THE INFLUENCE OF DIFFERENTIAL ROTATION ON MAGNETIC INSTABILITY, AND NONLINEAR MAGNETIC INSTABILITY IN THE MAGNETOSTROPHIC LIMIT

In rapidly rotating systems, a (and, in certain circumstances, the) mo st important nonlinear effect is the geostrophic how V-G(s)1(phi) asso ciated with Taylor's (1963) constraint. Its role has been extensively studied in the context of alpha(2) - and alpha omega-dynamos, and, to a lesser extent in magnetoconvection problems. Here, we investigate it s role in the magnetic stability problem, using a cylindrical geometry . First, we investigate the influence of a representative variety of a rbitrarily prescribed flows V(s)1(phi), with V(s) = s Omega(s), and fi nd that there can be a significant reduction in the critical held stre ngth for hows having a negative outward gradient (d Omega/ds < 0). We then choose a typical such flow (V = -R-m s(2) and focus attention on the interaction between the magnetic instability present (or not) when the flow is absent (R-m = 0) and the instability driven by differenti al rotation when the flow is stronger. It is found that instability (e ven when driven only by the differential rotation) exists only above a minimum field strength. Finally, having gained an understanding of th e roles that differential rotation can play, we investigate the nonlin ear magnetic stability problem, where the nonlinear effect is the geos trophic how. We find cases where the geostrophic flow has the property of destabilising the system. This can happen for the most unstable mo de, so the nonlinear effect of the geostrophic flow can be subcritical . Corresponding nonlinear calculations at finite Ekman number E (Hutch eson and Fearn, 1995a, b) did not find subcriticality so there must be some value of E < 10(-4) below which the geostrophic how dominates th e other nonlinear effects and subcriticality becomes possible. What th at value is may influence how low E must be taken in full geodynamo si mulations to correctly qualitatively describe the dynamics of the core .