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

## TL;DR

This study numerically investigates the decay process of Taylor-Couette turbulence after stopping the forcing, revealing distinct life stages influenced by large-scale structures, energy redistribution, transient growth, and wall-friction effects.

## Contribution

It identifies and characterizes the sequential life stages of turbulence decay in Taylor-Couette flow, including a novel modeling of the viscous decay stage with a heat equation.

## Key findings

- Decay dominated by large-scale rolls initially
- Non-monotonic energy behavior during energy redistribution
- Viscous decay modeled by a one-dimensional heat equation

## 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.