Effects of contaminant decay on the diffusion centre of a river

Many contaminants exhibit decay (radioactive decay, consumed by bacteria, heat loss or evaporation through the surface, dissolution by turbulence). For a non-symmetric river with non-reversing flow, the effects of decay are allowed for in specifying the diffusion centre i.e. the optimal postion for a steady discharge. Three families of exact solutions are presented that illustrate the effect on the diffusion centre of cross-channel variation in the decay (uniform, decreasing or increasing with depth). The diffusion centre is shifted to deeper or to shallower water accordingly as the temporal decay divided by flow speed decreases or increases with water depth.