Helical-wave instabilities of an annulus flow in a helical magnetic field

Abstract eng:
The stabilities of an annulus flow with an external helical magnetic field is studied theoretically and numerically by using the quasi-static approximation. For the case with zero axial pressure gradient, it is shown numerically that when the Reynolds number is larger than a threshold value, the helical magnetic field will yield a right-handed traveling-wave instability. At higher Reynolds numbers, the first wave mode is superposed by a secondary anti-symmetric helical wave mode, which travels in the opposite direction of the first one. Linear stability analysis is carried out, and the critical parameters of the most unstable mode are consistent quantitatively with the numerical observations. 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.

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