Weak-field dynamo emerging in a rotating spherical shell with stress-free top and no-slip bottom boundaries

Numerical experiments are performed in order to investigate an MHD dynamo in a rotating spherical shell with stress-free top and no-slip bottom boundaries. The Ekman number, the Prandtl number, and the ratio of inner to outer radii are fixed as 10(-3), 1, and 0.35, respectively. The magnetic Prandtl number is varied from 5 to 50, and the modified Rayleigh number is increased from 1.5 to 10 times the critical Rayleigh number. The initial imposed magnetic field is either a weak or strong magnetic field, where the magnetic energy of the initial field is approximately two orders of magnitude smaller or larger than the kinetic energy of the quasi-steady state of non-magnetic thermal convection. For cases involving a weak initial magnetic field, self-sustained dynamo solutions are established when the magnetic Prandtl number is larger than or equal to 5, and the modified Rayleigh number is larger than or equal to 5 times the critical Rayleigh number. The solutions are categorized as a weak field-dynamo, where the mean magnetic energy is one order of magnitude smaller than the mean kinetic energy. The dynamo solutions are characterized by a radially two-layer spatial structure. The upper layer is dominated by a strong prograde zonal mean zonal flow with large-scale prograde propagating spiral vortices having a longitudinal wavenumber of 3. Toroidal kinetic energy is converted to toroidal magnetic energy through stretching of the field lines by large-scale prograde propagating spiral vortices. On the other hand, the lower layer contains small-scale retrograde propagating columnar convective vortices having a longitudinal wavenumber of 8. The magnetic field lines are not concentrated in the vortices, but rather wind around the vortices in each layer. Poloidal kinetic energy is converted to poloidal magnetic energy through winding of the field lines around small-scale retrograde propagating columnar convective vortices. For cases involving a strong initial magnetic field, self-sustained dynamo solutions are established when the magnetic Prandtl number is greater than or equal to 4 and the modified Rayleigh number is greater than or equal to 3 times the critical Rayleigh number. In contrast with the cases involving a weak initial magnetic field, all of the dynamo solutions are strong-field solutions. Bistability is observed when the magnetic Prandtl number is 5, and the modified Rayleigh number is approximately equal to 10 times the critical Rayleigh number, where weak-field and strong-field dynamo solutions coexist. However, transition between the weak-field and strong-field solutions does not occur in this case. (C) 2011 Elsevier B.V. All rights reserved.