Resistive instabilities in rapidly rotating fluids: Linear theory of the tearing mode

Publisher Website
Google Scholar
Abstract
The linear stability of the sheet pinch is examined for a rapidly rotating fluid. The sheet pinch is a horizontal layer of uniform, incompressible, inviscid fluid of density p, electrical conductivity [sgrave], magnetic permeability μ, confined between two perfectly conducting planes z=0, d, where z is height. The prevailing magnetic field, B 0(z), is horizontal; at each height it is unidirectional, but that direction turns continuously (in one sense only) as z increases; the system is in magnetostatic equilibrium. The layer rotates about the vertical with an angular velocity, Ω, that is large: Ω>> VA /d, where VA = B 0/√(μp) is the Alfvén velocity and μ is the magnetic permeability. The dimensionless measure of [sgrave] is the Elsasser number A = [sgrave]B 0 2/2Ωp.