Hydromagnetic Stability of Dissipative Vortex Flow

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Abstract
An analysis which considers the stability of dissipative, conducting, incompressible, pure vortex flow (vortex flow with 1/r‐transverse velocity profile) in an axially applied magnetic field is presented. The vortex is assumed to be confined within two nonpermeable, rotating, perfectly conducting, cylindrical walls. The results of the analysis confirm the exact criteria reported previously for the limiting cases of inviscid flow with finite or infinite electrical conductivity. The paradox between the inviscid hydromagnetic results and Rayleigh's criterion for inviscid, incompressible, pure vortex flow without magnetic interaction is resolved. The analysis presented in this paper is quite general and does not require the usual assumptions pertaining to the magnitudes of the electrical conductivity and viscosity, or the gap‐width between the cylindrical walls.

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