Abstract
Drazin [1] studied the hydromagnetic stability characteristics of a perturbed vortex sheet. Omission of reckoning the total effective pressure in the hydromagnetic case as the sum of the hydrodynamic pressure and the magnetic pressure (or what is the same, neglect of the contribution of the magnetic field to the normal force at the interface) led Drazin to the erroneous result that the presence of a magnetic field did not affect the instability of the perturbed vortex sheet. This paper rectifies this error and shows the stabilising effect of the magnetic field on the perturbed vortex sheet in consistency with the conclusions reached earlier by Michael [4]. It is further shown that the hydromagnetic stability characteristics of a perturbed vortex sheet correspond to those of a smoothly-varying shear-layer flow for long-wave disturbances — a result that has been only conjectured in the hydromagnetic case in Drazin's analysis without proof (though an analogous result is well established for the hydrodynamic case).
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