open access publication

Article, 2024

Extension of the law of the wall exploiting weak similarity of velocity fluctuations in turbulent channels

Physics of Fluids, ISSN 1089-7666, 1070-6631, Volume 36, 1, Page 015134, 10.1063/5.0185334

Contributors

Hansen, Christoffer [1] Sørensen, Nørkær Sørensen 0000-0002-1974-2675 [2] Yang, Xiang I A (Corresponding author) [3] Abkar, Mahdi 0000-0002-6220-870X (Corresponding author) [1]

Affiliations

  1. [1] Aarhus University
  2. [NORA names: AU Aarhus University; University; Denmark; Europe, EU; Nordic; OECD];
  3. [2] Technical University of Denmark
  4. [NORA names: DTU Technical University of Denmark; University; Denmark; Europe, EU; Nordic; OECD];
  5. [3] Pennsylvania State University
  6. [NORA names: United States; America, North; OECD]

Abstract

This paper explores the similarity of the streamwise velocity fluctuations in turbulent channels. In the analysis, we employ a one-dimensional scalar variant of the proper orthogonal decomposition (POD). This approach naturally motivates the introduction of two different levels of similarity which we will refer to as strong and weak similarity. Strong similarity requires that the two-point correlation and thus, all POD modes, show Reynolds number similarity, while weak similarity only requires that the first few POD modes show similarity. As POD concerns information at more than one location, these similarities are more general than various similarities found in the literature concerning single-point flow statistics. We examine flows at Reτ=180, 540, 1000, and 5200. Strong similarity is observed in the viscous layer and the wake region, and weak similarity is found in both the viscous wall region and the outer part of the logarithmic layer. The presence of weak similarity suggests the existence of an extension to the law of the wall (LoW). We propose such an extension based on the results from the one-dimensional POD analysis. The usefulness of the LoW extension is then assessed by comparing flow reconstructions according to the conventional equilibrium LoW and the extended LoW. We show that the extended LoW provides accurate flow reconstructions in the wall layer, capturing fine-scale motions that are entirely missed by the equilibrium LoW.

Keywords

POD analysis, POD modes, Reynolds, Reynolds number similarity, Strong similarities, analysis, channel, correlation, equilibrium, extension, fine-scale motion, flow, flow reconstruction, flow statistics, fluctuations, information, introduction, layer, level of similarity, levels, literature, location, logarithmic layer, low extensibility, low-, mode, motion, pods, presence, reconstruction, region, results, scalar variant, similarity, statistically, streamwise, streamwise velocity fluctuations, turbulent channel, two-point correlations, use, variants, velocity fluctuations, viscous layer, viscous wall region, wake, wake region, wall, wall layers, wall region, weak similarity

Funders

  • Danish Ministry of Higher Education and Science
  • Danish Agency for Science and Higher Education
  • Office of Naval Research
  • United States Air Force Office of Scientific Research
  • United States Department of the Navy

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