A Sufficient Condition for Instability in a Sheared Incompressible Magnetofluid |
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Authors: | Cally PS |
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Institution: | (1) Department of Mathematics and Statistics, Monash University, Clayton, Victoria, 3800, Australia;(2) High Altitude Observatory, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO , 80307, U.S.A. |
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Abstract: | It is shown that a sufficient condition for the stability of an incompressible sheared gravitationally stratified ideal magnetofluid with flow-aligned horizontal magnetic field is that there exists a Galilean frame in which the flow is nowhere super-Alfvénic (similarly, stability is assured in a compressible shear flow without gravity if there exists a frame in which the flow nowhere exceeds the cusp speed). Complex eigenvalue bounds are presented for unstable flows. The stability condition is applied to the solar tachocline; it suggests that any shear instabilities associated with radial gradients in flow speed should be stabilized by fields of above about 7 kG. |
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