The Ekman-Hartmann layer in MHD Taylor-Couette flow

Abstract

We study magnetic effects induced by rigidly rotating plates enclosing a cylindrical MHD Taylor-Couette flow at the finite aspect ratio $H/D=10$. The fluid confined between the cylinders is assumed to be liquid metal characterized by small magnetic Prandtl number, the cylinders are perfectly conducting, an axial magnetic field is imposed $\Ha \approx 10$, the rotation rates correspond to $\Rey$ of order $10^2-10^3$. We show that the end-plates introduce, besides the well known Ekman circulation, similar magnetic effects which arise for infinite, rotating plates, horizontally unbounded by any walls. In particular there exists the Hartmann current which penetrates the fluid, turns into the radial direction and together with the applied magnetic field gives rise to a force. Consequently the flow can be compared with a Taylor-Dean flow driven by an azimuthal pressure gradient. We analyze stability of such flows and show that the currents induced by the plates can give rise to instability for the considered parameters. When designing an MHD Taylor-Couette experiment, a special care must be taken concerning the vertical magnetic boundaries so they do not significantly alter the rotational profile.

9 pages, 6 figures; accepted to PRE

References in corpus (11)

• Hydrodynamic turbulence cannot transport angular momentum effectively in astrophysical disks
• Magnetorotational Instability in a Rotating Liquid Metal Annulus
• Experimental evidence for magnetorotational instability in a helical magnetic field
• Experiments on the magnetorotational instability in helical magnetic fields
• The linear MHD Taylor-Couette instability for liquid sodium
• Numerical and Experimental Investigation of Circulation in Short Cylinders
• The traveling wave MRI in cylindrical Taylor-Couette flow: comparing wavelengths and speeds in theory and experiment
• The stability of MHD Taylor-Couette flow with current-free spiral magnetic fields between conducting cylinders
• Spherical Couette flow in a dipolar magnetic field
• Reduction of boundary effects in spiral MRI experiment PROMISE
• Nonlinear simulations of magnetic Taylor-Couette flow with current-free helical magnetic fields

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• Magnetized Ekman Layer and Stewartson Layer in a Magnetized Taylor-Couette Flow
• Weakly magnetized, Hall dominated plasma Couette flow
• Pseudo--magnetorotational instability in a Taylor-Dean flow between electrically connected cylinders
• Liquid metal experiments on the helical magnetorotational instability