Solar convection: Comparison of numerical simulations and mixing-length theory

We compare the results of realistic numerical simulations of convection in the superadiabatic layer near the solar surface with the predictions of mixing-length theory. We find that the peak values of such quantities as the temperature gradient, the temperature fluctuations, and the velocity fluctuations, as well as the entropy jump in the simulation, can be reproduced by mixing-length theory for a ratio of mixing length to pressure scale height alpha approximate to 1.5. However, local mixing-length theory neither reproduces the profiles of these variables with depth nor allows penetration of convective motions into the overlying stable photosphere.