian–Lagrangian simulations for polymer-turbulence interactions. J. Fluid Mech. 717, 535–575.CrossRefGoogle Scholar
Watanabea, T. & Gotoh, T. 2014 Power-law spectra formed by stretching polymers in decaying isotropic turbulence. Phys. Fluids 26, 035110.CrossRefGoogle Scholar
Wei, T., Kline, E.M., Lee, S.H.-K. & Woodruff, S. 1992 Görtler vortex formation at the inner cylinder in Taylor–Couette flow. J. Fluid Mech. 245, 47–68.CrossRefGoogle Scholar
White, C.M. & Mungal, M.G. 2008 Mechanics and prediction of turbulent drag reduction with polymer additives. Annu. Rev. Fluid Mech. 40, 235–256.CrossRefGoogle Scholar
Xi, L. & Graham, M.D. 2012 Dynamics on the laminar-turbulent boundary and the origin of the maximum drag reduction asymptote. Phys. Rev. Lett. 108, 028301.CrossRefGoogle ScholarPubMed
Yu, B. & Kawaguchi, Y. 2004 Direct numerical simulation of viscoelastic drag-reducing flow: a faithful finite difference method. J. Non-Newtonian Fluid Mech. 116, 431–466.CrossRefGoogle Scholar
Zhu, L. & Xi, L. 2020 Inertia-driven and elastoinertial viscoelastic turbulent channel flow simulated with a hybrid pseudo-spectral/finite-difference numerical scheme. J. Non-Newtonian Fluid Mech. 286, 104410.CrossRefGoogle Scholar
Zhu, Y., Song, J., Liu, N., Lu, X. & Khomami, B. 2020 Polymer-induced flow relaminarization and drag enhancement in spanwise-rotating plane Couette flow. J. Fluid Mech. 905, A19.CrossRefGoogle Scholar