Journal of Fluid Mechanics

Some data on the distance-neighbour function for relative diffusion

Paul J.  Sullivan a1p1
a1 W.M. Keck Laboratory, California Institute of Technology, Pasadena, California

Article author query
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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 [similar] 2·1 × 10−3 cm2sec−3.

(Published Online March 29 2006)
(Received October 3 1969)
(Revised January 9 1971)

p1 Permanent address: Department of Applied Mathematics, The University of Western Ontario, London 72, Ontario, Canada.