Instabilities of an annulus flow between rotating cylinders in a helical magnetic field

The stabilities of an annulus flow between the rotating inner and outer cylinders with an external helical magnetic field are studied by using the quasistatic approximation. It is shown numerically that for the spiral base flow with a zero axial pressure gradient, the helical magnetic field yields a helical traveling wave at a critical Reynolds number. This wave mode is revealed to be the most unstable mode by linear stability analysis. At higher Reynolds numbers, the first wave mode is superposed by a second antisymmetric helical wave mode, which travels with a higher phase velocity than the first mode. When the Reynolds number is increased further, the flow becomes turbulent, but the key features of the flow structure are still dominated by the first and the second wave modes. Furthermore, when a finite axial pressure gradient is applied to guarantee a zero axial flow rate, the annulus flow is found to be more unstable than the case with zero axial pressure gradient.