Core, Magnetic Instabilities

Introduction

The technique of considering the stability of some basic state to a perturbation is an essential one in fluid dynamics since it can give significant insight into fundamental mechanisms (see for example Chandrasekhar, 1961; Drazin and Reid, 1981). The classic example is that of Rayleigh‐Bénard convection, in which fluid is contained between two horizontal flat plates. The lower plate is heated and the upper cooled. Since colder fluid is heavier than warmer fluid, the basic state consists of fluid at rest, with density ρ increasing with height z. This configuration is potentially unstable (heavy fluid lying over light fluid). However, convection (overturning of the fluid) will only take place if the density gradient is sufficiently large; the buoyancy force arising from the variation in density must be large enough to overcome the viscous drag of the fluid. An alternative way of thinking about this is to consider a small parcel of fluid. Consider a perturbation of the basic...