Resistive instability in the absence of critical levels

Details Resistive instability in the absence of critical levels Resistive instability in the absence of critical levels

Mar 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994gapfd..74..181f&link_type=abstract

Geophysical and Astrophysical Fluid Dynamics (ISSN 0309-1929), vol. 74, no. 1-4, p. 181-206

Physics

Fluid Dynamics

7

Geomagnetism, Magnetic Effects, Magnetic Permeability, Mathematical Models, Earth (Planet), Magnetic Diffusion

Scientific paper

Fearn and Weiglhofer (1992) identified and investigated an instability of the magnetic field B(sub 0) = B(sub 0)(s)1(sub phi) that is resistive in character but which is unstable when the condition usually associated with resistive instability k x B(sub 0) = 0 is not satisfied. The instability is not present when the (cylindrical) container boundaries are perfect conductors. Fearn and Weiglhofer tried to determine what other conditions, particularly on the choice of B(sub 0), are required for instability, but they could find no simple condition. Here we adopt a simpler plane-layer model in which the z-direction is normal to the plane. B(sub 0) = B(sub 0)(z)1(sub y), and the rotation vector Omega lies in the x-z plane, making an angle theta with the z-direction. The case theta = pi /2, with Omega parallel to the boundaries, corresponds most closely to Fearn and Weiglhofer's (1992) cylindrical model, but is a singular case in the magnetostrophic approximation. We show that the instability exists in the plane-layer model, for all values of theta. The simpler geometry permits some analytical progress. This establishes some necessary conditions for instability.

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