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Turbulence decay towards the linearly stable regime of Taylor–Couette flow

  • Rodolfo Ostilla-Mónico (a1), Roberto Verzicco (a1) (a2), Siegfried Grossmann (a3) and Detlef Lohse (a1)
Abstract
Abstract

Taylor–Couette (TC) flow is used to probe the hydrodynamical (HD) stability of astrophysical accretion disks. Experimental data on the subcritical stability of TC flow are in conflict about the existence of turbulence (cf. Ji et al. (Nature, vol. 444, 2006, pp. 343–346) and Paoletti et al. (Astron. Astroph., vol. 547, 2012, A64)), with discrepancies attributed to end-plate effects. In this paper we numerically simulate TC flow with axially periodic boundary conditions to explore the existence of subcritical transitions to turbulence when no end plates are present. We start the simulations with a fully turbulent state in the unstable regime and enter the linearly stable regime by suddenly starting a (stabilizing) outer cylinder rotation. The shear Reynolds number of the turbulent initial state is up to $Re_s \lesssim 10^5$ and the radius ratio is $\eta =0.714$ . The stabilization causes the system to behave as a damped oscillator and, correspondingly, the turbulence decays. The evolution of the torque and turbulent kinetic energy is analysed and the periodicity and damping of the oscillations are quantified and explained as a function of shear Reynolds number. Though the initially turbulent flow state decays, surprisingly, the system is found to absorb energy during this decay.

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Corresponding author
Email address for correspondence: r.ostillamonico@utwente.nl
References
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Armitage P. J. 2011 Dynamics of protoplanetary disks. Annu. Rev. Astron. Astrophys. 49, 195236.
Avila M. 2012 Stability and angular-momentum transport of fluid flows between corotating cylinders. Phys. Rev. Lett. 108 (12), 124501.
Balbus S. A. & Hawley J. 1991 A powerful local shear instability in weakly magnetized disks. Astrophys. J. 376, 214233.
Borrero-Echeverry D., Schatz M. F. & Tagg R. 2010 Transient turbulence in Taylor–Couette flow. Phys. Rev. E 81, 025301.
Brauckmann H. & Eckhardt B. 2013 Direct numerical simulations of local and global torque in Taylor–Couette flow up to inline-graphic $Re=30\, 000$ . J. Fluid Mech. 718, 398427.
Chandrasekhar S. 1981 Hydrodynamic and Hydromagnetic Stability. Dover.
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.
Eckhardt B., Grossmann S. & Lohse D. 2007 Torque scaling in turbulent Taylor–Couette flow between independently rotating cylinders. J. Fluid Mech. 581, 221250.
Edlund E. M. & Ji H. 2014 Nonlinear stability of laboratory quasi-Keplerian flows. Phys. Rev. E 89, 021004.
Gallet B., Doering C. R. & Spiegel E. A. 2010 Destabilizing Taylor–Couette flow with suction. Phys. Fluids 22, 034105.
Gammie C. F. 1996 Layered accretion in T-Tauri disks. Astrophys. J. 457, 355362.
Grossmann S. 2000 The onset of shear flow turbulence. Rev. Mod. Phys. 72, 603618.
Grossmann S. & Lohse D. 2000 Scaling in thermal convection: a unifying view. J. Fluid Mech. 407, 2756.
Grossmann S. & Lohse D. 2001 Thermal convection for large Prandtl number. Phys. Rev. Lett. 86, 33163319.
Grossmann S. & Lohse D. 2011 Multiple scaling in the ultimate regime of thermal convection. Phys. Fluids 23, 045108.
Ji H. & Balbus S. A. 2013 Angular momentum transport in astrophysics and in the lab. Phys. Today 66 (8), 2733.
Ji H., Burin M., Schartman E. & Goodman J. 2006 Hydrodynamic turbulence cannot transport angular momentum effectively in astrophysical disks. Nature 444, 343346.
Klahr H. H. & Bodenheimer P. 2003 Turbulence in accretion disks: vorticity generation and angular momentum transport via the global baroclinic instability. Astrophys. J. 508 (2), 869892.
Lesur G. & Longaretti P. Y. 2005 On the relevance of subcritical hydrodynamic turbulence to accretion disk transport. Astron. Astrophys. 444, 2544.
Lopez J. M., Marques F. & Avila M. 2013 The Boussinesq approximation in rapidly rotating flows. J. Fluid Mech. 737, 5677.
Maretzke S., Hof B. & Avila M. 2014 Transient growth in lineraly stable Taylor–Couette flows. J. Fluid Mech. 742, 254290.
Ostilla R., Stevens R. J. A. M., Grossmann S., Verzicco R. & Lohse D. 2013 Optimal Taylor–Couette flow: direct numerical simulations. J. Fluid Mech. 719, 1446.
Ostilla-Monico R., van der Poel E. P., Verzicco R., Grossmann S. & Lohse D. 2014 Boundary layer dynamics at the transition between the classical and the ultimate regime of Taylor–Couette flow. Phys. Fluids 26, 015114.
Paczynski B. & Bisnovatyi-Kogan G. 1981 A model of a thin accretion disk around a black hole. Acta Astron. 31 (3), 283291.
Paoletti M. S. & Lathrop D. P. 2011 Angular momentum transport in turbulent flow between independently rotating cylinders. Phys. Rev. Lett. 106, 024501.
Paoletti M. S., van Gils D. P. M., Dubrulle B., Sun C., Lohse D. & Lathrop D. P. 2012 Angular momentum transport and turbulence in laboratory models of Keplerian flows. Astron. Astrophys. 547, A64.
Petersen M. R., Julien K. & Stewart G. R. 2007 Baroclinic vorticity production in protoplanetary disks. I. Vortex formation. Astrophys. J. 658, 12361251.
Proudman J. 1916 On the motion of solids in a liquid possessing vorticity. Proc. R. Soc. Lond. A 92, 408424.
Richard D.2001 Instabilités hydrodynamiques dans les ecoulements en rotation différentielle. PhD thesis, University of Paris 7.
Rincon F., Ogilvie G. I. & Cossu C. 2008 On self-sustaining processes in Rayleigh-stable rotating plane Couette flows and subcritical transitions to turbulence in accretion disks. Astron. Astrophys. 463, 817832.
Schartman E., Ji H., Burin M. J. & Goodman J. 2012 Stability of quasi-Keplerian shear flow in a laboratory experiment. Astron. Astrophys. 543, A94.
Shakura N. I. & Sunyaev R. A. 1973 Black holes in binary systems. Observational appearance. Astron. Astrophys. 24, 337355.
Taylor G. I. 1917 Motion of solids in fluids when the flow is not irrotational. Proc. R. Soc. Lond. A 93, 92113.
Trefethen L. N., Trefethen A. E., Reddy S. C. & Driscol T. A. 1993 Hydrodynamic stability without eigenvalues. Science 261, 578584.
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 counter-rotating cylinders. Phys. Rev. Lett. 106, 024502.
van Gils D. P. M., Huisman S. G., Grossmann S., Sun C. & Lohse D. 2012 Optimal Taylor–Couette turbulence. J. Fluid Mech. 706, 118149.
Velikhov E. P. 1959 Stability of an ideally conducting liquid flowing between rotating cylinders in a magnetic field. Zh. Eksp. Teor. Fiz. 36.
Verzicco R. & Orlandi P. 1996 A finite-difference scheme for three-dimensional incompressible flow in cylindrical coordinates. J. Comput. Phys. 123, 402413.
Withjack E. M. & Chen C. F. 1974 An experimental study of Couette instability of stratified fluids. J. Fluid Mech. 66, 725737.
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