Periodically driven Taylor-Couette turbulence

TL;DR

This study investigates how turbulent Taylor-Couette flow responds to periodic driving of the inner cylinder, revealing that the flow's phase delay and amplitude response depend on the modulation period and are similar to laminar cases, with turbulence homogenizing the response.

Contribution

First experimental analysis of turbulent Taylor-Couette flow response to periodic modulation, demonstrating flow homogenization and comparing turbulent and laminar response scalings.

Findings

Flow follows modulation at large periods (quasi-stationary behavior)

Flow cannot follow at small periods, showing phase delay and reduced amplitude response

Turbulent mixing leads to radius-independent flow response

Abstract

We study periodically driven Taylor-Couette turbulence, i.e. the flow confined between two concentric, independently rotating cylinders. Here, the inner cylinder is driven sinusoidally while the outer cylinder is kept at rest (time-averaged Reynolds number is $Re_i = 5 \times 10^5$). Using particle image velocimetry (PIV), we measure the velocity over a wide range of modulation periods, corresponding to a change in Womersley number in the range $15 \leq Wo \leq 114$. To understand how the flow responds to a given modulation, we calculate the phase delay and amplitude response of the azimuthal velocity. In agreement with earlier theoretical and numerical work, we find that for large modulation periods the system follows the given modulation of the driving, i.e. the system behaves quasi-stationary. For smaller modulation periods, the flow cannot follow the modulation, and the flow velocity responds with a phase delay and a smaller amplitude response to the given modulation. If we compare our results with numerical and theoretical results for the laminar case, we find that the scalings of the phase delay and the amplitude response are similar. However, the local response in the bulk of the flow is independent of the distance to the modulated boundary. Apparently, the turbulent mixing is strong enough to prevent the flow from having radius-dependent responses to the given modulation.