Longitudinal dispersion of a buoyant contaminant in a shallow channel

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Abstract
A nonlinear diffusion equation is derived for the longitudinal dispersion of a buoyant pollutant in a slowly varying current. The essential simplifying feature is that the (non-uniform) water depth is assumed to be much less than the channel width. It is found that for small concentration gradients there is a transverse circulation which leads to a marked reduction in the longitudinal dispersion. For large concentration gradients the longitudinal circulation predominates and the longitudinal dispersion increases.