Date of Award


Degree Type


Degree Name

Doctor of Philosophy


This thesis considers the spread of contaminant after the release of a cloud of toxic gas into the atmosphere. A new measure, the Expected Mass Fraction (EMF), presents an improvement over the mean dosage as an indicator of the risk associated with the cloud release. The study shows that the variability of estimates of the EMF should be comparable to that of the dosage, so that reliable evaluation should be possible in many situations. The theory is based on the Chatwin-Sullivan {dollar}\alpha{dollar}-{dollar}\beta{dollar} formulation, which relates the mean concentration to the moments of the probability density function of the concentration. The proposed new measure is validated with data from a wind tunnel study performed at the Warren Spring Laboratory in Great Britain. The thesis concludes with an extension of the theory to incorporate G. K. Batchelor's analysis of the rate of growth of a cloud released at the earth's surface into the atmospheric boundary layer. These results should have application in the analysis of risk from accidental release of toxic gases into the atmosphere. By extending the information available to include predictions of concentrations of contaminant, the analysis can assist in analyzing other problems such as flammability. The same methodology should also find application in dissipation problems in other turbulent flows, such as lakes, rivers or oceans.



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