Online material

Appendix A: Scaling laws

For our samples of models we compute the usual scaling laws that have been derived for the magnetic and velocity fields and the convective heat flux (Christensen & Aubert 2006; Yadav et al. 2013a; Stelzer & Jackson 2013; Yadav et al. 2013b). As in Schrinner et al. (2014), we do not attempt to solve any secondary dependence on Pm because we do not vary this parameter on a wide enough range. We transform our problem to a linear one by taking the logarithm and look for a law of the form lnŷ = β + αlnx. To quantify the misfit between data and fitted values, we follow Christensen & Aubert (2006) and compute the relative misfit (A.1)where stands for predicted values, y_i for measured values, and n is the number of data. Our results are summarized in Table A.1 and compared with those found in Schrinner et al. (2014) and Yadav et al. (2013a) in Table A.2. We did not find significant differences between the anelastic scalings and the scaling we obtained in the Boussinesq limit with the same mass distribution. The coefficients we obtained seem closer on average to the coefficients obtained by Yadav et al. (2013a) with Boussinesq models with a uniform mass distribution. However, it is not possible to deduce from our data set any influence of N_ϱ on the different coefficients of the scaling laws. In our models, the Nusselt number evaluated at the surface of the inner sphere S_i is defined by (A.2)which enables a flux based Rayleigh number to be defined, (A.3)which is used in derivating scaling laws, together with the fraction of ohmic to total dissipation f_ohm.

Appendix B: Numerical models

© ESO, 2014