Some Analytic Results in the Theory of Thermal Convection

An analytic approximation method is developed to treat the problem of thermal convection at large Rayleigh numbers R. The method is applied to a convection model in which the fluctuating self-interactions are omitted. The results of the method compare satisfactorily to the exact solutions at large Rayleigh numbers. The results include a derivation of the R½ law for the Nusselt number, and closed form estimates for the shape of the mean temperature field and temperature and velocity fluctuation fields.