The stability of compositional plumes in a rotating magnetic fluid

The solidification of the heavy iron component of the fluid alloy occupying the outer core of the earth which takes place at the Inner-Outer core interface leads to the formation of a mushy zone. The light fluid component in the mushy zone escapes upwards in the form of compositional plumes. Motivated by the idea that the convective motions resulting from such plume activity may contribute to the regeneration of the geodynamo, we study a simple model of an isolated plume. The stability of a compositional plume of circular cross-section rising in an infinite fluid, which is rotating uniformly in the presence of a magnetic field, is investigated. The fluid is assumed to have finite viscosity, thermal diffusivity and magnetic diffusivity but vanishing material diffusion. The stability is governed by a number of dimensionless parameters. These are the Taylor number, Ta, (which measures the strength of the rotation rate), the Chandrasekhar number, Q, (which measures the strength of the magnetic field), the radius of the plume, S₀, and the Prandtl and magnetic Prandtl numbers. The analysis is restricted to the case of small Reynolds numbers, R. It is found that to leading order the stability is independent of the Prandtl numbers and that the plume is unstable for all values of the parameters Ta, Q and s₀. The maximum growth rate of the instability and the zonal and vertical phase speeds, which are all proportional to R, have been identified for the whole space (s₀, Ta, Q). The application of the results to the theory of turbulence in the earth's core indicates that the wavelength of the instabilities is comparable with that of the small scale motions in the core. The motions posses reflectional asymmetry (non-zero helicity) and α-effect and it is then possible that they contribute to dynamo action. However, the time scales of propagation and growth are too small compared with the time scale of the geodynamo or even the secular variation.