Statistics of turbulence in the energy-containing range of Taylor-Couette compared to canonical wall-bounded flows

TL;DR

This study demonstrates the universality of large-scale turbulence statistics across different flow types, including Taylor-Couette flow, and explains the efficacy of the extended self-similarity framework through an attached-eddy hypothesis.

Contribution

It extends the universality of turbulence structure functions to Taylor-Couette flow and provides a theoretical explanation based on an attached-eddy model for the observed phenomena.

Findings

Large-scale statistics are universal across flow types.

The spanwise velocity structure function exhibits universal behavior.

Additive constants are flow-independent in high-Reynolds number flows.

Abstract

Considering structure functions of the streamwise velocity component in a framework akin to the extended self-similarity hypothesis (ESS), de Silva \textit{et al.} (\textit{J. Fluid Mech.}, vol. 823,2017, pp. 498-510) observed that remarkably the \textit{large-scale} (energy-containing range) statistics in canonical wall bounded flows exhibit universal behaviour. In the present study, we extend this universality, which was seen to encompass also flows at moderate Reynolds number, to Taylor-Couette flow. In doing so, we find that also the transversal structure function of the spanwise velocity component exhibits the same universal behaviour across all flow types considered. We further demonstrate that these observations are consistent with predictions developed based on an attached-eddy hypothesis. These considerations also yield a possible explanation for the efficacy of the ESS framework by showing that it relaxes the self-similarity assumption for the attached eddy contributions. By taking the effect of streamwise alignment into account, the attached eddy model predicts different behaviour for structure functions in the streamwise and in the spanwise directions and that this effect cancels in the ESS-framework --- both consistent with the data. Moreover, it is demonstrated here that also the additive constants, which were previously believed to be flow dependent, are indeed universal at least in turbulent boundary layers and pipe flow where high-Reynolds number data are currently available.