# THE SPECTRAL AMPLITUDE OF STELLAR CONVECTION AND ITS SCALING IN THE HIGH-RAYLEIGH-NUMBER REGIME

In spring of 2013, CIG initiated code development of Rayleigh a new HPC pseudospectral code for studying spherical dynamos such as those that occur in the planetary and stellar interiors.  This effort is lead by Nick Featherstone in conjunction with CIG’s Geodynamo Working Group. Featherstone and Hindman (2016) present the first results from Rayleigh with a series of three-dimensional stellar convection simulations designed to examine how the amplitude and spectral distribution of convective flows are established within a star's interior. Run on ALCF’s Mira supercomputer through the INCITE program, these nonmagnetic and nonrotating simulations demonstrate two robust phenomena. First, when run with sufficiently high Rayleigh number, the integrated kinetic energy of the convection becomes effectively independent of thermal diffusion, but the spectral distribution of that kinetic energy remains sensitive to both of these quantities. Second, a simulation that has converged to a diffusion-independent value of kinetic energy will divide that energy between spatial scales such that low-wavenumber power is overestimated and high-wavenumber power is underestimated relative to a comparable system possessing higher Rayleigh number. The models studied demonstrate that stellar convection simulations must be run in the high Rayleigh-number regime if they are to correctly capture even the grossest property of a star’s convection. The inclusion of rotation and magnetism will modify these findings and allow further assessment of current models.

Rayleigh is scheduled for release early summer 2016.

Temperature perturbations as realized by rotating convection in an Earth-like geometry using Rayleigh.  Warm perturbations (relative to the spherical mean) are rendered in yellow, and cool perturbations in violet.  The rendering viewpoint is such that the north pole is tilted slightly toward the user.  Rotation exerts a noticable influence  on the convective flow patterns, causing convective cells in the equatorial regions to elongate and align themselves relative to the rotation axis.  These columnar convective motions are more efficient at transporting heat than their polar counterparts, possessing a warm-temperature signature as a result.  Run parameters: Ekman Number = 1e-5, Prandtl Number = 1, Rayleigh Number = 1.25e8.  Simulation resolution:  512x512x1024 (Nr x Ntheta x Nphi).

Read the full paper for the discussion on the implications of these results in light of the current inconsistencies between models and observations of the Sun.

Featherstone, Nicholas A., and Bradley W. Hindman. "The Spectral Amplitude of Stellar Convection and its Scaling in the High-Rayleigh-Number Regime." arXiv preprint arXiv:1511.02396 (2015).