David R Fearn

While substantial numerical models of the solar dynamo have been available for over 10 years, it is only very recently (Glatzmaier and Roberts, 1995a,b) that a well-resolved fully dynamic model of the geodynamo has been produced. The reason for this is the importance of rotation and the very small viscosity in the core. Two approaches have been taken to make progress with this problem. One is to retain the viscous term in the Navier-Stokes equation and adopt numerical techniques designed to optimise resolution and so allow smaller values of the Ekman number Ek to be explored. The second is to make the magnetostrophic approximation which neglects both inertial and viscous effects. A consequence of this is Taylor's constraint and the 'undetermined'
geostrophic flow V_G(s). In practice, viscous effects are restored in Ekman boundary layers (only), giving a prescription for V_G. We review the progress of both approaches, summarising important points and highlighting recent developments.