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 $Re=3.5\times 10^4$. The effect of wall-friction is analysed 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, the energy of the azimuthal velocity behaves non-monotonically: 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.

References in corpus (6)

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• Universality of anisotropic fluctuations from numerical simulations of turbulent flows
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Cited by in corpus (4)

• Periodically driven Taylor-Couette turbulence
• Dynamics and evolution of Turbulent Taylor rolls
• Controlling secondary flows in Taylor-Couette flow using stress-free boundary conditions
• Longitudinal vortices in unsteady Taylor-Couette flow: solution to a 60-year-old mystery