Experiments on Turbulent Viscosity in Earth's Core

One of the main criticisms of the present generation of numerical geodynamo simulations is that they are carried out using non-dimensional parameter values far from those of the Earth. In particular, simulations use values of the fluid viscosity many orders of magnitude greater than molecular viscosity estimates for core fluid, such that the Ekman number, Ek, and the magnetic Prandtl number, Pm, have values of >= 10^-5 and ~ 1, respectively. Using molecular viscosity estimates, these parameters take on values of ~ 10^-15 and ~ 10^-6, respectively. Here, we present experimental measurements of turbulent viscosity, made in a rotating spherical shell of water, relevant to the dynamical conditions within planetary cores. In these ``spin-up'' experiments we increase the shell's rotation rate and measure the time for the fluid to re-equilibrate to the new rate. These measurements provide a value for the effective viscosity, which averages in the effects of small-scale turbulence on the large-scale fluid behaviour. Our results verify the theoretical prediction that the spin-up time is proportional to the inverse square-root of the fluid's molecular viscosity in the laminar regime. Beyond this, with turbulent convection, the effective viscosity increases by as much as 50% over molecular values. From these measurements, we have derived a phenomenological law that predicts that the effective viscosity of core fluid may be ~ 10⁶ times greater than molecular viscosity estimates. Using this effective viscosity estimate yields values of Ek ~ 10^-9 and Pm ~ 1 in the Earth's core. Thus, our experimental results suggest that the numerical dynamo simulations may be dynamically far more similar to the Earth's core than previously thought. This, in turn, may explain the gross agreement between magnetic fields generated in the numerical simulations and observations of the geomagnetic field.