Multi-scale analysis of contaminant transport in the ice-covered channel flows with bed absorption

Rivers in high-latitude regions frequently undergo a process of freezing during the winter, forming an ice cover on the water surface that effectively cuts off the exchange between the water body and the atmosphere. This results in a notable reduction in dissolved oxygen levels within the water body and hence makes it challenging for contaminants to volatilize and degrade. As a thorough understanding of contaminant transport in ice-covered channels is essential for managing water pollution in cold regions, this study concentrates on the issue of contaminant dispersion in such a channel with bed absorption under laminar flow conditions. An analytical solution for the temporal and spatial evolutions of concentration distribution is deduced here by solving the two-dimensional advection–diffusion equation using the multi-scale perturbation method. The satisfactory agreement between the analytical results of mean concentration distributions and the corresponding numerical results obtained from the finite difference method validates the reliability of the analytical solution. Subsequently, the spatiotemporal evolution of contaminants in ice-covered channels is evaluated by applying the validated analytical solution under the coupled effects of advective and molecular diffusion. Results indicate that the enhancement of the advective effect facilitates the longitudinal diffusion of contaminants and thus the corresponding peak concentrations are reduced. The vertical dispersion of contaminants exhibits a pronounced nonuniform distribution and the time scale required to reach the uniform distribution is closely related to the cross-sectional position and the absorption intensity. The maximum vertical concentration variation rate in ice-covered channels consistently occurs at the upstream cross-section as the time scale increases, which is a significant contrast to the contaminant dispersion observed in open-channel flows. This study can provide some reference for assessing the peak concentration locations and durations of contaminant clouds in ice-covered channels.