Logarithmic boundary layers in highly turbulent Taylor-Couette flow

TL;DR

This study measures boundary layer properties in highly turbulent Taylor-Couette flow, revealing a von Kármán log law with a Ta-dependent constant and universal velocity variance profiles, advancing understanding of turbulence in rotational flows.

Contribution

It provides the first detailed measurements of boundary layer profiles in high Ta Taylor-Couette flow, showing a Ta-dependent von Kármán constant and universal velocity variance features.

Findings

The velocity profiles follow a von Kármán log law with a Ta-dependent constant.

The variance profiles peak around y+ ≈ 12 and collapse when scaled with driving velocity.

The von Kármán constant approaches approximately 0.40 at high Ta.

Abstract

We provide direct measurements of the boundary layer properties in highly turbulent Taylor-Couette flow up to $\text{Ta}=6.2 \times 10^{12}$ using high-resolution particle image velocimetry (PIV). We find that the mean azimuthal velocity profile at the inner and outer cylinder can be fitted by the von K\'arm\'an log law $u^+ = \frac 1\kappa \ln y^+ +B$. The von K\'arm\'an constant $\kappa$ is found to depend on the driving strength $\text{Ta}$ and for large $\text{Ta}$ asymptotically approaches $\kappa \approx 0.40$. The variance profiles of the local azimuthal velocity have a universal peak around $y^+ \approx 12$ and collapse when rescaled with the driving velocity (and not with the friction velocity), displaying a log-dependence of $y^+$ as also found for channel and pipe flows [1,2].