Scale dependence of kinetic helicity and selection of the axial dipole in rapidly rotating dynamos

Abstract

The dominant polarity of the magnetic field in rapidly rotating spherical dynamos is the axial dipole. Studies of the onset of magnetoconvection in the limit of vanishing Ekman number have proposed that the dipole is favored over other polarities because its equatorial symmetry generates kinetic helicity that would be otherwise absent in nonmagnetic convection. This study explores the effect of the magnetic field in the selection of the axial dipole in rapidly rotating, supercritical dynamos. The strength of convection is such that the axial dipole grows from a starting seed field in the nonlinear dynamo but fails to grow in the kinematic dynamo at the same parameters. The magnetic field is shown to excite convection over a range of length scales larger than the energy injection scale and at the same time extract energy from smaller scales through the Lorentz force in order to feed itself. This leads to substantial helicity generation in a range of length scales and helicity loss in smaller scales, both relative to nonmagnetic convection. The crossover point between the helicity surplus and deficit regions is displaced to smaller length scales as the rotation rate is increased (by decreasing the Ekman number). The helicity deficit occurs in the region of the spectrum where the Lorentz force approximately balances the Coriolis force in the vorticity equation, so that energy may be drawn from these scales via vortex stretching. The timescale for the increase in convection intensity relative to the nonmagnetic state approximately coincides with the timescale for the formation of the axial dipole, which indicates that the Lorentz force has an important role in polarity selection. Crucially, the dipole forms from a chaotic state well before the saturation of the dynamo, implying that planetary dynamos choose their polarity during their nonlinear growth phase. The generation of the toroidal part of the dipole field is primarily through the classical Ω effect, although the pattern of the zonal flow switches from spherical harmonic degree l = 1 to l = 3 in the presence of the magnetic backreaction.