Some data on the distance-neighbour function for relative diffusion

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 cm^2/3 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.