HORIZONTAL DIFFUSION 



In the long run a more ambitious approach seems essential, with the 

 aim of developing formulae whose parameters correspond to factors of the 

 environment, and which take into account the total number of microbes 

 liberated (if known), allow for variations in weather, and use a standard 

 unit of distance. 



Diffusion as a Result of Atmospheric Turblt^ence 



Watching the drift of smoke from a bonfire or factory will convince 

 the observer that wind, instead of having a steady streaming motion, is 

 characteristically turbulent as described in Chapter III. According to 

 Brunt (1934), large numbers of small-scale eddies, whose periods are of 

 the order of i second, are usually present in the turbulent boundary 

 layer, and at least two-thirds of the eddying energy is associated with 

 eddies of less than 5 seconds. The action of these very numerous eddies 

 of varying size on the very numerous spores produced from plant sources, 

 makes some regularit}' in the dispersal pattern possible. 



The study of eddy diffusion has proved difhcult, but it provides the 

 most promising approach to the elucidation of dispersal. Before describing 

 the methods in detail, a few general notions — familiar to physicists, but 

 mostly unfamiliar to biologists — must be introduced. 



We are attempting to discover laws governing spore diffusion in the 

 atmosphere. In nature this is often a complex process, as there are obstacles 

 preventing the free flow of air. We therefore use a device familiar to 

 physicists — making a simplified model in the hope that, if we can under- 

 stand the process of diffusion under simple conditions, we shall be able 

 to attack the more complex situations found in nature. The assumptions 

 we have to make for a simplified model are as follows. 



(i) The field. Diffusion is assumed to be taking place in three dimen- 

 sions in the atmosphere over a plane surface which is of indefinite extent, 

 free from topographical irregularities — not necessarily 'smooth', but, if 

 aerod}'namically rough, then uniformly so. 



(ii) Co-ordinates. To describe movement over the plane surface we 

 need a system of co-ordinates. Their origin, 'O', is conveniently taken to 

 be the point of liberation of the pollen or spores. The 'x'-axis is horizontal 

 and positive in the down-wind direction, and the 'y'-axis is also hori- 

 zontal but at right-angles to the direction of the wind. Lengths above and 

 below the origin are measured on the vertical 'z'-axis. 



(iii) Sources. Particles are liberated from a source. The simplest 

 form of source is a 'point source', and this may either liberate a number 

 'Q^ of spores at a single instant (an 'instantaneous point source'), or it may 

 be a 'continuous point source' emitting Oospores per second. 



Instead of a point source we may have a 'line source'. For simplicity 

 we assume that the line is horizontal, and is emitting Oospores per centi- 

 metre of its (effectively) infinite length. The line source in turn may be 



47 



