The stability of inviscid incompressible flows between concentric cylinders is considered here. For pure axial flows with velocity (0,0, W(r)) it is proved that the growth rate tends to zero as the wave length tends to zero and also that the wave velocity of neutral modes is bounded. For swirling flows with velocity (0, V(r), W(r)) and magnetic field (0, H_θ(r), 0) an estimate for the growth rate of unstable modes and a semi elliptical instability region are obtained. Some numerical results are also presented for a family of velocity and magnetic field profiles.
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