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