Planetary Magnetic Fields and Fluid Dynamos

The magnetic fields of the planets, including the Earth, are generated by dynamo action in their fluid cores. Numerical models of this process have been developed that solve the fundamental magnetohydrodynamic equations driven by convection in a rotating spherical shell. New results from these theoretical models are compared with observations of the geomagnetic field and magnetic data gathered from space missions. The mechanism by which a magnetic field is created is examined. The effects of rotation and magnetic field on the convection are of paramount importance in the simulations. A wide range of simulations with different convection models, varying boundary conditions, and parameter values have been performed over the past 10 years. The effects of these differences are assessed. Numerical considerations mean that all dynamo simulations use much enhanced values of the diffusivities. We consider to what extent this affects results and show how the asymptotic behavior at low diffusion is starting to be inferred using scaling laws. The results of specific models relating to individual planets are reviewed.