  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.
