Sensitivity to luminosity, centrifugal force, and boundary conditions in spherical shell convection

ABSTRACT

We test the sensitivity of hydrodynamic and magnetohydrodynamic turbulent convection simulations with respect to Mach number, thermal and magnetic boundary conditions, and the centrifugal force. We find that varying the luminosity, which also controls the Mach number, has only a minor effect on the large-scale dynamics. A similar conclusion can also be drawn from the comparison of two formulations of the lower magnetic boundary condition with either vanishing electric field or current density. The centrifugal force has an effect on the solutions, but only if its magnitude with respect to acceleration due to gravity is by two orders of magnitude greater than in the Sun. Finally, we find that the parameterisation of the photospheric physics, either by an explicit cooling term or enhanced radiative diffusion, is more important than the thermal boundary condition. In particular, runs with cooling tend to lead to more anisotropic convection and stronger deviations from the Taylor-Proudman state. In summary, the fully compressible approach taken here with the Pencil Code is found to be valid, while still allowing the disparate timescales to be taken into account.

KEYWORDS:

• Convection
• turbulence
• dynamos
• magnetohydrodynamics

Acknowledgments

The anonymous referees are acknowledged for their constructive comments on the paper. The authors wish to acknowledge CSC – IT Center for Science, who are administered by the Finnish Ministry of Education; of Espoo, Finland, for computational resources. We also acknowledge the allocation of computing resources through the Gauss Center for Supercomputing for the Large-Scale computing project “Cracking the Convective Conundrum” in the Leibniz Supercomputing Centre's SuperMUC supercomputer in Garching, Germany.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 https://github.com/pencil-code/

Additional information

Funding

This work was supported in part by the Deutsche Forschungsgemeinschaft Heisenberg programme (grant No. KA 4825/1-1; PJK), the Academy of Finland ReSoLVE Centre of Excellence (grant No. 307411; MJK, PJK, FAG, NO), the Astronomy and Astrophysics Grants Program of the National Science Foundation (grant 1615100), and the University of Colorado through its support of the George Ellery Hale visiting faculty appointment.