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arXiv · 1602.02554

Sharp nonlinear stability criterion of viscous non-resistive MHD internal waves in 3D

Yanjin Wang
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Abstract

We consider the dynamics of two layers of incompressible electrically conducting fluid interacting with the magnetic field, which are confined within a 3D horizontally infinite slab and separated by a free internal interface. We assume that the upper fluid is heavier than the lower fluid so that the fluids are susceptible to the Rayleigh-Taylor instability. Yet, we show that the viscous and non-resistive problem around the equilibrium is nonlinearly stable provided that the strength of the vertical component of the steady magnetic field, $|\bar B_3|$, is greater than the critical value, $\mathcal{M}_c$, which we identify explicitly. We also prove that the problem is nonlinearly unstable if $|\bar B_3|<\mathcal{M}_c$. Our results indicate that the non-horizontal magnetic field has strong stabilizing effect on the Rayleigh-Taylor instability but the horizontal one does not have in 3D.

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Yanjin Wang. 2016-02-08. Sharp nonlinear stability criterion of viscous non-resistive MHD internal waves in 3D. https://arxiv.org/abs/1602.02554

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