HORIZONTAL DIFFUSION 



emission has continued long enough for the distribution to reach a steady 

 state, the concentration is given approximately by 



The cross-wind concentration shows a 'normal' distribution of particles. 

 On the axis of the cloud (y = z = O) the concentration is given by the 

 simpler expression 



^ ttOux'" 



and because, according to the theory, m cannot exceed 2-0, the fall-off 

 in concentration on the axis of a point-source cloud cannot be more rapid 

 than the inverse square, no matter how turbulent the wind may be. 



(iii) A continuous line source at right-angles to the mean direction of the 

 wind, emitting (^particles per second per centimetre, and assuming the 

 line to be of infinite lencfth 



a \ z 



,2 



^ V(^)Cuxi™^''P\ C^x" 

 Values obtained by Sutton suggest that, as a rough and ready rule, 

 a finite line source behaves as a line of infinite length for distances of 

 travel of the cloud up to 4 times the actual length of the line. For points on 

 the xOy plane 



g 



^ V(^)Cux^'« 

 Sutton's statistical method does not exhaust the possible approaches 

 to the problem of atmospheric diffusion, and attempts to find a still more 

 useful model continue {see H. L. Green & Lane, 1957). From the theory 

 of T. von Karman, Calder (1952) developed an equation which is said to 

 give better predictions than Sutton's theory up to distances of 100 metres, 

 but not for greater distances. It is also difficult to apply Calder's equations 

 except to point sources. Another theory of dispersion, based on fluctuations 

 in wind direction, is outlined by Sheldon & Hewson (1958), and a recent 

 theory by Clarenburg (i960) will have to be taken into account. 



Field Experiments on Diffusion of Spore-clouds 



Several experiments have now been reported that give data from which 

 it is possible to test the applicability of eddy diffusion theories to diffusion 

 of the spore-cloud in a horizontal direction. 



Stepanov (1935) used artificial sources of spores that were liberated 

 at a point in the open air. He trapped the spores on glass slides, coated 

 with glycerine jelly, placed on the ground at various distances from the 

 source and in various directions relative to the wind. At the end of the 

 experiment cover-glasses were placed on the slides, and the number of 

 single spores per unit area was counted (spore clusters were disregarded). 



51 



