Flow speeds and length scales in geodynamo models: The role of viscosity

• We develop scaling laws for the typical size and speed of flow for geodynamo models.
• The scalings rely on viscosity to fix length scales and limit kinetic energy production.
• The scalings fit data from a broad array of geodynamo models.
• We conclude that either (1) viscous effects are important in planetary dynamos; or (2) viscosity is inappropriately influential in the dynamo simulations.

The geodynamo is the process by which turbulent flow of liquid metal within Earth's core generates our planet's magnetic field. Numerical simulations of the geodynamo are commonly used to elucidate the rich dynamics of this system. Since these simulations cannot attain dynamic similarity with the geodynamo, their results must be extrapolated across many orders of magnitude of unexplored parameter space. For this purpose, scaling analysis is essential. We investigate the scaling behavior of the typical length scales, ℓℓ, and speeds, U  , of convection within a broad suite of geodynamo models. The model outputs are well fit by the scalings ℓ∝E1/3ℓ∝E1/3 and U∝C1/2E1/3U∝C1/2E1/3, which are derived from a balance between the influences of rotation, viscosity, and buoyancy (E   is the Ekman number and CC the convective power). Direct comparison with two previously proposed theories finds that the viscous scalings most favorably describe model data. The prominent role of viscosity suggested by these scaling laws may call into question the direct application of such simulations to the geodynamo, for which it is typically assumed that viscous effects are negligible.