Magnetized Ekman Layer and Stewartson Layer in a Magnetized Taylor-Couette Flow

TL;DR

This study uses nonlinear simulations to explore how magnetic fields influence Ekman and Stewartson layers in magnetized Taylor-Couette flow, revealing magnetic suppression effects and flow instabilities at high Reynolds numbers.

Contribution

It provides new insights into the behavior of magnetized Ekman and Stewartson layers, including magnetic suppression of Ekman suction and the onset of instabilities at high Reynolds numbers.

Findings

Magnetic field inhibits Ekman suction.

Stewartson layer becomes thinner with stronger magnetic field.

Instabilities occur at Reynolds number > 600, reducing Stewartson layer prominence.

Abstract

In this paper we present axisymmetric nonlinear simulations of magnetized Ekman and Stewartson layers in a magnetized Taylor-Couette flow with a centrifugally stable angular-momemtum profile and with a magnetic Reynolds number below the threshold of magnetorotational instability. The magnetic field is found to inhibit the Ekman suction. The width of the Ekman layer is reduced with increased magnetic field normal to the end plate. A uniformly-rotating region forms near the outer cylinder. A strong magnetic field leads to a steady Stewartson layer emanating from the junction between differentially rotating rings at the endcaps. The Stewartson layer becomes thinner with larger Reynolds number and penetrates deeper into the bulk flow with stronger magnetic field and larger Reynolds number. However, at Reynolds number larger than a critical value $\sim 600$, axisymmetric, and perhaps also nonaxisymmetric, instabilities occur and result in a less prominent Stewartson layer that extends less far from the boundary.