Summary of Atmospheric Diffusion Theories

This result is identical to (17.43) if ft = 7) which provides a nice connection between the statistical theory of turbulent diffusion and the simple example considered earlier. 

Turbulent diffusion is concerned with the behavior of individual particles that are supposed to follow faithfully the airflow or, in principle, are simply marked minute elements of the air itself. Because of the inherently random character of atmospheric motions, one can never predict with certainty the distribution of concentration of marked particles emitted from a source. Although the basic equations describing turbulent diffusion are available, there does not exist a single mathematical model that can be used as a practical means of computing atmospheric concentrations over all ranges of conditions. 

The basic issues of interest with respect to the K theory are (1) Under what conditions on the source configuration and the turbulent field can this theory be applied (2) To what extent can the eddy diffusivities be specified in an a priori manner from measured properties of the turbulence The first question has been addressed in Section 17.4.2. In summary, the spatial and temporal scales of the turbulence should be small in comparison with the corresponding scales of the concentration field. 

The statistical theory is concerned with the actual velocities of individual particles in stationary, homogeneous turbulence. Under this assumption the statistics of the motion of one typical particle provides a statistical estimate of the behavior of all particles, and that of two particles an estimate of the behavior of a cluster of particles. In the atmosphere one may expect the cross-wind component (v) of turbulence to be nearly homogeneous since 

The deciding factor in judging the validity of a theory for atmospheric diffusion is the comparison of its predictions with experimental data. It must be kept in mind, however, that the theories we have discussed are based on predicting the ensemble mean concentration (c). whereas a single experimental observation constitutes only one sample from the hypothetically infinite ensemble of observations from that identical experiment. Thus it is not to be expected that any one realization should agree precisely with the predicted mean concentration even if the theory used is applicable to the set of conditions under which the experiment has been carried out. Nevertheless, because it is practically impossible to repeat an experiment more than a few times under identical conditions in the atmosphere, one must be content with at most a few experimental realizations when testing any available theory. 

It has been recognized that the simple exponential function, exp (—t/TL), where t is travel time from the source, appears to approximate Ru(t) rather well (Neumann 1978 Tennekes 1979), If 

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The aim of this article is to give a short outline of current theories of molecule formation and destruction in interstellar clouds, together with a short summary of the observational material which has been accumulated up to early 1981. Although this article will address itself predominantly to simple molecules a section on complex molecules has been added. We will, therefore, discuss some general aspects of cosmochemistry and then turn to molecule formation in diffuse clouds followed by a discussion of the chemistry of dense interstellar clouds. A section has been added to summarize recent observational results and theoretical proposals in understanding the formation of intermediate and complex molecules, an area of considerable current activity. Finally the article closes with a short summary of the molecular species found in planetary atmospheres and a short discussion of what the relation might be to the interstellar molecules. 

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