Effect of the radiative background flux in convection
  Numerical simulations of turbulent stratified convection are used to study models with approximately the same convective flux, but different radiative fluxes. As the radiative flux is decreased, for constant convective flux: the entropy jump at the top of the convection zone becomes steeper, the temperature fluctuations increase and the velocity fluctuations decrease in magnitude, and the distance that low entropy fluid from the surface can penetrate increases. Velocity and temperature fluctuations follow mixing length scaling laws. 
A. Brandenburg (Nordita), K. L. Chan (Hong Kong), A. Nordlund   (Copenhagen), R. F. Stein (Michigan)