Some data on the distance-neighbour function for relative diffusion

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.