The evolution of the mass of a “preserved” chemical spill as it moves with the river current

A quantitative model describing the process of turbulent diffusion of the liquid mass of a chemical spill as it moves with the river current is constructed. The model contains a representation of the tensor components of the turbulent diffusion coefficients in terms of the initial parameters of the problem – the breadth and depth of the water flow in the river and the average flow velocity. According to the model proposed, the process consists of three stages: the initial, rapid stage, in which, owing to turbulent diffusion along the vertical coordinate, the pollutant concentration distribution evens out along this coordinate; the intermediate stage, in which, because of turbulent diffusion along the horizontal coordinates, the concentrations are likewise evened out along the horizontal coordinate transverse to the river channel; and the third, longest and slowest stage, in which quasi-one-dimensional turbulent diffusion occurs along the longitudinal (channel) coordinate, describing the “spreading” of the chemical slick (volume) carried downstream. Simple explicit formulae are obtained for a quantitative estimation of the characteristic pollutant concentrations at the end of the first and second stages and their “attenuation” with increasing distance as the chemical slick drifts with the current, and also the increasing longitudinal dimension of the slick with distance downstream.