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In this paper we present axisymmetric nonlinear simulations of magnetizedEkman and Stewartson layers in a magnetized Taylor-Couette flow with acentrifugally stable angular-momemtum profile and with a magnetic Reynoldsnumber below the threshold of magnetorotational instability. The magnetic fieldis found to inhibit the Ekman suction. The width of the Ekman layer is reducedwith increased magnetic field normal to the end plate. A uniformly-rotatingregion forms near the outer cylinder. A strong magnetic field leads to a steadyStewartson layer emanating from the junction between differentially rotatingrings at the endcaps. The Stewartson layer becomes thinner with larger Reynoldsnumber and penetrates deeper into the bulk flow with stronger magnetic fieldand larger Reynolds number. However, at Reynolds number larger than a criticalvalue $\sim 600$, axisymmetric, and perhaps also nonaxisymmetric, instabilitiesoccur and result in a less prominent Stewartson layer that extends less farfrom the boundary.

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