Abstract
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.
