Turbulence properties in the solar convection envelope: properties of the overshooting regions

We apply the turbulent convection model (TCM) to investigate properties of turbulence in the solar convective envelope, especially in overshooting regions. The results show TCM gives negative turbulent heat flux in overshooting regions, which is similar to other nonlocal turbulent convection theories. The turbulent temperature fluctuation shows peaks in overshooting regions. Most important, we find that the downward overshooting region below the base of the solar convection zone is a thin cellular layer filled with roll-shaped convective cells. The overshooting length for the temperature gradient is much shorter than that for element mixing because turbulent heat flux of downward and upward moving convective cells counteract each other in this cellular overshooting region. Comparing the models' sound speed with observations, we find that taking the convective overshooting into account helps to improve the sound speed profile of our nonlocal solar models. Comparing differences of the p-mode oscillation frequencies with observations, we validated that increasing the diffusion parameters and decreasing the dissipation parameters of TCM make the p-mode oscillation frequencies of the solar model be in better agreement with observations.