Dynamos with weakly convecting outer layers: implications for core-mantle boundary interaction

Convection in the Earth's core is driven much harder at the bottom than the top. This is partly because the adiabatic gradient steepens towards the top, partly because the spherical geometry means the area involved increases towards the top, and partly because compositional convection is driven by light material released at the lower boundary and remixed uniformly throughout the outer core, providing a volumetric sink of buoyancy. We have therefore investigated dynamo action of thermal convection in a Boussinesq fluid contained within a rotating spherical shell driven by a combination of bottom and internal heating or cooling. We first apply a homogeneous temperature on the outer boundary in order to explore the effects of heat sinks on dynamo action; we then impose an inhomogeneous temperature proportional to a single spherical harmonic Y2² in order to explore core-mantle interactions. With homogeneous boundary conditions and moderate Rayleigh numbers, a heat sink reduces the generated magnetic field appreciably; the magnetic Reynolds number remains high because the dominant toroidal component of flow is not reduced significantly. The dipolar structure of the field becomes more pronounced as found by other authors. Increasing the Rayleigh number yields a regime in which convection inside the tangent cylinder is strongly affected by the magnetic field. With inhomogeneous boundary conditions, a heat sink promotes boundary effects and locking of the magnetic field to boundary anomalies. We show that boundary locking is inhibited by advection of heat in the outer regions. With uniform heating, the boundary effects are only significant at low Rayleigh numbers, when dynamo action is only possible for artificially low magnetic diffusivity. With heat sinks, the boundary effects remain significant at higher Rayleigh numbers provided the convection remains weak or the fluid is stably stratified at the top. Dynamo action is driven by vigorous convection at depth while boundary thermal anomalies dominate in the upper regions. This is a likely regime for the Earth's core

Rapidly rotating plane layer convection with zonal flow

The onset of convection in a rapidly rotating layer in which a thermal wind is present is studied. Diffusive effects are included. The main motivation is from convection in planetary interiors, where thermal winds are expected due to temperature variations on the core-mantle boundary. The system admits both convective instability and baroclinic instability. We find a smooth transition between the two types of modes, and investigate where the transition region between the two types of instability occurs in parameter space. The thermal wind helps to destabilise the convective modes. Baroclinic instability can occur when the applied vertical temperature gradient is stable, and the critical Rayleigh number is then negative. Long wavelength modes are the first to become unstable. Asymptotic analysis is possible for the transition region and also for long wavelength instabilities, and the results agree well with our numerical solutions. We also investigate how the instabilities in this system relate to the classical baroclinic instability in the Eady problem. We conclude by noting that baroclinic instabilities in the Earth's core arising from heterogeneity in the lower mantle could possibly drive a dynamo even if the Earth's core were stably stratified and so not convecting.Comment: 20 pages, 7 figure

Kinematic dynamo action in a sphere: Effects of periodic time-dependent flows on solutions with axial dipole symmetry

Choosing a simple class of flows, with characteristics that may be present in the Earth's core, we study the ability to generate a magnetic field when the flow is permitted to oscillate periodically in time. The flow characteristics are parameterised by D, representing a differential rotation, M, a meridional circulation, and C, a component characterising convective rolls. Dynamo action is sensitive to these flow parameters and fails spectacularly for much of the parameter space where magnetic flux is concentrated into small regions. Oscillations of the flow are introduced by varying the flow parameters in time, defining a closed orbit in the space (D,M). Time-dependence appears to smooth out flux concentrations, often enhancing dynamo action. Dynamo action can be impaired, however, when flux concentrations of opposite signs occur close together as smoothing destroys the flux by cancellation. It is possible to produce geomagnetic-type reversals by making the orbit stray into a region where the steady flows generate oscillatory fields. In this case, however, dynamo action was not found to be enhanced by the time-dependence. A novel approach is taken to solving the time-dependent eigenvalue problem, where by combining Floquet theory with a matrix-free Krylov-subspace method we avoid large memory requirements for storing the matrix required by the standard approach.Comment: 22 pages, 12 figures. Geophys. Astrophys. Fluid Dynam., as accepted (2004