Logarithmic boundary layers in highly turbulent Taylor-Couette flow

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 Kármán log law $u^{+}=\frac{1}{\kappa }\ln y^{+}+B$. The von Kármán 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].