*Coherent structures in elastoinertial Taylor–Couette flows*

consistent with the literature (Dinic & Sharma 2020; Jimenez, Martínez-Narváez & Sharma 2020).

**Appendix B. Degradation of polymers/effect of mica flakes**

The effect of polymer degradation during long visualisation experiments was examined by measuring the viscosity curves before and after every run. Selected curves are shown in figure 19(a). The deviation is less than 10%. The same protocol has been used to measure the effect of the mica flakes on the fluid viscosity figure 19(b). The deviation is less than 1% for all cases so both the effects of degradation and mica flakes contribution are considered negligible.

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DUBIEF, Y., TERRAPON, V.E. & HOF, B. 2023 Elasto-inertial turbulence. *Annu. Rev. Fluid Mech.* **55**, 675–705.

DUBIEF, Y., TERRAPON, V.E. & SORIA, J. 2013 On the mechanism of elasto-inertial turbulence. *Phys. Fluids* **25**, 110817.

DUTCHER, C.S. & MULLER, S.J. 2009 Spatio-temporal mode dynamics and higher order transitions in high aspect ratio newtonian Taylor–Couette flows. *J. Fluid Mech.* **641**, 85–113.

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.

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.

EKMAN, V.W. 1905 On the influence of the earth's rotation on ocean-currents. *Ark. Mat. Astron. Fys.* **2**, 1–52.

FENSTERMACHER, 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.

FOUXON, A. & LEBEDEV, V. 2003 Spectra of turbulence in dilute polymer solutions. *Phys. Fluids* **15**, 2060–2072.

GOLLUB, J.P. & SWINNEY, H.L. 1975 Onset of turbulence in a rotating fluid. *Phys. Rev. Lett.* **35**, 143–145.

GORMAN, M. & SWINNEY, H.L. 1982 Spatial and temporal characteristics of modulated waves in the circular Couette system. *J. Fluid Mech.* **117**, 123–142.

GRAESSLEY, W.W. 1980 Polymer chain dimensions and the dependence of viscoelastic properties on concentration, molecular weight and solvent power. *Polymer* **21**, 258–262.

GROISMAN, A. & STEINBERG, V. 1996 Couette–Taylor flow in a dilute polymer solution. *Phys. Rev. Lett.* **77**, 1480–1483.

GROISMAN, A. & STEINBERG, V. 1997 Solitary vortex pairs in viscoelastic Couette flow. *Phys. Rev. Lett.* **78**, 1460–1463.

GROISMAN, A. & STEINBERG, V. 1998 Mechanism of elastic instability in Couette flow of polymer solutions: experiment. *Phys. Fluids* **10**, 2451–2463.

GROISMAN, A. & STEINBERG, V. 2004 Elastic turbulence in curvilinear flows of polymer solutions. *New J. Phys.* **6**, 29–29.

GROSSMANN, S., LOHSE, D. & SUN, C. 2016 High-reynolds number Taylor–Couette turbulence. *Annu. Rev. Fluid Mech.* **48**, 53–80.

HAWARD, S.J., MCKINLEY, G.H. & SHEN, A.Q. 2016 Elastic instabilities in planar elongational flow of monodisperse polymer solutions. *Sci. Rep.* **6**, 33029.

HOPKINS, S.D., GOGOVI, G.K., WEISEL, E., HANDLER, R.A. & BLAISTEN-BAROJAS, E. 2020 Polyacrylamide in glycerol solutions from an atomistic perspective of the energetics, structure, and dynamics. *AIP Adv.* **10**, 085011.

JHA, N.K. & STEINBERG, V. 2020 Universal coherent structures of elastic turbulence in straight channel with viscoelastic fluid flow. *arXiv:2009.12258*.

JHA, N.K. & STEINBERG, V. 2021 Elastically driven Kelvin–Helmholtz-like instability in straight channel flow. *Proc. Natl Acad. Sci.* **118**, 1–7.

JIMENEZ, L.N., MARTÍNEZ-NARVÁEZ, C.D.V. & SHARMA, V. 2020 Capillary breakup and extensional rheology response of food thickener cellulose gum (NaCMC) in salt-free and excess salt solutions. *Phys. Fluids* **32**, 012113.

JUNG, S.Y. & SUNG, H.J. 2006 Characterization of the three-dimensional turbulent boundary layer in a concentric annulus with a rotating inner cylinder. *Phys. Fluids* **18**, 1–11.

KUMAR, K.A. & GRAHAM, M.D. 2000 Solitary coherent structures in viscoelastic shear flow: computation and mechanism. *Phys. Rev. Lett.* **85**, 4056–4059.

KUMAR, K.A. & GRAHAM, M.D. 2001 Finite-amplitude solitary states in viscoelastic shear flow: computation and mechanism. *J. Fluid Mech.* **443**, 301–328.

LACASSAGNE, T., BOULAFENTIS, T., CAGNEY, N. & BALABANI, S. 2021a Modulation of elasto-inertial transitions in Taylor–Couette flow by small particles. *J. Fluid Mech.* **929**, R2.

LACASSAGNE, T., CAGNEY, N. & BALABANI, S. 2021b Shear-thinning mediation of elasto-inertial Taylor–Couette flow. *J. Fluid Mech.* **915**, A91.

LACASSAGNE, T., CAGNEY, N., GILLISSEN, J.J.J. & BALABANI, S. 2020 Vortex merging and splitting: A route to elastoinertial turbulence in Taylor–Couette flow. *Phys. Rev. Fluids* **5**, 113303.

LANGE, M. & ECKHARDT, B. 2001 Vortex pairs in viscoelastic Couette–Taylor flow. *Phys. Rev. E* **64**, 4.

LATRACHE, N., ABCHA, N., CRUMEYROLLE, O. & MUTABAZI, I. 2016 Defect-mediated turbulence in ribbons of viscoelastic Taylor–Couette flow. *Phys. Rev. E* **93**, 043126.

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**, 1–6.
LATRACHE, N. & MUTABAZI, I. 2021 Transition to turbulence via flame patterns in viscoelastic Taylor–Couette flow. *Eur. Phys. J.* **E** 44, 63.

LELLEP, M., LINKMANN, M. & MOROZOV, A. 2023 Linear stability analysis of purely elastic travelling-wave solutions in pressure-driven channel flows. *J. Fluid Mech.* **959**, R1.

LEMOULT, G., SHI, L., AVILA, K., JALIKOP, S.V., AVILA, M. & HOF, B. 2016 Directed percolation phase transition to sustained turbulence in couette flow. *Nat. Phys.* **12**, 254–258.

LENG, X.Y., KRASNOV, D., LI, B.W. & ZHONG, J.Q. 2021 Flow structures and heat transport in Taylor–Couette systems with axial temperature gradient. *J. Fluid Mech.* **920**, A42.

LIN, F., SONG, J., ZHAO, Z., LIU, N., LU, X.Y. & KHOMAMI, B. 2023 A novel transition route to elastically dominated turbulence in viscoelastic Taylor–Couette flow. *J. Non-Newtonian Fluid Mech.* **312**, 104968.

LIU, N. & KHOMAMI, B. 2013 Elastically induced turbulence in Taylor–Couette flow: direct numerical simulation and mechanistic insight. *J. Fluid Mech.* **737**, R4.

LOPEZ, J.M. 2022 Vortex merging and splitting events in viscoelastic Taylor–Couette flow. *J. Fluid Mech.* **946**, A27.

MARTÍNEZ-ARIAS, B. 2015 *Torque Measurement in Turbulent Couette–Taylor Flows*. Doctoral dissertation, University of Le Havre.

MARTÍNEZ-ARIAS, B. & PEIXINHO, J. 2017 Torque in Taylor–Couette flow of viscoelastic polymer solutions. *J. Non-Newtonian Fluid Mech.* **247**, 221–228.

MOAZZEN, M., LACASSAGNE, T., THOMY, V. & BAHRANI, S.A. 2022 Torque scaling at primary and secondary bifurcations in a Taylor–Couette flow of suspensions. *J. Fluid Mech.* **937**, A2.

MOAZZEN, M., LACASSAGNE, T., THOMY, V. & BAHRANI, S.A. 2023 Friction dynamics of elasto-inertial turbulence in Taylor–Couette flow of viscoelastic fluids. *Phil. Trans. R. Soc. A* **381**, 20220300.

MOROZOV, A. 2022 Coherent structures in plane channel flow of dilute polymer solutions with vanishing inertia. *Phys. Rev. Lett.* **129**, 17801.

OSTILLA-MÓNICO, R., POEL, E.P.V.D., VERZICCO, R., GROSSMANN, S. & LOHSE, D. 2014 Exploring the phase diagram of fully turbulent Taylor–Couette flow. *J. Fluid Mech.* **761**, 1–26.

PAKDEL, P. & MCKINLEY, G.H. 1996 Elastic instability and curved streamlines. *Phys. Rev. Lett.* **77**, 2459–2462.

RAFFEL, M., WILLERT, C.E., SCARANO, F., KÄHLER, C.J., WERELEY, S.T. & KOMPENHANS, J. 2018 *Particle Image Velocimetry*. Springer International Publishing.

RAMESH, P., BHARADWAJ, S. & ALAM, M. 2019 Suspension Taylor–Couette flow: co-existence of stationary and travelling waves, and the characteristics of Taylor vortices and spirals. *J. Fluid Mech.* **870**, 901–940.

ROSTI, M.E., PERLEKAR, P. & MITRA, D. 2023 Large is different: nonmonotonic behavior of elastic range scaling in polymeric turbulence at large Reynolds and Deborah numbers. *Sci. Adv.* **9**, eadd3831.

RUBINSTEIN, M. & COLBY, R.H. 2003 *Polymer Physics*. Oxford University Press.

SCHAFER, C. 2013 *Elastic Flow Instabilities of Non-Newtonian Fluids in Shear Flows*. Doctoral dissertation, Saarland University.

SHNAPP, R. & STEINBERG, V. 2022 Nonmodal elastic instability and elastic waves in weakly perturbed channel flow. *Phys. Rev. Fluids* **7**, 063901.

SOARES, E.J., SILVA, I.M., ANDRADE, R.M. & SIQUEIRA, R.N. 2020 The role played by the flexible polymer polyacrylamide (PAM) and the rigid polymer xanthan gum (XG) on drag in Taylor–Couette geometry: from Taylor’s vortexes to fully turbulent flow. *J. Braz. Soc. Mech. Sci. Engng* **42**, 392.

SOBOLÍK, V., IZRAR, B., LUSSEYRAN, F. & SKALI, S. 2000 Interaction between the ekman layer and the Couette–Taylor instability. *Intl J. Heat Mass Transfer* **43**, 4381–4393.

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SONG, J., LIN, F., LIU, N., LU, X.Y. & KHOMAMI, B. 2021a Direct numerical simulation of inertia-elastic turbulent Taylor–Couette flow. *J. Fluid Mech.* **926**, A37.

SONG, J., LIN, F., ZHU, Y., WAN, Z.H., LIU, N., LU, X.Y. & KHOMAMI, B. 2023a Self-sustaining cycle of purely elastic turbulence. *Phys. Rev. Fluids* **8**, 014602.

SONG, J., LIU, N., LU, X.Y. & KHOMAMI, B. 2022 Direct numerical simulation of elastic turbulence in the Taylor–Couette flow: transition pathway and mechanistic insight. *J. Fluid Mech.* **949**, A49.

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.

SONG, J., WAN, Z.H., LIU, N., LU, X.Y. & KHOMAMI, B. 2021b A reverse transition route from inertial to elasticity-dominated turbulence in viscoelastic Taylor–Couette flow. *J. Fluid Mech.* **927**, 3217–3226.

SONG, J., ZHU, Y., LIN, F., LIU, N. & KHOMAMI, B. 2023b Turbulent Taylor–Couette flow of dilute polymeric solutions: a 10-year retrospective. *Phil. Trans. R. Soc. A* **381**, 20220132.
LATRACHE, N. & MUTABAZI, I. 2021 Transition to turbulence via flame patterns in viscoelastic Taylor–Couette flow. *Eur. Phys. J.* **E** 44, 63.

LELLEP, M., LINKMANN, M. & MOROZOV, A. 2023 Linear stability analysis of purely elastic travelling-wave solutions in pressure-driven channel flows. *J. Fluid Mech.* **959**, R1.

LEMOULT, G., SHI, L., AVILA, K., JALIKOP, S.V., AVILA, M. & HOF, B. 2016 Directed percolation phase transition to sustained turbulence in couette flow. *Nat. Phys.* **12**, 254–258.

LENG, X.Y., KRASNOV, D., LI, B.W. & ZHONG, J.Q. 2021 Flow structures and heat transport in Taylor–Couette systems with axial temperature gradient. *J. Fluid Mech.* **920**, A42.

LIN, F., SONG, J., ZHAO, Z., LIU, N., LU, X.Y. & KHOMAMI, B. 2023 A novel transition route to elastically dominated turbulence in viscoelastic Taylor–Couette flow. *J. Non-Newtonian Fluid Mech.* **312**, 104968.

LIU, N. & KHOMAMI, B. 2013 Elastically induced turbulence in Taylor–Couette flow: direct numerical simulation and mechanistic insight. *J. Fluid Mech.* **737**, R4.

LOPEZ, J.M. 2022 Vortex merging and splitting events in viscoelastic Taylor–Couette flow. *J. Fluid Mech.* **946**, A27.

MARTÍNEZ-ARIAS, B. 2015 *Torque Measurement in Turbulent Couette–Taylor Flows*. Doctoral dissertation, University of Le Havre.

MARTÍNEZ-ARIAS, B. & PEIXINHO, J. 2017 Torque in Taylor–Couette flow of viscoelastic polymer solutions. *J. Non-Newtonian Fluid Mech.* **247**, 221–228.

MOAZZEN, M., LACASSAGNE, T., THOMY, V. & BAHRANI, S.A. 2022 Torque scaling at primary and secondary bifurcations in a Taylor–Couette flow of suspensions. *J. Fluid Mech.* **937**, A2.

MOAZZEN, M., LACASSAGNE, T., THOMY, V. & BAHRANI, S.A. 2023 Friction dynamics of elasto-inertial turbulence in Taylor–Couette flow of viscoelastic fluids. *Phil. Trans. R. Soc. A* **381**, 20220300.

MOROZOV, A. 2022 Coherent structures in plane channel flow of dilute polymer solutions with vanishing inertia. *Phys. Rev. Lett.* **129**, 17801.

OSTILLA-MÓNICO, R., POEL, E.P.V.D., VERZICCO, R., GROSSMANN, S. & LOHSE, D. 2014 Exploring the phase diagram of fully turbulent Taylor–Couette flow. *J. Fluid Mech.* **761**, 1–26.

PAKDEL, P. & MCKINLEY, G.H. 1996 Elastic instability and curved streamlines. *Phys. Rev. Lett.* **77**, 2459–2462.

RAFFEL, M., WILLERT, C.E., SCARANO, F., KÄHLER, C.J., WERELEY, S.T. & KOMPENHANS, J. 2018 *Particle Image Velocimetry*. Springer International Publishing.

RAMESH, P., BHARADWAJ, S. & ALAM, M. 2019 Suspension Taylor–Couette flow: co-existence of stationary and travelling waves, and the characteristics of Taylor vortices and spirals. *J. Fluid Mech.* **870**, 901–940.

ROSTI, M.E., PERLEKAR, P. & MITRA, D. 2023 Large is different: nonmonotonic behavior of elastic range scaling in polymeric turbulence at large Reynolds and Deborah numbers. *Sci. Adv.* **9**, eadd3831.

RUBINSTEIN, M. & COLBY, R.H. 2003 *Polymer Physics*. Oxford University Press.

SCHAFER, C. 2013 *Elastic Flow Instabilities of Non-Newtonian Fluids in Shear Flows*. Doctoral dissertation, Saarland University.

SHNAPP, R. & STEINBERG, V. 2022 Nonmodal elastic instability and elastic waves in weakly perturbed channel flow. *Phys. Rev. Fluids* **7**, 063901.

SOARES, E.J., SILVA, I.M., ANDRADE, R.M. & SIQUEIRA, R.N. 2020 The role played by the flexible polymer polyacrylamide (PAM) and the rigid polymer xanthan gum (XG) on drag in Taylor–Couette geometry: from Taylor’s vortexes to fully turbulent flow. *J. Braz. Soc. Mech. Sci. Engng* **42**, 392.

SOBOLÍK, V., IZRAR, B., LUSSEYRAN, F. & SKALI, S. 2000 Interaction between the ekman layer and the Couette–Taylor instability. *Intl J. Heat Mass Transfer* **43**, 4381–4393.

SOLOMON, O.F. & CIUTĂ, I.Z. 1962 Détermination de la viscosité intrinsèque de solutions de polymères par une simple détermination de la viscosité. *J. Appl. Polym. Sci.* **6** (24), 683–686.

SONG, J., LIN, F., LIU, N., LU, X.Y. & KHOMAMI, B. 2021a Direct numerical simulation of inertia-elastic turbulent Taylor–Couette flow. *J. Fluid Mech.* **926**, A37.

SONG, J., LIN, F., ZHU, Y., WAN, Z.H., LIU, N., LU, X.Y. & KHOMAMI, B. 2023a Self-sustaining cycle of purely elastic turbulence. *Phys. Rev. Fluids* **8**, 014602.

SONG, J., LIU, N., LU, X.Y. & KHOMAMI, B. 2022 Direct numerical simulation of elastic turbulence in the Taylor–Couette flow: transition pathway and mechanistic insight. *J. Fluid Mech.* **949**, A49.

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.

SONG, J., WAN, Z.H., LIU, N., LU, X.Y. & KHOMAMI, B. 2021b A reverse transition route from inertial to elasticity-dominated turbulence in viscoelastic Taylor–Couette flow. *J. Fluid Mech.* **927**, 3217–3226.

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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.

THOMAS, D.G., SURESHKUMAR, R. & KHOMAMI, B. 2006 Pattern formation in Taylor–Couette flow of dilute polymer solutions: dynamical simulations and mechanism. *Phys. Rev. Lett.* **97**, 054501.

VARSHNEY, A. & STEINBERG, V. 2019 Elastic alfven waves in elastic turbulence. *Nat. Commun.* **10**, 1–7.

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WATANABE, K., SUMJO, S. & OGATA, S. 2006 Formation of Taylor vortex flow of polymer solutions. *Trans. ASME J. Fluids Engng* **128**, 95–100.

WERELEY, S.T. & LUEPTOW, R.M. 1998 Spatio-temporal character of non-wavy and wavy Taylor–Couette flow. *J. Fluid Mech.* **364**, 59–80.

WERELEY, S.T. & LUEPTOW, R.M. 1999 Velocity field for Taylor–Couette flow with an axial flow. *Phys. Fluids* **11**, 3637–3649.

XI, L. & GRAHAM, M.D. 2010a Active and hibernating turbulence in minimal channel flow of Newtonian and polymeric fluids. *Phys. Rev. Lett.* **104**, 15–18.

XI, L. & GRAHAM, M.D. 2010b Turbulent drag reduction and multistage transitions in viscoelastic minimal flow units. *J. Fluid Mech.* **647**, 421–452.

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**, 1–5.

XIAO, Q., LIM, T.T. & CHEW, Y.T. 2002 Effect of acceleration on the wavy Taylor vortex flow. *Exp. Fluids* **32**, 639–644.

YAMANI, S., KESHAVARZ, B., RAJ, Y., ZAKI, T.A., MCKINLEY, G.H. & BISCHOFBERGER, I. 2021 Spectral universality of elastoinertial turbulence. *Phys. Rev. Lett.* **127** (7), 074501.

YAMANI, S., RAJ, Y., ZAKI, T.A., MCKINLEY, G.H. & BISCHOFBERGER, I. 2023 Spatiotemporal signatures of elastoinertial turbulence in viscoelastic planar jets. *Phys. Rev. Fluids* **8**, 064610.

ZHANG, Y.-B., BODENSCHATZ, E., XU, H. & XI, H.-D. 2021 Experimental observation of the elastic range scaling in turbulent flow with polymer additives. *Sci. Adv.* **7**, 1–9.

ZHANG, L.H. & SWINNEY, H.L. 1985 Nonpropagating oscillatory modes in Couette–Taylor flow. *Phys. Rev.* A **31**, 1006–1009.
SOUSA, P.C., VEGA, E.J., SOUSA, R.G., MONTANERO, J.M. & ALVES, M.A. 2017 Measurement of relaxation times in extensional flow of weakly viscoelastic polymer solutions. *Rheol. Acta* **56**, 11–20.

STEINBERG, V. 2021 Elastic turbulence: an experimental view on inertialess random flow. *Annu. Rev. Fluid Mech.* **53**, 27–58.

STEINBERG, V. & GROISMAN, A. 1998 Elastic versus inertial instability in Couette–Taylor flow of a polymer solution review. *Phil. Mag.* **B** **78**, 253–263.

TAYLOR, G.I. 1923 Viii. stability of a viscous liquid contained between two rotating cylinders. *Phil. Trans. R. Soc.* **A** **223**, 289–343.

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.

THOMAS, D.G., SURESHKUMAR, R. & KHOMAMI, B. 2006 Pattern formation in Taylor–Couette flow of dilute polymer solutions: dynamical simulations and mechanism. *Phys. Rev. Lett.* **97**, 054501.

VARSHNEY, A. & STEINBERG, V. 2019 Elastic alfven waves in elastic turbulence. *Nat. Commun.* **10**, 1–7.

VAZQUEZ, M., SCHMALZING, D., MATSUDAIRA, P., EHRLICH, D. & MCKINLEY, G. 2001 Shear-induced degradation of linear polyacrylamide solutions during pre-electrophoretic loading. *Anal. Chem.* **73**, 3035–3044.

WATANABE, K., SUMJO, S. & OGATA, S. 2006 Formation of Taylor vortex flow of polymer solutions. *Trans. ASME J. Fluids Engng* **128**, 95–100.

WERELEY, S.T. & LUEPTOW, R.M. 1998 Spatio-temporal character of non-wavy and wavy Taylor–Couette flow. *J. Fluid Mech.* **364**, 59–80.

WERELEY, S.T. & LUEPTOW, R.M. 1999 Velocity field for Taylor–Couette flow with an axial flow. *Phys. Fluids* **11**, 3637–3649.

XI, L. & GRAHAM, M.D. 2010a Active and hibernating turbulence in minimal channel flow of Newtonian and polymeric fluids. *Phys. Rev. Lett.* **104**, 15–18.

XI, L. & GRAHAM, M.D. 2010b Turbulent drag reduction and multistage transitions in viscoelastic minimal flow units. *J. Fluid Mech.* **647**, 421–452.

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**, 1–5.

XIAO, Q., LIM, T.T. & CHEW, Y.T. 2002 Effect of acceleration on the wavy Taylor vortex flow. *Exp. Fluids* **32**, 639–644.

YAMANI, S., KESHAVARZ, B., RAJ, Y., ZAKI, T.A., MCKINLEY, G.H. & BISCHOFBERGER, I. 2021 Spectral universality of elastoinertial turbulence. *Phys. Rev. Lett.* **127** (7), 074501.

YAMANI, S., RAJ, Y., ZAKI, T.A., MCKINLEY, G.H. & BISCHOFBERGER, I. 2023 Spatiotemporal signatures of elastoinertial turbulence in viscoelastic planar jets. *Phys. Rev. Fluids* **8**, 064610.

ZHANG, Y.-B., BODENSCHATZ, E., XU, H. & XI, H.-D. 2021 Experimental observation of the elastic range scaling in turbulent flow with polymer additives. *Sci. Adv.* **7**, 1–9.

ZHANG, L.H. & SWINNEY, H.L. 1985 Nonpropagating oscillatory modes in Couette–Taylor flow. *Phys. Rev.* A **31**, 1006–1009.