An examination of diffusion modeling in second-moment turbulence closu
res is presented. The main objectives are to gain a better understandi
ng of the processes that are grouped into the net diffusive transport
of the Reynolds stresses, D-ij, and to assess existing models for D-ij
. The benchmark case of zero-mean-shear (ZMS) turbulence is used as a
guide. The analysis of ZMS turbulence shows that the pressure-velocity
processes in D-ij play a central role in establishing the anisotropy
level in diffusive turbulence. Existing models for D-ij based solely o
n the triple velocity correlation are shown to be inadequate in the di
ffusive limit. The present evaluation of diffusion models using ZMS tu
rbulence and subsequent analysis of ZMS turbulence show that the Lumle
y (Lumley; J. L., ''Computational Modelling of Turbulent Flows,'' Adva
nces in Applied Mechanics, Vol. 18, Academic, New York, 1978, pp. 123-
176) model is the most viable existing diffusion model. A modification
to Lumley's model that enables exact predictions in the diffusive lim
it is suggested.