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Dynamics and evolution of turbulent Taylor rolls

  • Francesco Sacco (a1), Roberto Verzicco (a1) (a2) (a3) and Rodolfo Ostilla-Mónico (a4)


In many shear- and pressure-driven wall-bounded turbulent flows secondary motions spontaneously develop and their interaction with the main flow alters the overall large-scale features and transfer properties. Taylor–Couette flow, the fluid motion developing in the gap between two concentric cylinders rotating at different angular velocities, is not an exception, and toroidal Taylor rolls have been observed from the early development of the flow up to the fully turbulent regime. In this manuscript we show that under the generic name of ‘Taylor rolls’ there is a wide variety of structures that differ in the vorticity distribution within the cores, the way they are driven and their effects on the mean flow. We relate the rolls at high Reynolds numbers not to centrifugal instabilities, but to a combination of shear and anti-cyclonic rotation, showing that they are preserved in the limit of vanishing curvature and can be better understood as a pinned cycle which shows similar characteristics as the self-sustained process of shear flows. By analysing the effect of the computational domain size, we show that this pinning is not a product of numerics, and that the position of the rolls is governed by a random process with the space and time variations depending on domain size.


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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, 155183.
Avsarkisov, V., Hoyas, S., Oberlack, M. & García-Galache, J. P. 2014 Turbulent plane Couette flow at moderately high Reynolds number. J. Fluid Mech. 751, R1.
Brauckmann, H., Salewski, M. & Eckhardt, B. 2015 Momentum transport in Taylor–Couette flow with vanishing curvature. J. Fluid Mech. 790, 419452.
Brauckmann, H. J. & Eckhardt, B. 2017 Marginally stable and turbulent boundary layers in low-curvature Taylor–Couette flow. J. Fluid Mech. 815, 149168.
Busse, F. H. 2012 Viewpoint: the twins of turbulence research. Physics 5, 4.
Dessup, T., Tuckerman, L. S., Wesfreid, J. E., Barkley, D. & Willis, A. P. 2018 The self-sustaining process in Taylor–Couette flow. Phys. Rev. Fluid. 3 (12), 123902.
Dubrulle, B., Dauchot, O., Daviaud, F., Longaretti, P. Y., Richard, D. & Zahn, J. P. 2005 Stability and turbulent transport in Taylor–Couette flow from analysis of experimental data. Phys. Fluids 17, 095103.
Faisst, H. & Eckhardt, B. 2000 Transition from the Couette–Taylor system to the plane Couette system. Phys. Rev. E 61 (6), 72277230.
Grossmann, S., Lohse, D. & Sun, C. 2016 High–Reynolds number Taylor–Couette turbulence. Annu. Rev. Fluid Mech. 48, 5380.
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317348.
Huisman, S. G., van der Veen, R. C. A., Sun, C. & Lohse, D. 2014 Multiple states in highly turbulent Taylor–Couette flow. Nat. Commun. 5, 3280.
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213240.
Jones, C. A. 1985 The transition to wavy Taylor vortices. J. Fluid Mech. 157, 135162.
Lathrop, D. P., Fineberg, J. & Swinney, H. L. 1992 Transition to shear-driven turbulence in Couette–Taylor flow. Phys. Rev. A 46, 63906405.
Lee, M. & Moser, R. D. 2018 Extreme-scale motions in turbulent plane Couette flows. J. Fluid Mech. 842, 128145.
Moser, R. D. & Moin, P. 1987 The effect of curvature in wall-bounded turbulent flows. J. Fluid Mech. 175, 479510.
Nagata, M. 1990 Three-dimensional finite-amplitude solutions in plane Couette flow: bifurcation from infinity. J. Fluid Mech. 217, 519527.
Ostilla, R., Stevens, R. J. A., Grossmann, S., Verzicco, R. & Lohse, D. 2013 Optimal Taylor–Couette flow: direct numerical simulations. J. Fluid Mech. 719, 1446.
Ostilla-Mónico, R., Lohse, D. & Verzicco, R. 2016 Effect of roll number on the statistics of turbulent Taylor–Couette flow. Phys. Rev. Fluids 1, 054402.
Ostilla-Mónico, R., van der Poel, E. P., Verzicco, R., Grossmann, S. & Lohse, D. 2014a Boundary layer dynamics at the transition between the classical and the ultimate regime of Taylor–Couette flow. Phys. Fluids 26, 015114.
Ostilla-Mónico, R., van der Poel, E. P., Verzicco, R., Grossmann, S. & Lohse, D. 2014b Exploring the phase diagram of fully turbulent Taylor–Couette flow. J. Fluid Mech. 761, 126.
Ostilla-Mónico, R., Verzicco, R., Grossmann, S. & Lohse, D. 2016 The near-wall region of highly turbulent Taylor–Couette flow. J. Fluid Mech. 768, 95117.
Ostilla-Mónico, R., Verzicco, R. & Lohse, D. 2015 Effects of the computational domain size on DNS of Taylor–Couette turbulence with stationary outer cylinder. Phys. Fluids 27, 025110.
Ostilla-Mónico, R., Zhu, X., Spandan, V., Verzicco, R. & Lohse, D. 2017 Life stages of wall-bounded decay of Taylor–Couette turbulence. Phys. Rev. Fluids 2 (11), 114601.
Pirozzoli, S., Bernardini, M. & Orlandi, P. 2014 Turbulence statistics in Couette flow at high Reynolds number. J. Fluid Mech. 758, 327343.
Pirozzoli, S., Modesti, D., Orlandi, P. & Grasso, F. 2018 Turbulence and secondary motions in square duct flow. J. Fluid Mech. 840, 631655.
van der Poel, E. P., Ostilla-Mónico, R., Donners, J. & Verzicco, R. 2015 A pencil distributed finite difference code for strongly turbulent wall-bounded flows. Comput. Fluids 116, 1016.
Taylor, G. I. 1923 Experiments on the motion of solid bodies in rotating fluids. Proc. R. Soc. Lond. A 104, 213218.
Tobias, S. M. & Marston, J. B. 2017 Three-dimensional rotating Couette flow via the generalised quasilinear approximation. J. Fluid Mech. 810, 412428.
Tsukahara, T., Kawamura, H. & Shingai, K. 2006 DNS of turbulent Couette flow with emphasis on the large-scale structure in the core region. J. Turbul. 7, N19.
van der Veen, R. C. A., Huisman, S. G., Merbold, S., Harlander, U., Egbers, C., Lohse, D. & Sun, C. 2016 Taylor–Couette turbulence at radius ratio 𝜂 = 0. 5: scaling, flow structures and plumes. J. Fluid Mech. 799, 334351.
Verzicco, R. & Orlandi, P. 1996 A finite-difference scheme for three-dimensional incompressible flow in cylindrical coordinates. J. Comput. Phys. 123, 402413.
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9, 883900.
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Dynamics and evolution of turbulent Taylor rolls

  • Francesco Sacco (a1), Roberto Verzicco (a1) (a2) (a3) and Rodolfo Ostilla-Mónico (a4)


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