Diffusivity-free Scaling Laws for Earth and Planetary Dynamos: A Reassessment

Numerical dynamo models notoriously do not operate in the adequate region of parameter space, since the stiffnessof the problem at hand makes it mandatory to resort to enhanced values of transport properties for a solution to be within reach. Accordingly, the application of scaling laws derived from numerical simulations to planetaryinteriors implicitly assumes that simulations operate in the adequate dynamical regime. Christensen and Aubert (2006, CA06 henceforth) proposed along these lines power-based, diffusivity-free scaling laws for magnetic field strength and flow speed, based on the analysis of an ensemble of such simulations. The CA06 laws were subsequently applied to a large number of bodies in the solar system, including Earth. They have received some criticism in the past few years, in particular with regard to a residual effect of diffusivites on the properties deduced from the CA06 dataset. In view of providing a refreshing look at this issue, and noting that simulation have improved since 2006, we complement the CA06 dataset with simulations performed during the last decade. This amounts to doubling the size of the dataset (from O(100) to 0(200) members), while enabling a broader sampling of parameter space. Physics-based selection criteria (most notably the magnetic energy to kinetic energy ratio) further allow us to select those dynamos which we think are indeed in the appropriate dynamical regime. This reduced dataset (comprising O(5O) members) convincingly reveals power-based, diffusion-free scalings for magnetic field strength and flow speed. We further discuss the exponents found in light of the theoretical predictions of Davidson (2013), which rest on the assumption that the main departure from geostrophy in planetary cores is achieved through a Magnetic-Archimedean-Coriolis 3-term force balance.