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Dynamics and evolution of turbulent Taylor rolls

Published online by Cambridge University Press:  15 May 2019

Francesco Sacco Open the ORCID record for Francesco Sacco [Opens in a new window] ,
Roberto Verzicco Open the ORCID record for Roberto Verzicco [Opens in a new window]  and
Rodolfo Ostilla-Mónico Open the ORCID record for Rodolfo Ostilla-Mónico [Opens in a new window]
Francesco Sacco*
Affiliation:
Gran Sasso Science Institute, Viale Francesco Crispi 7, L’Aquila 67100, Italy
Roberto Verzicco
Affiliation:
Gran Sasso Science Institute, Viale Francesco Crispi 7, L’Aquila 67100, Italy Dipartimento di Ingegneria Industriale, University of Rome ‘Tor Vergata’, Via del Politecnico 1, Roma 00133, Italy Physics of Fluids Group, Faculty of Science and Technology, MESA+ Research Institute, and J. M. Burgers Centre for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Rodolfo Ostilla-Mónico*
Affiliation:
Department of Mechanical Engineering, Cullen College of Engineering, University of Houston, Houston, TX 77204, USA
*
†Email addresses for correspondence: francesco.sacco@gssi.it, rostilla@central.uh.uk
†Email addresses for correspondence: francesco.sacco@gssi.it, rostilla@central.uh.uk
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Abstract

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.

JFM classification

Turbulent Flows: Rotating turbulence Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 870 , 10 July 2019 , pp. 970 - 987
Copyright
© 2019 Cambridge University Press 

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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.Google Scholar
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.Google Scholar
Brauckmann, H., Salewski, M. & Eckhardt, B. 2015 Momentum transport in Taylor–Couette flow with vanishing curvature. J. Fluid Mech. 790, 419–452.Google Scholar
Brauckmann, H. J. & Eckhardt, B. 2017 Marginally stable and turbulent boundary layers in low-curvature Taylor–Couette flow. J. Fluid Mech. 815, 149–168.Google Scholar
Busse, F. H. 2012 Viewpoint: the twins of turbulence research. Physics 5, 4.Google Scholar
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.Google Scholar
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.Google Scholar
Faisst, H. & Eckhardt, B. 2000 Transition from the Couette–Taylor system to the plane Couette system. Phys. Rev. E 61 (6), 7227–7230.Google Scholar
Grossmann, S., Lohse, D. & Sun, C. 2016 High–Reynolds number Taylor–Couette turbulence. Annu. Rev. Fluid Mech. 48, 53–80.Google Scholar
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348.Google Scholar
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.Google Scholar
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.Google Scholar
Jones, C. A. 1985 The transition to wavy Taylor vortices. J. Fluid Mech. 157, 135–162.Google Scholar
Lathrop, D. P., Fineberg, J. & Swinney, H. L. 1992 Transition to shear-driven turbulence in Couette–Taylor flow. Phys. Rev. A 46, 6390–6405.Google Scholar
Lee, M. & Moser, R. D. 2018 Extreme-scale motions in turbulent plane Couette flows. J. Fluid Mech. 842, 128–145.Google Scholar
Moser, R. D. & Moin, P. 1987 The effect of curvature in wall-bounded turbulent flows. J. Fluid Mech. 175, 479–510.Google Scholar
Nagata, M. 1990 Three-dimensional finite-amplitude solutions in plane Couette flow: bifurcation from infinity. J. Fluid Mech. 217, 519–527.Google Scholar
Ostilla, R., Stevens, R. J. A., Grossmann, S., Verzicco, R. & Lohse, D. 2013 Optimal Taylor–Couette flow: direct numerical simulations. J. Fluid Mech. 719, 14–46.Google Scholar
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.Google Scholar
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.Google Scholar
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, 1–26.Google Scholar
Ostilla-Mónico, R., Verzicco, R., Grossmann, S. & Lohse, D. 2016 The near-wall region of highly turbulent Taylor–Couette flow. J. Fluid Mech. 768, 95–117.Google Scholar
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.Google Scholar
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.Google Scholar
Pirozzoli, S., Bernardini, M. & Orlandi, P. 2014 Turbulence statistics in Couette flow at high Reynolds number. J. Fluid Mech. 758, 327–343.Google Scholar
Pirozzoli, S., Modesti, D., Orlandi, P. & Grasso, F. 2018 Turbulence and secondary motions in square duct flow. J. Fluid Mech. 840, 631–655.Google Scholar
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, 10–16.Google Scholar
Taylor, G. I. 1923 Experiments on the motion of solid bodies in rotating fluids. Proc. R. Soc. Lond. A 104, 213–218.Google Scholar
Tobias, S. M. & Marston, J. B. 2017 Three-dimensional rotating Couette flow via the generalised quasilinear approximation. J. Fluid Mech. 810, 412–428.Google Scholar
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.Google Scholar
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, 334–351.Google Scholar
Verzicco, R. & Orlandi, P. 1996 A finite-difference scheme for three-dimensional incompressible flow in cylindrical coordinates. J. Comput. Phys. 123, 402–413.Google Scholar
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9, 883–900.Google Scholar