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

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.

24 pages, 12 figures, accepted by PRE, revision according to referees

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• Absolute versus convective helical magnetorotational instability in a Taylor-Couette flow
• The role of boundaries in the MagnetoRotational Instability
• Inviscid helical magnetorotational instability in cylindrical Taylor-Couette flow
• Numerical Study of the Magnetorotational Instability in Princeton MRI Experiment
• Noise-Sustained Convective Instability in a Magnetized Taylor-Couette Flow
• On the saturation of non-axisymmetric instabilites of magnetized spherical Couette flow
• Pseudo--magnetorotational instability in a Taylor-Dean flow between electrically connected cylinders