We examine the physical basis for algorithms to replace mixing-length theory
(MLT) in stellar evolutionary computations. Our 321D procedure is based on
numerical solutions of the Navier-Stokes equations. These implicit large eddy
simulations (ILES) are three-dimensional (3D), time-dependent, and turbulent,
including the Kolmogorov cascade. We use the Reynolds-averaged Navier-Stokes
(RANS) formulation to make concise the 3D simulation data, and use the 3D
simulations to give closure for the RANS equations. We further analyze this
data set with a simple analytical model, which is non-local and time-dependent,
and which contains both MLT and the Lorenz convective roll as particular
subsets of solutions. A characteristic length (the damping length) again
emerges in the simulations; it is determined by an observed balance between (1)
the large-scale driving, and (2) small-scale damping.
The nature of mixing and convective boundaries is analyzed, including
dynamic, thermal and compositional effects, and compared to a simple model.
We find that
(1) braking regions (boundary layers in which mixing occurs) automatically
appear {\it beyond} the edges of convection as defined by the Schwarzschild
criterion,
(2) dynamic (non-local) terms imply a non-zero turbulent kinetic energy flux
(unlike MLT),
(3) the effects of composition gradients on flow can be comparable to thermal
effects, and
(4) convective boundaries in neutrino-cooled stages differ in nature from
those in photon-cooled stages (different P\'eclet numbers).
The algorithms are based upon ILES solutions to the Navier-Stokes equations,
so that, unlike MLT, they do not require any calibration to astronomical
systems in order to predict stellar properties. Implications for solar
abundances, helioseismology, asteroseismology, nucleosynthesis yields,
supernova progenitors and core collapse are indicated.Comment: 22 pages, 4 figures, 2 tables; significantly re-written, critique of
Pasetto, et al. model added, accepted for publication by Ap
