Magnetic fields generated by hydromagnetic dynamos at the low Prandtl number in dependence on the Ekman and magnetic Prandtl numbers

Abstract

This article investigates the dependence of hydromagnetic dynamos on the magnetic Prandtl number at low Prandtl number. In all the investigated cases, the generated magnetic fields are dipolar and neither transition to hemispherical dynamos nor weaker magnetic fields (which are less dipole dominated) were observed, although the inertia becomes important. The magnetic field becomes weak in the polar regions (is “convected out of polar regions”) only for low Prandtl numbers, when the inertia becomes important. It is a basic condition. However, whether the magnetic field gets weak in the polar regions (is “convected out of polar regions”) or not depends also on the magnetic Prandtl number. The magnetic Prandtl number has to exceed a minimum value in order to sustain dynamo action. If the magnetic diffusion is small (large magnetic Prandtl numbers) then this phenomenon does not exist but if it is large (small magnetic Prandtl numbers) it exists because the strong magnetic diffusion significantly weakens the magnetic field inside the tangent cylinder. The magnetic diffusion and inertia seem to act in the same direction as to weaken the magnetic field inside the tangent cylinder.