On the application of direct-interaction approximation to the turbulent convection problem

In this paper, we seek to clarify some issues associated with the application of the direct-interaction approximation (DIA) to the turbulent-convection problem. The small-Prandtl number and the large-Prandtl number regimes are investigated separately. The DIA is confirmed to lead to some unphysical features in the Pr⪡1 regime. However, in the Pr⪢1 regime where the perturbative treatment is valid, the unphysical features of the DIA formulation are shown to be actually artifacts of the perturbative aspect itself and the renormalization added on in the DIA does not change this very much.