Log law of the wall revisited in Taylor-Couette flows at intermediate Reynolds numbers.

Abstract

We provide Reynolds averaged azimuthal velocity profiles, measured in a Taylor-Couette system in turbulent flow, at medium Reynolds (7800 < Re < 18000) number with particle image velocimetry technique. We find that in the wall regions, close to the inner and outer cylinders, the azimuthal velocity profile reveals a significant deviation from classical logarithmic law. In order to propose a new law of the wall, the profile of turbulent mixing length was estimated from data processing; it was shown to behave nonlinearly with the radial wall distance. Based on this turbulent mixing length expression, a law of the wall was proposed for the Reynolds averaged azimuthal velocity, derived from momentum balance and validated by comparison to different data. In addition, the profile of viscous dissipation rate was investigated and compared to the global power needed to maintain the inner cylinder in rotation.