  We present a statistical analysis of turbulent convection in stars within our
Reynolds-Averaged Navier Stokes (RANS) framework in spherical geometry which we
derived from first principles. The primary results reported in this document
include: (1) an extensive set of mean-field equations for compressible,
multi-species hydrodynamics, and (2) corresponding mean-field data computed
from various simulation models. Some supplementary scale analysis data is also
presented.
  The simulation data which is presented includes: (1) shell convection during
oxygen burning in a 23 solar mass supernova progenitor, (2) envelope convection
in a 5 solar mass red giant, (3) shell convection during the helium flash, and
(4) a hydrogen injection flash in a 1.25 solar mass star. These simulations
have been partially described previously in Meakin [2006], Meakin and Arnett
[2007a,b, 2010], Arnett et al. [2009, 2010], Viallet et al. [2011, 2013a,b] and
Mocak et al. [2009, 2011]. New data is also included in this document with
several new domain and resolution configurations as well as some variations in
the physical model such as convection zone depth and driving source term.
  The long term goal of this work is to aid in the development of more
sophisticated models for treating hydrodynamic phenomena (e.g., turbulent
convection) in the field of stellar evolution by providing a direct link
between 3D simulation data and the mean fields which are modeled by 1D stellar
evolution codes. As such, this data can be used to test previously proposed
turbulence models found in the literature and sometimes used in stellar
modeling. This data can also serve to test basic physical principles for model
building and inspire new prescriptions for use in 1D evolution codes.
