Turbulent transport in wall-bounded flows. Evaluation of model coefficients using direct numerical simulation

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Abstract
The modeling of the turbulent diffusion of quantities such as the turbulent kinetic energy and its dissipation rate in the outer part of wall-bounded flows is examined with the aid of simulation data. The channel-flow data of Mansour et al. [J. Fluid Mech. 194, 15 (1988)] and those of Spalart [J. Fluid Mech. 187, 61 (1988)] for a flat-plate boundary layer with zero pressure gradient are used to examine the differences between turbulent flows with and without a free-stream edge. The ratio of the diffusivity of the above-mentioned turbulent quantities to the diffusivity of momentum is roughly constant, as assumed in most models, and little affected by the presence of the free-stream edge. However, the diffusivity ratios are found to deviate significantly from so-called ‘‘standard’’ values. Furthermore, current models for the momentum diffusivity fail badly at the edge of the boundary layer: the modeling constant Cμ used in the (k,ε) and related models exhibits a rapid rise there. In this respect, the simulation data confirm earlier experimental studies. The consequences of these findings for turbulence modeling are briefly examined.