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  • Letter
  • Open Access

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

Sergio Hoyas*

Ricardo Vinuesa†

Peter Schmid‡

Hassan Nagib§

  • Mechanical, Materials and Aerospace Engineering, Armour College of Engineering, ILLINOIS TECH, Chicago, Illinois 60616, USA

  • *Contact author: serhocal@mot.upv.es
  • †Contact author: rvinuesa@mech.kth.se
  • ‡Contact author: peter.schmid@kaust.edu.sa
  • §Contact author: nagib@iit.edu
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Phys. Rev. Fluids 9, L082601 – Published 5 August, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.L082601

Abstract

Direct numerical simulations (DNSs) are among the most powerful tools for studying turbulent flows. Even though the achievable Reynolds numbers are lower than those obtained through experimental means, DNS offers a clear advantage: The entire velocity field is known, allowing for the evaluation of any desired quantity. This capability includes the computation of derivatives of all relevant terms. One such derivative provides the indicator function, which is 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. The indicator function is crucial for 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 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-Reτ 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.

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Phys. Rev. Fluids 9, L082601– Published 5 August, 2024
  • Received 30 October 2023
  • Accepted 25 June 2024
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