Semianalytical analysis of hyporheic flow induced by alternate bars

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We investigate the effects of alternate bar morphology on the hyporheic flow in gravel bed rivers. Our goal is to investigate the relations between residence time distribution of a conservative tracer and the parameters controlling bed form morphology. We assume homogeneous, isotropic or anisotropic hydraulic properties of the streambed sediment and constant flow regime in equilibrium with the bed form, which is considered fixed because its formation timescale is much longer than that of the subsurface flow. Under these assumptions, we solve the in‐stream and hyporheic flow fields analytically in a three‐dimensional domain. We approximate the former with the shallow water equations and model the latter as a Darcian flow. The two systems are linked through the hydraulic head distribution, which is predicted at the streambed by the surface model and applied as a boundary condition to the hyporheic flow model. We solve the solute transport equation in the hyporheic zone for a conservative tracer by means of particle tracking. Our model predicts that the mean value and variance of the hyporheic residence time depend on the alternate bar amplitude at equilibrium. This result is found to be applicable also to discharges that are lower (70% in our simulations) than the formative and submerge the bars entirely. Moreover, our analysis shows that 95% of the hyporheic flow is confined in a near‐bed layer, whose depth is about the width of the channel and shallows from low to steep gradient streams. This causes the hyporheic mean residence time to reach a threshold when the alluvial depth is deeper than the channel width. Our results also show that as the stream slope increases, the streamlines compact near to the streambed, thereby reducing the mean residence time and its variance. Finally, we observe that the hyporheic residence time of pulse injections of passive solutes is lognormally distributed, with the mean value depending in a simple manner on the amplitude of the alternate bars.