Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-18T09:25:00.692Z Has data issue: false hasContentIssue false
  • English
  • Français

Two-point correlation in wall turbulence according to the attached-eddy hypothesis

Published online by Cambridge University Press:  26 May 2017

Hideaki Mouri Open the ORCID record for Hideaki Mouri [Opens in a new window]
Hideaki Mouri*
Affiliation:
Meteorological Research Institute, Nagamine, Tsukuba 305-0052, Japan
*
†Email address for correspondence: hmouri@mri-jma.go.jp
Get access Rights & Permissions [Opens in a new window]

Abstract

For the constant-stress layer of wall turbulence, two-point correlations of velocity fluctuations are studied theoretically by using the attached-eddy hypothesis, i.e. a phenomenological model of a random superposition of energy-containing eddies that are attached to the wall. While previous studies had invoked additional assumptions, we focus on the minimum assumptions of the hypothesis to derive the most general forms of the correlation functions. They would allow us to use or assess the hypothesis without any effect of those additional assumptions. We also study the energy spectra and the two-point correlations of the rate of momentum transfer and of the rate of energy dissipation.

JFM classification

Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 821 , 25 June 2017 , pp. 343 - 357
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.Google Scholar
Chung, D., Marusic, I., Monty, J. P., Vallikivi, M. & Smits, A. J. 2015 On the universality of inertial energy in the log layer of turbulent boundary layer and pipe flows. Exp. Fluids 56, 141.Google Scholar
Davidson, P. A. & Krogstad, P.-Å. 2014 A universal scaling for low-order structure functions in the log-law region of smooth- and rough-wall boundary layers. J. Fluid Mech. 752, 140–156.Google Scholar
Davidson, P. A., Nickels, T. B. & Krogstad, P.-Å. 2006 The logarithmic structure function law in wall-layer turbulence. J. Fluid Mech. 550, 51–60.Google Scholar
Fernholz, H. H. & Finley, P. J. 1996 The incompressible zero-pressure-gradient turbulent boundary layer: an assessment of the data. Prog. Aerosp. Sci. 32, 245–311.Google Scholar
Hultmark, M., Vallikivi, M., Bailey, S. C. C. & Smits, A. J. 2012 Turbulent pipe flow at extreme Reynolds numbers. Phys. Rev. Lett. 108, 094501.CrossRefGoogle ScholarPubMed
Jiménez, J. & Hoyas, S. 2008 Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215–236.Google Scholar
Lee, M. & Moser, R. D. 2015 Direct numerical simulation of turbulent channel flow up to Re 𝜏 ≈ 5200. J. Fluid Mech. 774, 395–415.Google Scholar
Marusic, I. 2001 On the role of large-scale structures in wall turbulence. Phys. Fluids 13, 735–743.Google Scholar
Marusic, I., Monty, J. P., Hultmark, M. & Smits, A. J. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3.Google Scholar
Meneveau, C. & Marusic, I. 2013 Generalized logarithmic law for high-order moments in turbulent boundary layers. J. Fluid Mech. 719, R1.Google Scholar
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics, vol. I, pp. 222–237, 249–256. MIT Press.Google Scholar
Mouri, H., Takaoka, M., Hori, A. & Kawashima, Y. 2006 On Landau’s prediction for large-scale fluctuation of turbulence energy dissipation. Phys. Fluids 18, 015103.Google Scholar
Perry, A. E. & Abell, C. J. 1977 Asymptotic similarity of turbulence structures in smooth- and rough-walled pipes. J. Fluid Mech. 79, 785–799.Google Scholar
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173–217.Google Scholar
Sillero, J. A., Jiménez, J. & Moser, R. D. 2013 One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to 𝛿+ ≈ 2000. Phys. Fluids 25, 105102.Google Scholar
Townsend, A. A. 1961 Equilibrium layers and wall turbulence. J. Fluid Mech. 11, 97–120.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. pp. 150–156. Cambridge University Press.Google Scholar
Vallikivi, M., Ganapathisubramani, B. & Smits, A. J. 2015 Spectral scaling in boundary layers and pipes at very high Reynolds numbers. J. Fluid Mech. 771, 303–326.Google Scholar
Wyngaard, J. C. 2004 Toward numerical modeling in the ‘terra incognita’. J. Atmos. Sci. 61, 1816–1826.Google Scholar