ON THE EFFECT OF BOUNDARY-CONDITIONS ON RESISTIVE INSTABILITIES IN RAPIDLY ROTATING FLUIDS

The effect of boundary conditions on resistive instability is examined in a plane layer that rotates rapidly about an axis at an angle 0 to vertical. A uniform, incompressible, inviscid fluid of density rho, electrical conductivity sigma, magnetic permeability mu, is confined between two walls z = 0, d. The prevailing magnetic field, B-0(z), studied in this paper is a horizontal, sheared, force-free field of constant strength B. The angular velocity Omega of the layer is large: Omega much greater than V-A/d, where V-a = B/root mu rho is the Alfven velocity. The (nondimensional) Elsasser number, Lambda = sigma B-2/2 Omega rho, measures sigma. Kuang and Roberts (1990) showed that when the walls z = 0, d are perfect electrical conductors, B-0 is unstable only if at least one ''critical level'' exists within the layer, i.e. a value of z at which B-0 is parallel to the perturbation rolls. The energy of the instability is provided dominantly by the field line reconnection processes in the critical layers around the critical levels (''tearing modes''). Fearn and Kuang (1994) found that, when there is no critical level, instability may occur in a rapidly rotating layer if at least one boundary wall is a perfect electrical insulator. The energy of the instability is provided dominantly by the diffusive processes in the resistive layers at insulating boundaries (''boundary mode''). In this paper we studied the effect of insulating boundaries on tearing modes and the effect of critical levels on boundary modes. We found that resistive layers at insulating boundaries influence to leading order the tearing modes. The diffusive processes in these boundary layers enhance the tearing instability. Boundary modes depend not only on insulating boundaries, but also on the derivative of the field B-0 at the boundaries. To leading order, critical levels behave like perfectly conducting walls to the boundary modes and the perturbations cannot penetrate through the critical levels, resulting in suppressing the instability. In certain parameter space boundary modes and tearing modes may coexist. In this situation the most unstable mode is always a boundary mode, In other word, boundary modes have a smaller critical Elsasser number Lambda(c) and a larger growth rate s than tearing modes.