The Spectral Amplitude of Stellar Convection and its Scaling in the High-Rayleigh-Number Regime

TL;DR

This study investigates how stellar convection's amplitude and spectral distribution behave at high Rayleigh numbers through 3D simulations, revealing scale-dependent effects and implications for modeling stellar interiors.

Contribution

It demonstrates that at high Rayleigh numbers, the kinetic energy becomes independent of diffusion but the spectral distribution remains sensitive, highlighting scale-dependent effects in stellar convection models.

Findings

Kinetic energy becomes diffusion-independent at high Rayleigh numbers.

Spectral distribution of convection energy depends on Rayleigh number.

Large-scale convection overestimates, small-scale underestimates energy in high-Rayleigh regimes.

Abstract

Convection plays a central role in the dynamics of any stellar interior, and yet its operation remains largely-hidden from direct observation. As a result, much of our understanding concerning stellar convection necessarily derives from theoretical and computational models. The Sun is, however, exceptional in that regard. The wealth of observational data afforded by its proximity provides a unique testbed for comparing convection models against observations. When such comparisons are carried out, surprising inconsistencies between those models and observations become apparent. Both photospheric and helioseismic measurements suggest that convection simulations may overestimate convective flow speeds on large spatial scales. Moreover, many solar convection simulations have difficulty reproducing the observed solar differential rotation due to this apparent overestimation. We present a series of 3-dimensional (3-D) stellar convection simulations designed to examine how the amplitude and spectral distribution of convective flows are established within a star's interior. While these simulations are non-magnetic and non-rotating in nature, they demonstrate two robust phenomena. 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. 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. We discuss the implications of these results in light of the current inconsistencies between models and observations.