Presenter: Hassan Nagib

With exception of ZPG boundary layers, wall bounded flows contain an overlap region for mean flow of “Log + Lin” terms with coefficients depending on flow configuration and pressure gradient; i.e., non universal. DNS of wall bounded flows require long convergence with Eddy Turnover Times (ETT) in the range 20 to 50, and highly resolved grid spacing; e. g., y⁺ less than around 2 throughout the flow domain, a limit which depends on order of numerical method (example given for 7^th&12^th order methods). All quality-DNS of channel flows over a very wide Re_τ range do not display a pure log overlap region in mean flow and the “Log + Lin” coefficients are approximately κ ≈ 0.413 and S₀ ≈ 1.15 . From some DNS for pipe flow and the CICLoPE center-line measurements the “Log + Lin” coefficients are approximately κ ≈ 0.44 and S₀ ≈ 3.4. It is more important and fruitful to perform highly resolved and converged DNS with higher order codes in an adequate size domain than to chase high Reynolds number records; i.e., recommended approximate range 2, 000 < Re_τ < 5, 000. Mean flow does not converge before turbulence stresses, and possibly even slightly after turbulence, and higher resolution DNS with new criterion recently established converges slower.