Tests of Diffusion-Free Scaling Behaviors in Numerical Dynamo Data Sets

Abstract:

In order to describe the fluid physics of the dynamo generating regions of planets, the geoscience community has largely adopted a set of scaling laws proposed in the seminal work of Christensen and Aubert (2006).^[1] 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. In the work presented here, we test the validity of diffusion-free heat transfer scaling laws by constructing synthetic heat transfer datasets and examining their scaling properties alongside those proposed by Christensen and Aubert (2006). These tests demonstrate that the seemingly robust collapse of heat transfer data using diffusion-free parameters is not indicative of fully turbulent, diffusion-free physics, but is instead an a priori consequence of the way such parameters are constructed. In particular, the diffusion-free heat transfer scaling is determined by the onset of convection, which is itself determined by the viscous diffusivity of the fluid. Our results, in conjunction with those of Stelzer and Jackson (2013),^[2] show that diffusion-free scalings are not validated by current-day numerical dynamo datasets, and that it still remains to be established under what conditions dynamo generation becomes free of fluid diffusivities.

References

[1] Christensen, U.R., Aubert, J., 2006. Geophys. J. Int. 166, 97–114.
[2] Stelzer, Z., Jackson, A., 2013. Geophys. J. Int. ggt083.