HORIZONTAL DIFFUSION 



cloud has travelled farther down-wind it will have a new mean position, 

 and during the time the cloud has been travelling it will have been further 

 diluted by eddies, its particles will have got farther apart, and consequently 

 their standard deviation will have become larger. 



The next problem is to find a relation between the standard deviation 

 and the distance travelled. How does a grow as x grows ? This is a prob- 

 lem that has excited the interest of many workers since the First World 

 War, who were attempting to predict the concentration of gas clouds, 

 smoke screens, smoke trails, and crop pathogens. 



The pioneer in the subject was the Austrian meteorologist, Wilhelm 

 Schmidt (191 8, 1925), who put forward a theory similar to those being 

 developed almost simultaneously in Britain by G. I. Taylor and L. F. 

 Richardson. Schmidt supposed that, with a given state of turbulence of 

 the air, dijffusion of particles proceeds like the diffusion of heat in a solid, 

 but with an atmospheric turbulence coefficient A/p replacing the coeffi- 

 cient of thermal conductivity. He showed that for these conditions 



CT^ = 2(A//3)t, where t = time. 



His work is now mainly of historical interest, but we should note one 

 interesting feature : according to Schmidt the standard deviation squared 

 is proportional to the time during which diffiasion has been taking place, 

 so that on his theory the standard deviation will not be constant at a given 

 distance, but will depend on the time taken to reach that distance, i.e. 

 upon the speed of the wind. 



Schmidt also assumed that the particles in the diffijsing cloud are 

 brought to ground-level by their fall under gravity, and he used measured 

 values of terminal velocity to fix dispersal limits for various organisms 

 (cf. Table XXVII). 



Sutton (1932) recognized that diffiasion in the atmosphere diffisrs 

 from molecular diffusion of heat in a solid in one important respect. 

 Diffusion in a solid is constant (depending on the mean free path of the 

 molecules) however long the diffusion has been going on. Diffusion in the 

 atmosphere is much more complex, because atmospheric eddies are of a 

 vast range of sizes, varying from a centimetre or so up to eddies that we 

 recognize as fluctuations in wind direction, and even to cyclones and anti- 

 cyclones. Sutton realized that the size of eddy effective at a given moment 

 in diluting a cloud is of the same order as the size of the cloud itself at that 

 moment. Thus a i-cm. eddy would not effectively dilute a cloud i-metre 

 in diameter, and a 1,000-metre eddy would merely carry a i-metre cloud 

 around bodily without diluting it. The eddy that dilutes a i-metre cloud 

 is itself of the order of i metre. This led Sutton to an equation for the 

 standard deviation which is fundamentally different from that of Schmidt : 



a2 = iC2(ut)"\ 



where t = time; u = wind-speed; 'C is a new coefficient of diffusion 

 D 49 



