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Convection plays a central role in the dynamics of any stellar interior, andyet its operation remains largely-hidden from direct observation. As a result,much of our understanding concerning stellar convection necessarily derivesfrom theoretical and computational models. The Sun is, however, exceptional inthat regard. The wealth of observational data afforded by its proximityprovides a unique testbed for comparing convection models against observations.When such comparisons are carried out, surprising inconsistencies between thosemodels and observations become apparent. Both photospheric and helioseismicmeasurements suggest that convection simulations may overestimate convectiveflow speeds on large spatial scales. Moreover, many solar convectionsimulations have difficulty reproducing the observed solar differentialrotation due to this apparent overestimation. We present a series of3-dimensional (3-D) stellar convection simulations designed to examine how theamplitude and spectral distribution of convective flows are established withina star's interior. While these simulations are non-magnetic and non-rotating innature, they demonstrate two robust phenomena. When run with sufficiently highRayleigh number, the integrated kinetic energy of the convection becomeseffectively independent of thermal diffusion, but the spectral distribution ofthat kinetic energy remains sensitive to both of these quantities. A simulationthat has converged to a diffusion-independent value of kinetic energy willdivide that energy between spatial scales such that low-wavenumber power isoverestimated, and high-wavenumber power is underestimated relative to acomparable system possessing higher Rayleigh number. We discuss theimplications of these results in light of the current inconsistencies betweenmodels and observations.

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