  Direct Numerical Simulations (DNSs) are one of the most powerful tools for
studying turbulent flows. Even if achievable Reynolds numbers are lower than
those obtained with experimental means, there is a clear advantage since the
entire velocity field is known, and any desired quantity can be evaluated. This
also includes the computation of derivatives of all relevant terms. One such
derivative provides the indicator function, which is the product of wall
distance by wall-normal derivative of the mean streamwise velocity. This
derivative may depend on mesh spacing and distribution. However, it is
extremely affected by the convergence of the simulation. The indicator function
is a cornerstone to understanding inner and outer interactions in wall-bounded
flows and describing the overlap region between them. We find a clear
dependence of this indicator function on mesh distributions we examined,
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, and a path
is revealed to establishing their high-$Re_\tau$ or near-asymptotic values at
modest Reynolds numbers accessible by high-quality DNS with reasonable
``cost''.
