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Some data on the distance-neighbour function for relative diffusion

  • Paul J. Sullivan (a1) (a2)
Abstract

Repeated observations of dye plumes on Lake Huron are interpreted according to the theoretical proposals of Richardson (1926) and Batchelor (1952) about the characteristics of a dispersing cloud of marked fluid within a field of homogeneous turbulence. The results show the average of several instantaneous concentration distributions about their centre of gravity to be approximately Gaussian and the distance-neighbour function to be of approximately Gaussian form. The data are consistent with the theoretical description given by Batchelor, namely, \[ q(y,t) = (2\pi\overline{y^2})^{-\frac{1}{2}}\exp (-y^2/2\overline{y^2}),\quad (\overline{y^2} = (\frac{2}{3}\alpha t)^3), \] where q(y, t) is the distance-neighbour function and α is the constant of the ‘4/3-power law’. The average value of α is estimated to be 0·12 cm2/3 sec−1. The rate of turbulent energy dissipation in the near-surface currents of Lake Huron is estimated as ε ∼ 2·1 × 10−3 cm2sec−3.

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Batchelor, G. K. 1950 Quart. J. Roy. Met. Soc. 76, 133146.
Batchelor, G. K. 1952 Proc. Camb. Phil. Soc. 48, 345362.
Csanady, G. T. 1966 Proceedings of Conference on Great Lakes Research, 9th Ann Arbor, (Great Lakes Research Division Publication no. 15), 283293.
Ozmidov, R. V. 1957 Akademiia Nauk SSSR, Bulletin Geophysics Series, no. 6, 7383.
Ozmidov, R. V. 1960 Akademiia Nauk SSSR, Doklady Earth Sciences, Sections 126, 536538.
Ozmidov, R. V. 1961 Akademiia Nauk SSSR, Bulletin Geophysics Series, no. 8, 821823.
Richardson, L. F. 1926 Proc. Roy. Soc A 110, 709737.
Richardson, L. F. 1929 Beitr. Phys. frei Atmos. 15, 2429.
Richardson, L. F. & Stommel, H. 1948 J. Meteorol. 5, 238240.
Sullivan, P. J. 1965 M.Sc. Thesis, University of Waterloo.
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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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