Atmospheric diffusion shown on a distance-neighbour graph

Abstract

If the diffusivity K of a substance whose mass per volume of atmosphere is χ be defined by an equation of Fick’s type ū ∂χ/∂x + v- ∂χ/∂y + w- ∂χ/∂z + ∂χ/∂t = ∂/∂x (K ∂χ/∂x) + ∂/∂y (K ∂χ/∂y) ∂/∂z (K ∂χ/∂z), (1) x, y, z, t being Cartesian co-ordinates and time, ū, v-, w- being the components of mean velocity, then the measured values of K have been found to be 0·2 cm.2 sec.-1 in capillary tubes (Kaye and Laby’s Tables), 105 cm.2 sec.-1 when gusts are smoothed out of the mean wind (Akerblom, G. I. Taylor, Hesselberg, etc.), 108 cm.2 sec.-1 when the means extend over a time comparable with 4 hours (L. F. Richardson and D. Proctor), 1011 cm.2 sec.-1 when the mean wind is taken to be the general circulation characteristic of the latitude (Defant). Thus the so-called constant K varies in a ratio of 2 to a billion. The present paper records an attempt to comprehend all this range of diffusivity in one coherent scheme. Lest the method which I shall adopt should strike the reader as queer and roundabout, I wish to justify it by showing first why some known methods are in difficulties.