Ring vortices generated electromagnetically

Abstract

If an electric current of uniform densityj0is passed axially through a stationary fluid between concentric cylinders of radiir1andr2(>r1), the fluid is stable to axisymmetric disturbances only if the damping provided by viscosity and electrical resistivity is sufficiently large. It is shown herein that the fluid may also be stabilized by passing a line currentJalong the axis, sufficient conditions for stability being$J \le -\pi j _0(r^2_2 - r^2_1)$, or$\ge J\; \pi j _0r^2_1$The values ofJneeded to stabilize the fluid when the fluid has non-zero viscosity and finite conductivity are calculated for the caser2-r1[Lt ]r1. In this latter case, the ring vortices which exist under conditions of neutral stability are exactly the same as those for flow between rotating cylinders ifJandj0have the same sign, and ifJis not very small compared with πj0r2.