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The inertial subrange in turbulent pipe flow: centreline

Published online by Cambridge University Press:  11 January 2016

J. F. Morrison ,
M. Vallikivi  and
A. J. Smits
J. F. Morrison*
Affiliation:
Department of Aeronautics, Imperial College, London SW7 2AZ, UK
M. Vallikivi
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
A. J. Smits
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA Department of Mechanical and Aerospace Engineering, Monash University, VIC 3800, Australia
*
†Email address for correspondence: [email protected]
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Abstract

The inertial-subrange scaling of the axial velocity component is examined for the centreline of turbulent pipe flow for Reynolds numbers in the range $249\leqslant Re_{{\it\lambda}}\leqslant 986$. Estimates of the dissipation rate are made by both integration of the one-dimensional dissipation spectrum and the third-order moment of the structure function. In neither case does the non-dimensional dissipation rate asymptote to a constant; rather than decreasing, it increases indefinitely with Reynolds number. Complete similarity of the inertial range spectra is not evident: there is little support for the hypotheses of Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 32, 1941a, pp. 16–18; Dokl. Akad. Nauk SSSR, vol. 30, 1941b, pp. 301–305) and the effects of Reynolds number are not well represented by Kolmogorov’s ‘extended similarity hypothesis’ (J. Fluid Mech., vol. 13, 1962, pp. 82–85). The second-order moment of the structure function does not show a constant value, even when compensated by the extended similarity hypothesis. When corrected for the effects of finite Reynolds number, the third-order moments of the structure function accurately support the ‘four-fifths law’, but they do not show a clear plateau. In common with recent work in grid turbulence, non-equilibrium effects can be represented by a heuristic scaling that includes a global Reynolds number as well as a local one. It is likely that non-equilibrium effects appear to be particular to the nature of the boundary conditions. Here, the principal effects of the boundary conditions appear through finite turbulent transport at the pipe centreline, which constitutes a source or a sink at each wavenumber.

JFM classification

Turbulent Flows: Isotropic turbulence Boundary Layers: Pipe flow boundary layer Turbulent Flows: Turbulence theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 788 , 10 February 2016 , pp. 602 - 613
Copyright
© 2016 Cambridge University Press 

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