Nonlinear magnetohydrodynamic convective flows in the Earth's fluid core

Convective motions in the Earth's fluid core are strongly affected by a com bination of the Coriolis and magnetic forces. For a long-timescale phenomen on such as the geomagnetic reversals, the Earth's magnetic fields are gener ated by dynamo processes. For a shorter-timescale phenomenon such as the se cular variation, dynamics of the Earth's fluid core can be understood by ex amining convective motions in the presence of an imposed magnetic field wit hout 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, i t is demonstrated that magnetoconvection is nearly independent of the Ekman number E when E less than or equal to 10(-3). In our nonlinear calculation , which includes all nonlinear effects, two different types of magnetoconve ction solutions are found. The primary nonlinear solution bifurcating from the onset of magnetoconvection corresponds to steadily travelling magnetoco nvection waves with equatorial and azimuthal symmetries. The secondary solu tion after the instability of the steadily travelling waves is characterise d by vacillating magnetoconvective motions which breaks both the temporal a nd azimuthal symmetries of the primary solution simultaneously. Implication of nonlinear solutions for the Earth's dynamo is also discussed. (C) 1999 Elsevier Science B.V. All rights reserved.