# Logarithmic boundary layers in highly turbulent Taylor-Couette flow

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.

Author: Sander G. Huisman; Sven Scharnowski; Christian Cierpka; Christian J. Kahler; Detlef Lohse; Chao Sun

Source: https://archive.org/