In the Reynolds stress equation, the turbulent transportation can be taught of as the sum of molecular diffusion, turbulent transportation and pressure diffusion of the Reynolds stress, which in analogue to specific turbulent kinetic energy equation and dissipation equation. So why isn't this term in the equation modelled in the same manner, using the gradient-diffusion hypothesises for the turbulent Stresses

i.e. (the sum of a eddy viscoity + molecular viscoity) by (gradient of the Reynold Stress) ?.

Also could anyone, give me a physical description of the the pressure strain correlation term?.

Thanks in advance

Oliver

It is almost always modelled by gradient-diffusion. You do not say which model you are looking at but I would guess it uses an anisotropic "eddy viscosity" (by far the most popular model) which may the source of confustion. Some of us have tended to use an isotropic eddy viscosity model like the k-e model on pragmatic grounds - it is the simplest and most robust. However, it is a poor model when turbulent transport becomes significant relative to the other terms but the more complicated models (although a bit better) are still poor models as well. As you describe it - the pressure strain correlation term is the effect of the interaction of the fluctuating pressure and rate of strain of the fluid on the Reynolds stress components. Having moved the transportive "pressure diffusion" term elsewhere, it is traceless and moves turbulent energy between the Reynolds stress components without directly contributing to the level.

Thanks Andy for your expertise and time.

Oliver