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

TL;DR

This study investigates how mesh resolution and convergence affect the accuracy of the indicator function in DNS of wall-bounded turbulence, revealing sensitivities that influence the understanding of the overlap region at high Reynolds numbers.

Contribution

It provides a detailed analysis of the impact of mesh distribution on the indicator function and overlap parameters in DNS, challenging classical convergence assumptions.

Findings

Indicator function depends strongly on mesh distribution.

Classical DNS convergence criteria may need revision.

High-Reynolds number overlap parameters can be estimated at moderate Reynolds numbers.

Abstract

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''.