Nonlinear magnetohydrodynamic convective flows in the Earth's fluid core

Abstract

Convective motions in the Earth's fluid core are strongly affected by a combination of the Coriolis and magnetic forces. For a long-timescale phenomenon such as the geomagnetic reversals, the Earth's magnetic fields are generated by dynamo processes. For a shorter-timescale phenomenon such as the secular variation, dynamics of the Earth's fluid core can be understood by examining convective motions in the presence of an imposed magnetic field without involving the complex dynamo processes. The present paper investigates both linear and nonlinear convection in a rapidly rotating fluid spherical shell like the Earth's fluid core in the presence of a strong axisymmetric toroidal magnetic field with dipole symmetry. In our linear calculation, it is demonstrated that magnetoconvection is nearly independent of the Ekman number E when E≤10 −3. In our nonlinear calculation, which includes all nonlinear effects, two different types of magnetoconvection solutions are found. The primary nonlinear solution bifurcating from the onset of magnetoconvection corresponds to steadily travelling magnetoconvection waves with equatorial and azimuthal symmetries. The secondary solution after the instability of the steadily travelling waves is characterised by vacillating magnetoconvective motions which breaks both the temporal and azimuthal symmetries of the primary solution simultaneously. Implication of nonlinear solutions for the Earth's dynamo is also discussed.