Modelling of inhomogeneous turbulence in the absence of mean velocity gradients

In this paper we propose a new rational model for turbulent transport of Reynolds stresses and dissipation. For this purpose we first analyse some properties of diffused turbulence i.e. turbulence where dissipation is balanced by turbulent diffusion arising from inhomogeneity. Then we use some of these results to deduce some mathematical requirements that must be satisfied by any rational model and we show that they are not verified by available models. Consequently we derive a more general model taking into account the various properties of diffused turbulence.