Effects of rotation and input energy flux on convective overshooting

We study convective overshooting by means of local 3D convection calculations. Using a mixing length model of the solar convection zone (CZ) as a guide, we determine the Coriolis number (Co), which is the inverse of the Rossby number, to be of the order of ten or larger at the base of the solar CZ. Therefore we perform convection calculations in the range Co = 0. . .10 and interpret the value of Co realised in the calculation to represent a depth in the solar CZ. In order to study the dependence on rotation, we compute the mixing length parameters α_T and α_u relating the temperature and velocity fluctuations, respectively, to the mean thermal stratification. We find that the mixing length parameters for the rapid rotation case, corresponding to the base of the solar CZ, are 3-5 times smaller than in the nonrotating case. Introducing such depth-dependent α into a solar structure model employing a non-local mixing length formalism results in overshooting which is approximately proportional to α at the base of the CZ. Although overshooting is reduced due to the reduced α, a discrepancy with helioseismology remains due to the steep transition to the radiative temperature gradient.