Modelling of Shallow and Inefficient Convection in the Outer Layers of   the Sun Using Realistic Physics
  In an attempt to understand the properties of convective energy transport in the solar convection zone, a numerical model has been constructed for turbulent flows in a compressible, radiation-coupled, non-magnetic, gravitationally stratified medium using a realistic equation of state and realistic opacities. The time-dependent, three-dimensional hydrodynamic equations are solved with minimal simplifications.   The statistical information obtained from the present simulation provides an improved understanding of solar photospheric convection. The characteristics of solar convection in shallow regions is parameterized and compared with the results of Chan and Sofia's simulations of deep and efficient convection (Chan and Sofia 1989). We assess the importance of the zones of partial ionization in the simulation, and confirm that the radiative energy transfer is negligible throughout the region except in the uppermost scale heights of the convection zone, a region of very high super-adiabaticity.   When the effects of partial ionization are included, the dynamics of flows are altered significantly. However, we confirm the Chan and Sofia result that kinetic energy flux is non-negligible and can have a negative value in the convection zone. 
Yong -Cheol Kim, Peter A. Fox, Sabatino Sofia, and Pierre Demarque