An Over-Driven Axial Dipole Dynamo Model

Planetary dynamos typically operate in the regime where inertial forces are far smaller than Coriolis forces. The ratio of these two forces is the Rossby number, Ro. In the low Ro regime, weakly nonlinear convection in planetary dynamo models occurs via well-organized, axially-aligned columnar flow structures. These models are capable of generating axially-aligned dipolar magnetic fields, but typically require magnetic Prandtl values Pm ∼ 1 in order to reach magnetic Reynolds numbers Rm ≈ 50 and higher. When the columnar motions break down in higher Ro cases, the axial dipole field collapse and small-scale fields tend to develop. Based on these results, the presently accepted regime diagram for planetary dynamos is taken to be a relatively simple transition from axial dipole fields at low Ro values to small-scale, fluctuating solutions at higher Ro values. Here we present the results of a novel planetary dynamo model run in the high Ro regime. Because the three-dimensional turbulent flows are strong in this model (Ro ≃ 1.5; Reynolds numbers Re ∼ 3 × 10⁴), dynamo action can be generated using values of the magnetic Prandtl number that are well below unity (Pm = 4 × 10^-2), approaching turbulent Pm values in planetary cores. This high Ro, low Pm dynamo model produces an axial dipole dynamo field, a case result which alters the planetary dynamo regime diagram. In low Pm fluids, the transition between dipolar and non-dipolar dynamos is not controlled by the relative strength of inertial terms. Furthermore, our finding suggests the possibility of generating axial dipolar laboratory dynamos using mechanically-driven high Rm, high Ro flows, which are far easier to generate in the laboratory than high Rm, low Ro flows.