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 η=0.716, an aspect ratio of Γ=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. This regime is linearly stable and is characterized by radially increasing specific angular momentum. We present several Rayleigh-stable profiles for shear Reynolds numbers ReS ∼ O(105), for both Ωi>Ωo>0 (quasi-Keplerian regime) and Ωo>Ωi>0 (sub-rotating regime), where Ωi,o is the inner/outer cylinder rotation rate. None of the velocity profiles match the non-vortical laminar Taylor-Couette profile. The deviation from that profile increases as solid-body rotation is approached at fixed ReS. Flow super-rotation, an angular velocity greater than those 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 are 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.