Combined role of advective pumping and mechanical dispersion on time scales of bed form-induced hyporheic exchange

This study analyzes the effect of advective pumping and pore scale dispersion on bed form-induced hyporheic exchange. Advection and dispersion play a competitive role in the exchange dynamics between the porous medium and the overlying stream: Advective fluxes first lead solutes deep into the bed and then back to the stream water, whereas dispersive fluxes favor the transfer of solutes deep into the bed leading to a permanent mass retention. The combined effect of advective exchange and dispersive fluxes produces complexity in the shape of the tails of the residence time distributions (RTDs), which follow at various stages of the process either a power law or an exponential decay. The seepage velocity induced by the stream gradient and, in case of a moving bed, the celerity of the translating bed forms limit the thickness of the advective hyporheic zone, inducing the RTDs to decrease rapidly at late time. This rapid decay can be preceded by a temporal region where the probability density functions (pdf's) tend to be inversely proportional to the square of time, and is followed by a region dominated by dispersion where the pdf's tend to be inversely proportional to the 3/2 power of time. The process shows distinct temporal ranges identified here by appropriate dimensionless parameters. Because of this complex exchange dynamics, models considering pure advection in the porous medium can significantly underestimate solute transfer at long time scales, whereas purely diffusive models of hyporheic exchange appear inadequate to represent the physical processes at an intermediate stage.