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), 10 5 cm. 2 sec. -1 when gusts are smoothed out of the mean wind (Akerblom, G. I. Taylor, Hesselberg, etc.), 10 8 cm. 2 sec. -1 when the means extend over a time comparable with 4 hours (L. F. Richardson and D. Proctor), 10 11 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.