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We consider a Taylor-Dean-type flow of an electrically conducting liquid inan annulus between two infinitely long perfectly conducting cylinders subjectto a generally helical magnetic field. The cylinders are electrically connectedthrough a remote, perfectly conducting endcap, which allows a radial electriccurrent to pass through the liquid. The radial current interacting with theaxial component of magnetic field gives rise to the azimuthal electromagneticforce, which destabilizes the base flow by making its angular momentum decreaseradially outwards. This instability, which we refer to as thepseudo--magnetorotational instability (MRI), looks like an MRI although itsmechanism is basically centrifugal. In a helical magnetic field, the radialcurrent interacting with the azimuthal component of the field gives rise to anaxial electromagnetic force, which drives a longitudinal circulation. First,this circulation advects the Taylor vortices generated by the centrifugalinstability, which results in a traveling wave as in the helical MRI (HMRI).However, the direction of travel of this wave is opposite to that of the trueHMRI. Second, at sufficiently strong differential rotation, the longitudinalflow becomes hydrodynamically unstable itself. For electrically connectedcylinders in a helical magnetic field, hydrodynamic instability is possible atany sufficiently strong differential rotation. In this case, there is nohydrodynamic stability limit defined in the terms of the critical ratio ofrotation rates of inner and outer cylinders that would allow one to distinguisha hydrodynamic instability from the HMRI. These effects can criticallyinterfere with experimental as well as numerical determination of MRI.

Pseudo--magnetorotational instability in a Taylor-Dean flow between electrically connected cylinders