Turbulence gradient transport hypothesis

The structures are often of large scale, for example, of the same order as that of the mean flow. They have been found to be responsible for mechanisms that relate to the transport and the production in almost all commonly observed turbulent flows. Findings show the existence of the underlying orderliness in the apparent chaos of turbulent flows and have fostered many modifications to the traditional thinking of turbulence, such as the turbulent gradient transport hypothesis. Weakly nonlinear analysis has been shown to reproduce the large-scale phenomena in simple flows. 

The modeled transport equations for z differ mainly in the diffusion and secondary source term. Launder and Spalding (1972) and Chambers and Wilcox (1977) discuss the differences and similarities in more detail. The variable, z = e is generally preferred since it does not require a secondary source, and a simple gradient diffusion hypothesis is fairly good for the diffusion (Launder and Spalding, 1974 Rodi, 1984). The turbulent Prandtl number for s has a reasonable value of 1.3, which fits the experimental data for the spread of various quantities at locations far from the walls, without modification of any constants. Because of these factors, the k-s model of turbulence has been the most extensively studied and used and is recommended as a baseline model for typical internal flows encountered by reactor engineers. 

The covariance is modeled by use of the gradient hypothesis and the Boussinesq turbulent transport coefficient concept ... 

The turbulent transport processes are often described as diffusive fluxes being proportional to the mean variable gradient of the transported quantities. The turbulent transport terms may then be expressed in a form analogous to their laminar equivalents in accordance with the hypothesis of Boussinesq [17] ... 

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