Sensitivity study of resolution and convergence requirements for the extended overlap region in wall-bounded turbulence

Even though the achievable Reynolds numbers computed by Direct numerical simulations (DNSs) are lower than those obtained through experimental means, DNS offers a clear advantage: Any desired quantity can be evaluated. This capability includes the computation of derivatives of all relevant terms. One such derivative provides the indicator function, which is crucial for understanding inner and outer interactions. It is defined as the product of the wall distance and the wall-normal derivative of the mean streamwise velocity. This derivative may depend on mesh spacing and distribution, but it is extremely affected by the convergence of the simulation. We find a clear dependence of this indicator function on the mesh distributions we examine, raising questions about classical mesh and convergence requirements for DNS and achievable accuracy. Within the framework of the logarithmic plus linear overlap region, coupled with a parametric study of channel flows and some pipe flows, sensitivities of extracted overlap parameters are examined. This study reveals a path to establishing their high-Re_τ or nearly asymptotic values at modest Reynolds numbers, but larger than the ones used in this work, accessible by high-quality DNS with reasonable cost.