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The mean logarithm emerges with selfsimilar energy balance.
Abstract
The attached eddy hypothesis of Townsend (The Structure of Turbulent Shear Flow, 1956, Cambridge University Press) states that the logarithmic mean velocity admits selfsimilar energycontaining eddies which scale with the distance from the wall. Over the past decade, there has been a significant amount of evidence supporting the hypothesis, placing it to be the central platform for the statistical description of the general organisation of coherent structures in wallbounded turbulent shear flows. Nevertheless, the most fundamental question, namely why the hypothesis has to be true, has remained unanswered over many decades. Under the assumption that the integral length scale is proportional to the distance from the wall y , in the present study we analytically demonstrate that the mean velocity is a logarithmic function of y if and only if the energy balance at the integral length scale is selfsimilar with respect to y , providing a theoretical basis for the attached eddy hypothesis. The analysis is subsequently verified with the data from a direct numerical simulation of incompressible channel flow at the friction Reynolds number Reτ≃5200 (Lee & Moser, J. Fluid Mech., vol. 774, 2015, pp. 395–415).
 Authors:

 Imperial College, London (United Kingdom)
 Sandia National Lab. (SNLCA), Livermore, CA (United States)
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLCA), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1671808
 Report Number(s):
 SAND20209115J
Journal ID: ISSN 00221120; 690287
 Grant/Contract Number:
 AC0494AL85000
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Fluid Mechanics
 Additional Journal Information:
 Journal Volume: 903; Journal ID: ISSN 00221120
 Country of Publication:
 United States
 Language:
 English
 Subject:
 42 ENGINEERING
Citation Formats
Hwang, Yongyun, and Lee, Myoungkyu. The mean logarithm emerges with selfsimilar energy balance.. United States: N. p., 2020.
Web. https://doi.org/10.1017/jfm.2020.730.
Hwang, Yongyun, & Lee, Myoungkyu. The mean logarithm emerges with selfsimilar energy balance.. United States. https://doi.org/10.1017/jfm.2020.730
Hwang, Yongyun, and Lee, Myoungkyu. Thu .
"The mean logarithm emerges with selfsimilar energy balance.". United States. https://doi.org/10.1017/jfm.2020.730.
@article{osti_1671808,
title = {The mean logarithm emerges with selfsimilar energy balance.},
author = {Hwang, Yongyun and Lee, Myoungkyu},
abstractNote = {The attached eddy hypothesis of Townsend (The Structure of Turbulent Shear Flow, 1956, Cambridge University Press) states that the logarithmic mean velocity admits selfsimilar energycontaining eddies which scale with the distance from the wall. Over the past decade, there has been a significant amount of evidence supporting the hypothesis, placing it to be the central platform for the statistical description of the general organisation of coherent structures in wallbounded turbulent shear flows. Nevertheless, the most fundamental question, namely why the hypothesis has to be true, has remained unanswered over many decades. Under the assumption that the integral length scale is proportional to the distance from the wall y , in the present study we analytically demonstrate that the mean velocity is a logarithmic function of y if and only if the energy balance at the integral length scale is selfsimilar with respect to y , providing a theoretical basis for the attached eddy hypothesis. The analysis is subsequently verified with the data from a direct numerical simulation of incompressible channel flow at the friction Reynolds number Reτ≃5200 (Lee & Moser, J. Fluid Mech., vol. 774, 2015, pp. 395–415).},
doi = {10.1017/jfm.2020.730},
journal = {Journal of Fluid Mechanics},
number = ,
volume = 903,
place = {United States},
year = {2020},
month = {10}
}
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