Research papersConcentration distribution of environmental dispersion in a wetland flow: Extended solution

•To rigorously extend the first order estimate of vertical distribution on small time scale.•To account for high order effects as skewness and kurtosis by the Aris-Gill expansion method.•To illustrate the impact of damping vegetation factor on performance of series expansion and contaminant transport in wetland flows.

Hydrological processes of contaminant transport in wetland flows are characterized by environmental dispersion. For concentration distribution of scalar dispersion, the preliminary estimate of vertical distribution (Wu et al., 2015) on small time scale is rigorously extended to account for high order effects as skewness and kurtosis. Based on a combination of Aris' method of concentration moments and Gill's generalized dispersion model, up to fourth order terms of vertical distribution functions and full-time two-dimensional concentration distribution are derived. The increments of damping factor, mainly representing the density of vegetation in wetlands, is shown to strengthen the mean distribution asymmetry and reduce the longitudinal dispersivity (with respect to skewness and kurtosis), and to increase the non-uniformity of vertical distribution. Therefore, dense vegetation corresponding to a large damping factor will postpone the time when Taylor's dispersion model holds, and the first order approximation becomes rough on small time scale, demanding higher order modifications. The results provide more detailed and more accurate analytical solution for the typical environmental dispersion in wetland flows.