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Constraints on the wall layer in turbulent pipe flow

Published online by Cambridge University Press:  01 July 2022

G.G. Rooney Open the ORCID record for G.G. Rooney [Opens in a new window]
G.G. Rooney*
Affiliation:
Met Office, FitzRoy Road, Exeter EX1 3PB, UK School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
*
†Email address for correspondence: gabriel.rooney@metoffice.gov.uk
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Abstract

Dynamical constraints on the wall layer in turbulent pipe flow imply both a narrow peak in the streamwise component of the turbulent Lamb vector near the wall, and a scaling of the wall layer depth proportional to the depth of the viscous sublayer. An approximation of the Lamb vector distribution, which equates to the gradient of Reynolds stress, is proposed. Hence the equation for streamwise mean flow may be integrated to obtain an expression for the velocity profile in the wall layer.

JFM classification

Turbulent Flows: Pipe flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 944 , 10 August 2022 , A32
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Copyright
© Crown Copyright - Met Office, 2022. Published by Cambridge University Press

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References

REFERENCES

Corrsin, S. 1961 Turbulent flow. Am. Sci. 49 (3), 300–325.Google Scholar
Hamman, C.W., Klewicki, J.C. & Kirby, R.M. 2008 On the Lamb vector divergence in Navier–Stokes flows. J. Fluid Mech. 610, 261–284.CrossRefGoogle Scholar
Hinze, J.O. 1959 Turbulence. McGraw-Hill.Google Scholar
Hof, B., De Lozar, A., Avila, M., Tu, X. & Schneider, T.M. 2010 Eliminating turbulence in spatially intermittent flows. Science 327 (5972), 1491–1494.CrossRefGoogle ScholarPubMed
von Kármán, T. 1931 Mechanical similitude and turbulence. NACA Tech. Rep. NACA-TM-611. National Advisory Committee for Aeronautics, USA, English translation from Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, 1930.Google Scholar
Klewicki, J.C. 2021 Properties of turbulent channel flow similarity solutions. J. Fluid Mech. 915, A39.CrossRefGoogle Scholar
Prandtl, L. 1933 Recent results of turbulence research. NACA Tech. Rep. NACA-TM-720. National Advisory Committee for Aeronautics, USA, English translation from Zeitschrift des Vereines Deutscher Ingenieure, 1933.Google Scholar
Tennekes, H. & Lumley, J.L. 1972 A First Course in Turbulence. MIT.CrossRefGoogle Scholar
Townsend, A.A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Wu, X. & Moin, P. 2008 A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow. J. Fluid Mech. 608, 81–112 (Data are available from https://ctr.stanford.edu/research-data).CrossRefGoogle Scholar