Magnetic stability under the magnetostrophic approximation

Details Magnetic stability under the magnetostrophic approximation Magnetic stability under the magnetostrophic approximation

Feb 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999pepi..111..123m&link_type=abstract

Physics of the Earth and Planetary Interiors, Volume 111, Issue 1-2, p. 123-139.

Physics

2

Scientific paper

We determine the stability of s- and z-dependent basic fields under the magnetostrophic approximation in a cylindrical geometry. The geostrophic flow VG is the dominant nonlinearity in the nonlinear regime. This work assesses the impact of the geostrophic flow at critical linear stability Λ=Λc by imposing VG as a differential rotation. Here, the Elsasser number Λ is the appropriate nondimensional measure of imposed field strength. Fearn et al. [Fearn, D.R., Lamb, C.J., McLean, D.R., Ogden, R.R., 1997. The influence of differential rotation on magnetic instability and nonlinear magnetic instability in the magnetostrophic limit. Geophys. Astrophys. Fluid Dyn. 86, 173-200] showed that for simple s-dependent basic fields, certain imposed differential rotations could lower Λc. McLean and Fearn [McLean, D.R., Fearn, D.R., 1999. The geostrophic nonlinearity and its effect on magnetic instability. Geophys. Astrophys. Fluid Dyn., In Press.] then showed that the geostrophic flow-induced subcritical behaviour in the most unstable mode for various combinations of basic fields and aspect ratios. Here, both linear and nonlinear results are new; previous analyses only considered radially (s-)dependent basic fields. We will derive a consistency condition necessary for the existence of solutions before investigating whether subcriticality exists under a dipolar basic field configuration.

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