Validity Tests of the Mixing-Length Theory of Deep Convection

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Abstract
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.

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