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

Published online by Cambridge University Press:  12 May 2014

Rodolfo Ostilla-Mónico ,
Roberto Verzicco ,
Siegfried Grossmann  and
Detlef Lohse
Rodolfo Ostilla-Mónico*
Affiliation:
Physics of Fluids, Mesa+ Institute, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Roberto Verzicco
Affiliation:
Physics of Fluids, Mesa+ Institute, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands Dipartimento di Ingegneria Meccanica, University of Rome ‘Tor Vergata’, Via del Politecnico 1, Roma 00133, Italy
Siegfried Grossmann
Affiliation:
Department of Physics, University of Marburg, Renthof 6, D-35032 Marburg, Germany
Detlef Lohse
Affiliation:
Physics of Fluids, Mesa+ Institute, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Instability: Nonlinear instability Turbulent Flows: Rotating turbulence Turbulent Flows: Turbulent convection
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 748 , 10 June 2014 , R3
Copyright
© 2014 Cambridge University Press 

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