Validity Tests of the Mixing-Length Theory of Deep Convection

The construction of solar or stellar models is hindered by the difficulty of computing, with sufficient accuracy, the convective fluxes in unstable regions. Although the mixing-length theory of convection has been used for more than three decades, its validity has neither been tested by experiment nor verified by computation. This report presents the results of a three-dimensional numerical simulation of deep and efficient convection that support two conclusions: (i) the basic picture proposed by the mixing-length theory is physically valid-the vertical correlation of the motion of fluid elements is proportional to the pressure scale height; and (ii) some dynamical variables, including the convective flux, can be approximately computed from the structure of the stratification with mixing-length approximations.