Life stages of wall-bounded decay of Taylor-Couette turbulence

Abstract

The decay of Taylor-Couette turbulence, i.e., the flow between two coaxial and independently rotating cylinders, is numerically studied by instantaneously stopping the forcing from an initially statistically stationary flow field at a Reynolds number of Re = 3.5 x 10(4). The effect of wall friction is analyzed by comparing three separate cases, in which the cylinders are either suddenly made no-slip or stress-free. Different life stages are observed during the decay. In the first stage, the decay is dominated by large-scale rolls. Counterintuitively, when these rolls fade away, if the flow inertia is small a redistribution of energy occurs and the energy of the azimuthal velocity behaves nonmonotonically, first decreasing by almost two orders of magnitude and then increasing during the redistribution. The second stage is dominated by non-normal transient growth of perturbations in the axial (spanwise) direction. Once this mechanism is exhausted, the flow enters the final life stage, viscous decay, which is dominated by wall friction. We show that this stage can be modeled by a one-dimensional heat equation, and that self-similar velocity profiles collapse onto the theoretical solution

Dynamics and evolution of turbulent Taylor rolls

“…Additional evidence for a general similarity between the rolls and the SSP is given by a previous study performed by Ostilla-Mónico et al (2017) on decaying Taylor-Couette turbulence. In channel flow, the self-sustaining process regenerates itself with slow timescales (100tU/d).…”

On the stages of vortex decay in an impulsively stopped, rotating cylinder

“…When a large fraction of the total energy has been dissipated, turbulence does not self-sustain and a stage of viscous decay occurs yielding relaminarisation. As mentioned in studies on decaying Stages of vortex decay in an impulsively stopped cylinder 885 A6-3 Taylor-Couette (TC) flow by Verschoof et al (2016) and Ostilla-Mónico et al (2017), the rate at which energy is dissipated during the sustained and decaying turbulent regimes is not known a priori. In a similar manner, the details of production and dissipation of energy associated with turbulent fluctuations are also poorly understood.…”

“…layers (Meroney & Bradshaw 1975) and the decay of anisotropic turbulence in wall-bounded flows (Verschoof et al 2016;Ostilla-Mónico et al 2017). The present study describes a relatively simple flow which encompasses laminar, transitional, turbulent and decaying regimes under the influence of concave walls.…”

Turbulence generation and decay in the Taylor–Couette system due to an abrupt stoppage

“…How this decay happens is still a subject of vast research due to non-consensus on its major aspects: (i) Do initial conditions influence the decay (George 1992;Biferale et al 2003;Thormann & Maneveau 2014;Sinhuber et al 2015)? (ii) Is the decay self-similar (Batchelor et al 1948a;George 1992;Eyink & Thomson 2000;Biferale et al 2003;Sinhuber et al 2015;Verschoof et al 2016;Antonia et al 2017;Ostilla-Mónico et al 2017)? (iii) Is the decay dependent on the Reynolds number (de Kármán & Howarth 1938;Saffman 1967;George 1992;Lohse 1994;McComb et al 2014;Sinhuber et al 2015)?…”