Self-similar decay of high Reynolds number Taylor-Couette turbulence

TL;DR

This study investigates the decay of high-Reynolds number Taylor-Couette turbulence after stopping the inner cylinder, revealing self-similar velocity profiles and a faster decay rate influenced by wall friction, with implications for understanding wall-bounded turbulence decay.

Contribution

It provides the first detailed experimental analysis of turbulence decay in Taylor-Couette flow at high Reynolds numbers, highlighting self-similarity and wall effects.

Findings

Velocity profile becomes self-similar during decay.

Decay rate is faster than in homogeneous isotropic turbulence.

Wall friction significantly influences the decay process.

Abstract

We study the decay of high-Reynolds number Taylor-Couette turbulence, i.e. the turbulent flow between two coaxial rotating cylinders. To do so, the rotation of the inner cylinder (Re$_i=2 \times 10^6$, the outer cylinder is at rest) is stopped within 12 s, thus fully removing the energy input to the system. Using a combination of laser Doppler anemometry and particle image velocimetry measurements, six decay decades of the kinetic energy could be captured. First, in the absence of cylinder rotation, the flow-velocity during the decay does not develop any height dependence in contrast to the well-known Taylor vortex state. Second, the radial profile of the azimuthal velocity is found to be self-similar. Nonetheless, the decay of this wall-bounded inhomogeneous turbulent flow does not follow a strict power law as for decaying turbulent homogeneous isotropic flows, but it is faster, due to the strong viscous drag applied by the bounding walls. We theoretically describe the decay in a quantitative way by taking the effects of additional friction at the walls into account.