Non-Fickian dispersion in open-channel flow over a porous bed

Solute transport in rivers has been traditionally represented using one-dimensional models assuming advection and Fickian dispersion along the main flow direction and transient storage in surface and subsurface dead zones. Experimental evidence from several stream tracer studies has shown that the longitudinal scaling of the moments of the breakthrough curves (BTCs) is inconsistent with classic 1-D solute transport models. In this work, simulations of advection and diffusion in a 2-D and 3-D channel flow over a porous bed are presented assuming an exponentially attenuated profile of the transverse mixing coefficient in the porous medium, as suggested by recent experimental and numerical studies. It is shown that the longitudinal transport in the channel is superdiffusive, and the skewness of the concentration distributions can be almost constant over a broad temporal range, with no sign of approaching zero at large times. A sensitivity analysis shows that, at large times, longitudinal dispersion is controlled by the cross-sectional profile of the in-bed transverse mixing coefficient, and by the difference between the average velocity in the channel and in the porous bed. The normalized concentration distributions can be approximated by beta-distributions with time-dependent parameters, and relationships are derived between the scaling of the parameters under power-law approximation and the scaling of the spatial and temporal moments. The results provide new insights into the physical mechanisms that control the anomalous scaling of the moments observed in field tracer studies and opens new possibilities for predictive and inverse modeling of transport processes in rivers and their catchments.