The authors derive a full system of boundary layer equations for turbulent Rayleigh-Benard convection that incorporates all the relevant physical effects, namely, buoyancy, fluctuations, and vanishing large-scale circulation velocity in the central bulk region of the convection cell. The theory predicts the time-averaged temperature and velocity profiles for fluids with a general Prandtl number.
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Ching et al. (2019) studied this question.
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