Energetics of the Dipolar Magnetic Field

Dynamo simulations show that the dipole magnetic energy saturates and becomes relatively constant over a wide range of Rayleigh numbers, and then drops precipitously at a specific value of the Rayleigh number where the dynamo becomes predominantly multipolar. This saturation process is not well-understood. We use the results of convection-driven spherical dynamo simulations to better understand this process. We ran a suite of simulations that spans a large range of magnetic Prandtl numbers and reaches Rayleigh numbers up to 30 times supercritical. Most of the resulting dynamos exhibit strongly dipolar fields, with a few cases showing a multipolar magnetic field. All of the strongly dipolar cases exhibit roughly the same dipolar magnetic energy, independent of the Rayleigh number. We analyze the energetics of all the cases, in particular, the evolution equation for the dipolar magnetic energy and its source terms. We find that the dissipation of the dipole component remains constant over the Rayleigh numbers studied. We will discuss the implications of these results in relation to the dipolar field of the geodynamo.