Azimuthal velocity profiles in Rayleigh-stable Taylor-Couette flow and implied axial angular momentum transport

Abstract

We present azimuthal velocity profiles measured in a Taylor-Couette apparatus, which has been used as a model of stellar and planetary accretion disks. The apparatus has a cylinder radius ratio of $\eta = 0.716$, an aspect-ratio of $\Gamma = 11.74$, and the plates closing the cylinders in the axial direction are attached to the outer cylinder. We investigate angular momentum transport and Ekman pumping in the Rayleigh-stable regime. The regime is linearly stable and is characterized by radially increasing specific angular momentum. We present several Rayleigh-stable profiles for shear Reynolds numbers $Re_S \sim O(10^5) \,$, both for $\Omega_i > \Omega_o > 0$ (quasi-Keplerian regime) and $\Omega_o > \Omega_i > 0$ (sub-rotating regime) where $\Omega_{i,o}$ is the inner/outer cylinder rotation rate. None of the velocity profiles matches the non-vortical laminar Taylor-Couette profile. The deviation from that profile increased as solid-body rotation is approached at fixed $Re_S$. Flow super-rotation, an angular velocity greater than that of both cylinders, is observed in the sub-rotating regime. The velocity profiles give lower bounds for the torques required to rotate the inner cylinder that were larger than the torques for the case of laminar Taylor-Couette flow. The quasi-Keplerian profiles are composed of a well mixed inner region, having approximately constant angular momentum, connected to an outer region in solid-body rotation with the outer cylinder and attached axial boundaries. These regions suggest that the angular momentum is transported axially to the axial boundaries. Therefore, Taylor-Couette flow with closing plates attached to the outer cylinder is an imperfect model for accretion disk flows, especially with regard to their stability.