A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough UniversityMany contaminants exhibit decay. Decay mechanisms include consumption by bacteria\ud or radioactive decay (temporal decay uniform across the flow), heat loss or evaporation\ud through the surface (decay decreasing with depth), and break up by turbulence (decay\ud proportional to the product of velocity and depth). This thesis investigates how the decay\ud of pollutants in a river effects the dilution process and the selection of discharge siting to\ud achieve minimum environmental impact.\ud For a non-symmetric river with non-reversing flow, exact solutions are presented that\ud illustrate the effect on the optimal position for a steady discharge of cross-channel variation\ud in the decay (uniform, decreasing or increasing with depth). The optimal position is shifted\ud to deeper or to shallower water accordingly as the temporal decay divided by flow speed\ud decreases or increases with water depth.\ud When advection dominates diffusion, there are special directions (rays) along which information\ud is carried. For steady, unstratified, plane parallel flow, the effects of decay are\ud allowed for in specifying these special directions. Two special cases are considered. Firstly,\ud for a smoothly varying depth, a general result has been derived for the curvature of the\ud rays as effected by spatial non-uniformity in decay, mixing, flow speed and flow direction.\ud Secondly, for discontinuous variations in depth, diffusivity, velocity and decay, approximate\ud concentration formulae are derived. Ray bending indicates that the downstream propagation\ud of pollutant is principally in the low-decay region.\ud Computational results are used to give pictorial illustration of the concentration distributions\ud and of the difference between discharging at non-optimal and optimal sites
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