Effects of bar topography on hyporheic flow in gravel-bed rivers

Solute mass exchange between river stream and the underneath hyphorheic zone has a profound impact on the river ecosystem. In this study we analyse, by means of a Lagrangian approach, the effect of the hyporheic flow on solute transport along a river reach. Hyporheic flow is generated by an uneven distribution of the water pressure at the riverbed, which is tied dynamically with the bed topography. We focus here on a gravel-bed river developing free bars, assuming for simplicity that water discharge is constant and that the typical time scale of subsurface flow is small with respect to the morphological time scale controlling bar development and migration. In such a situation the bed topography can be assumed as fixed in time. Furthermore, since in most practical situations hyporheic flow is a small fraction of the total streamflow, surface and subsurface flows can be uncoupled, with the latter reducing to a Darcyan flow controlled by the water head at the riverbed. First the flow equation is solved analytically in a three dimensional domain which is vertically unbounded and with the horizontal dimensions equal to the bar wavelength and the river width. Then the velocity field is obtained through the Darcy’s equation. Solute transport in the hyporheic zone is then modeled numerically by particle tracking. We show that the residence time of the solute is Log-Normally distributed, with the mean depending on the same set of parameters describing the flow field and bed topography, namely the aspect ratio of the channel, the relative roughness and the parameter of Shields. This result is valid locally on a spatial scale of the order of the distance between two consecutive bars.