Tests of diffusion-free scaling behaviors in numerical dynamo datasets

Abstract

Many dynamo studies extrapolate numerical model results to planetary conditions by empirically constructing scaling laws. The seminal work of Christensen and Aubert (2006) proposed a set of scaling laws that have been used throughout the geoscience community. These scalings make use of specially-constructed parameters that are independent of fluid diffusivities, anticipating that large-scale turbulent processes will dominate the physics in planetary dynamo settings. With these ‘diffusion-free’ parameterizations, the results of current numerical dynamo models extrapolate directly to fully-turbulent planetary core systems; the effects of realistic fluid properties merit no further investigation. In this study, we test the validity of diffusion-free heat transfer scaling arguments and their applicability to planetary conditions. We do so by constructing synthetic heat transfer datasets and examining their scaling properties alongside those proposed by Christensen and Aubert (2006). We find that the diffusion-free parameters compress and stretch the heat transfer data, eliminating information and creating an artificial alignment of the data. Most significantly, diffusion-free heat transfer scalings are found to be unrelated to bulk turbulence and are instead controlled by the onset of non-magnetic rotating convection, itself determined by the viscous diffusivity of the working fluid. Ultimately, our results, in conjunction with those of Stelzer and Jackson (2013) and King and Buffett (2013), show that diffusion-free scalings are not validated by current-day numerical dynamo datasets and cannot yet be extrapolated to planetary conditions.