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The dispersion of marked fluid in turbulent shear flow

  • J. W. Elder (a1)
Abstract

The analysis used by Taylor (1954) and based on the Reynolds analogy has been extended to describe the diffusion of marked fluid in the turbulent flow in an open channel. The coefficient of longitudinal diffusion arising from the combined action of turbulent lateral diffusion and convection by the mean flow is computed to be 5·9uτh, where h is the depth of fluid and uτ the friction velocity. This is in agreement with experiments described herein. The laterla diffusion coefficient is found by experiment to be 0·23uτh, which is three times larger than the value obtained by the assumption of isotropy. The same analysis can be used to describe the longitudinal dispersion of discrete particles, both of zero buoyancy and of finite buoyancy, and comparison is made with observations by Batchelor, Binnie & Phillips (1955) and Binnie & Phillips (1958).

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References
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Batchelor, G. K. & Townsend, A. A. 1956 Article in Surveys in Mechanics (eds. G. K. Batchelor and R. M. Davies). Cambridge University Press.
Binnie, A. M., Davies, P. A. O. L. & Orkney, J. C. 1955 Proc. Roy. Soc. A, 230, 225.
Binnie, A. M. & Phillips, O. M. 1958 J. Fluid Mech. 4, 87.
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Klebanoff, P. S. 1954 NACA Tech. Note 3178.
Levenspiel, O. & Smith, W. K. 1957 Chem. Engng Sci. 6, 227.
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Rouse, H. 1937 Trans. Amer. Soc. Civ. Engrs, 102, 534.
Taylor, G. I. 1922 Proc. Lond. Math. Soc. (2), 20, 196.
Taylor, G. I. 1953 Proc. Roy. Soc. A, 219, 186; see also 225, 473.
Taylor, G. I. 1954 Proc. Roy. Soc. A, 223, 446.
Vanoni, V. A. 1946 Trans. Amer. Soc. Civ. Engrs, 111, 67.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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