ABSTRACT
Substantial progress has been made in modeling the geodynamo in recent years, with Earthlike magnetic fields emerging from convectiondriven simulations of the liquid outer core of the Earth. These models are based on self-consistent numerical solutions of the Navier-Stokes equation and the magnetic induction equation. This work has been reviewed recently by Kono and Roberts (2002) and from a more observational standpoint by Dormy et al. (2000). There is, however, a disturbing feature of these simulations; the dimensionless parameters used are very different from those suggested by the molecular diffusion constants relevant to the outer core. For example, the Ekman number E = ν/2d2, where ν is the kinematic viscosity, is the Earth’s angular velocity and d is the outer core radius, is about 10−15 in the core, but values of order 10−4 are typically used in simulations. Similarly, the heat flux Rayleigh number, which is defined as Ra = Fgα¯d2/2κ2ρcp where F is the heat flux per unit area emerging from the core, g is gravity, α¯ is the thermal expansion coefficient, κ is the thermal diffusivity, ρ is the density and cp is the specific heat, is approximately 1015, whereas values between the order 102 − 103 are used in simulations. The Prandtl number Pr = ν/κ in the core is about 0.1, and the magnetic Prandtl number Pm = ν/η is estimated to be about 10−6, where η is the magnetic diffusivity, but in simulations O(1) values of Pm are assumed. Indeed, no successful simulations have been performed with q = Pm/Pr small; even using such modest values as q ∼ 0.1 is currently out of reach (Christensen et al., 1999). It is therefore rather surprising that geodynamo simulations give results that apparently agree well with observation.
