Geophysical Research Letters

Hyporheic flow under periodic bed forms influenced by low-density gradients

Authors

  • Guangqiu Jin,

    1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, China
    2. Centre for Eco-Environment Modelling, College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, China
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  • Hongwu Tang,

    1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, China
    2. Centre for Eco-Environment Modelling, College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, China
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  • Ling Li,

    1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, China
    2. National Centre for Groundwater Research and Training, School of Civil Engineering, University of Queensland, Brisbane, Queensland, Australia
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  • D. A. Barry

    1. Laboratoire de Technologie Écologique, Institut d'Ingénierie de l'Environnement, Faculté de l'Environnement Naturel, Architectural et Construit, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
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Abstract

[1] Small density variations across streambeds due to low solute concentrations in stream water exist commonly in streams and rivers. Using laboratory experiments and numerical modeling, we demonstrated that even small density variations can influence hyporheic flow in streambeds with periodic bed forms. The circulating pore water flow patterns in the bed were modified constantly as the solute front moved downward. Density-induced head gradients eventually overwhelmed the regional hydraulic gradient and drove the circulating flow below a hydraulic divide that would have existed without the density influence. The density-modified hyporheic flow provided a relatively fast solute transport mechanism and enhanced the overall mass exchange between the stream and bed. These results highlight the important role of weak, upward density gradients in modulating hyporheic flow.

1. Introduction

[2] Hyporheic flow induces significant solute exchange across streambeds, affecting water quality in both the stream and bed (Figure S1a in the auxiliary material) [Hill et al., 1998; Pretty et al., 2006]. Numerous investigations have been carried out to examine hyporheic flow and associated solute transport processes under the influences of stream water flow, stream network morphology and bed forms, sediment properties, and regional hydraulic gradients in the shallow aquifer [Bencala et al., 1984; Cardenas et al., 2004; Salehin et al., 2004; Boano et al., 2006; Packman et al., 2006; Cardenas, 2008; Revelli et al., 2008]. Many studies focused on hyporheic flow driven by hydraulic head gradients due to stream flow and bed form interactions (Figure S1b) [Elliott and Brooks, 1997; Cardenas and Wilson, 2007; Jin et al., 2010].

[3] Laboratory experiments have been conducted to quantify the hyporheic exchange using salt or other solutes as the tracer [Marion et al., 2003; Salehin et al., 2004; Jin et al., 2010]. The solutes in these experiments were typically released at low concentrations, a common condition that also exists in natural streams and rivers [Boano et al., 2009]. The low solute concentrations led to only small density variations between the stream water and underlying pore water in the bed [Boano et al., 2009]. Such small density variations have been assumed to have little effect on the hyporheic flow and solute transport, and hence have been largely neglected [Marion et al., 2003; Salehin et al., 2004; Jin et al., 2010]. However, Boano et al. [2009] demonstrated that the weak density gradient due to low solute concentrations in the stream water was capable of driving significant hyporheic exchange between a model stream and its flat streambed in a flume experiment. The flow driven by the density gradient provided an advective solute transport mechanism, overwhelming the diffusive transport.

[4] The purpose of this study was to examine effects of low-density gradients on hyporheic flow and solute transport processes in a streambed with periodic bed forms. In contrast to a flat bed, a streambed with periodic bed forms is subjected to the influence of relatively strong hydraulic head gradients generated by stream flow and bed form interactions (Figure S1). The flow and associated solute transport driven by such gradients dominate the hyporheic exchange processes and have been the focus of many previous studies [Elliott and Brooks, 1997; Salehin et al., 2004; Jin et al., 2010]. The question addressed here is whether the relatively weak density gradients impose modulating effects on the hyporheic flow. We are particularly interested in how flow and solute transport behave under the influence of density gradients in the deep area of the hyporheic zone where a hydraulic divide would exist without the density effects due to the presence of an underflow (Figure S1c). Previous studies have shown that, constrained by this hydraulic divide, solute transport to the deeper area occurs slowly through diffusion/dispersion [Bottacin-Busolin and Marion, 2010; Jin et al., 2010]. Here we address the question of whether density gradients induce flow and advective transport that enhances solute transfer to the deeper area (Figure S1d).

[5] To address this question, laboratory flume experiments similar to those of Jin et al. [2010] were conducted with continuous measurements of solute concentrations in the stream and pore water samples collected from two vertical arrays of sampling ports at different depths (100-μl solution taken for each sample), located at the stoss and lee slopes of a bed form (Figure S1c). These measurements allowed assessment of density effects on the downward movement of the solute front. In simulating the experiments, we employed both constant-density and variable-density models. Comparison between predictions of these two models and the experimental data enabled the discernment of density effects on the hyporheic flow and solute transport processes.

2. Laboratory Experiments and Numerical Simulations

[6] The experimental set-up follows that of Jin et al. [2010] based on a circulating flume system. To avoid possible initial contamination of the pore water by residual materials in the sediment prior to the experiment, artificial sand supplied by Nanjing Ninglei Sand and Stone Factory (China) was used for the streambed. Our previous experiments conducted with river sand did not reveal properly the density effect [Jin et al., 2010]; we suspect that residual materials in the river sand used might have raised the initial density of pore water, reducing the density contrast between the stream water and pore water to a minor level in the experiment. The artificial sand used for the present experiment was sieved between 30 mesh (D1 = 0.60 mm) and 60 mesh sieves (D2 = 0.25 mm), and made of 99% pure silicon dioxide. The bulk porosity was measured to be 0.46 using the water evaporation method. The saturated hydraulic conductivity, measured using the constant-head method [Chinese National Standard, 1999], was found to be around 4.35 × 10−3 m s−1. The sand was thoroughly cleaned before all experiments following the method described by Jin et al. [2010]. The average flow velocity, water depth and pH in the stream water were 12.26 cm s−1, 10.21 cm and ∼6.8, respectively. The experiment started with freshwater in the streambed and a relatively low initial solute concentration (1.73 kg m−3) in the stream water. As the exchange between the stream and bed took place, the solute concentration in the stream water decreased but remained spatially uniform due to mixing through the flume circulation system [Jin et al., 2010].

[7] A one-way sequential coupling method was used to simulate the stream water flow, and pore water flow and solute transport in the streambed. First, the stream water flow was computed using the CFD package FLUENT based on the Reynolds-averaged Navier-Stokes equations together with the k-ω turbulence closure scheme [Jin et al., 2010]. The predicted pressure at the sediment-water interface was then input into a COMSOL-based model as boundary conditions to drive coupled pore water flow and solute transport in the streambed [Jin et al., 2010].

[8] Density-dependent fluid flow in the bed is governed by [COMSOL, 2006]:

equation image

where hf (m), the equivalent freshwater hydraulic head, is given by p/ρg + Dv with p (Pa) being the pore water pressure and Dv (m) the vertical coordinate directing upward; C (kg m−3) is the solute concentration; ρ (kg m−3) is the fluid density; ρf (1000 kg m−3) is the freshwater density; S (m−1) is the equivalent freshwater specific storativity, representing storage due to compressibility of the fluid and porous medium [Bear, 1972]; t (s) is the time; θ is the porosity; and K (m s−1) is the equivalent freshwater hydraulic conductivity. The density of the fluid as a function of concentration is given by:

equation image

where γ is 0.7143 for the salt solution applied in the experiments [Langevin et al., 2003].

[9] The second term on the left hand side of equation (1) represents change in storage due to concentration variations and is likely to dominate the compressible storage term due to the relatively small compressibility of the artificial sand used in the study [Bear, 1972]. Coupled with the pore water flow, the salt solute transport in the porous bed is governed by the conservative transport equation (e.g., Jin et al., 2010).

[10] The initial and boundary conditions for both the stream flow model, and pore water flow and solute transport model were essentially the same as those used by Jin et al. [2010], simulating the conditions in the laboratory experiment. The predicted hydraulic heads at the sediment-water interface from the stream flow simulation were converted to the equivalent freshwater head based on the density of the stream water before its application to define the boundary condition at the top of the bed for the pore water flow simulation. Since the solute concentration and hence the density of the stream water change with time as a result of solute exchange across the sediment-water interface, the converted equivalent freshwater head prescribed at the interface varied temporally. Periodic boundary conditions were applied to the lateral (vertical) boundaries for velocity, pressure, concentration and solute flux. A no flow condition was applied at the bottom boundary [Jin et al., 2010]. The initial solute concentration in the pore water of the bed was zero and a relatively low initial solute concentration (C0 = 1.73 kg m−3) set for the stream water.

3. Results and Discussion

3.1. Simulation Cases

[11] A large number of simulations were conducted to examine the density effects on the hyporheic flow and solute transport, in comparison with the experimental results. These simulations covered cases (Table S1) with and without density effects, and with measured and adjusted values of key model parameters (θ, K). The aim of the simulations was to ascertain the effect of density gradients on hyporheic flow and solute transport, i.e., whether the density effects are essential for the model to predict the experimental results or whether adjustment of the θ and K values is sufficient. Details of the results and discussions for all the cases can be found in the auxiliary material. Here the focus is on the first four cases:

[12] Case 1: Neglecting density variations and using the measured hydraulic conductivity (K = 4.35 × 10−3);

[13] Case 2: Neglecting density variations and using an adjusted K (= 21.8 × 10−3 m s−1);

[14] Case 3: Including density variations and using the measured K; and

[15] Case 4: Including density variations and using an adjusted K (= 2.5 × 10−3 m s−1).

[16] These cases took into account uncertainty in the measurements of the sediment properties, in particular, hydraulic conductivity, and hence allowed more rigorous assessment of density effects. The results are plotted in Figures 1, 2, 3, and S2 where comparison between the data and model predictions for the different cases can be made with regard to solute concentration in the stream water, and flow and solute transport in the bed.

Figure 1.

Comparison of experimental data and modeled solute concentrations in the stream water. The solid horizontal line indicates the calculated steady state concentration, C0Vs/(Vs + Vp). Hydraulic conductivity K (×10−3 m s−1) and density effect (DE) in all figures below are the same as this figure.

Figure 2.

Comparison between measured and predicted solute concentrations varying with depth. The solid horizontal line indicates the location of the hydraulic divide at sampling array N1 or N2 (locations of the sampling points are shown in Figure S1c).

Figure 3.

Comparison of modeled solute concentration distribution, flow velocity (white arrows) and streamline (grey line) at different elapsed times for different cases with and without density effects. The color scale represents solute concentration (C) in the streambed, with warm colors for high concentration and cool for low concentration. The thick grey line shows the hydraulic divide predicted by the constant-density flow model. This divide is also shown in the results of the variable-density model for comparison. The results from case 3 (shown in Figure S2) exhibit similar trends to those from case 4 except for over-predictions of hyporheic flow and downward solute transfer.

3.2. Density Effects on Hyporheic Flow Dynamics, Solute Transport and Exchange Across the Interface

[17] A distinctive feature of the simulated density-dependent hyporheic flow is the temporal variations of the flow, which are linked to the downward movement of the solute front (case 4, Figure 3 and case 3, Figure S2). This is in contrast to the steady state condition of the simulated constant-density flow (i.e., without the density influence), in particular, the existence of a hydraulic divide separating the upper and lower flow zones throughout the simulation (case 1, Figure 3 and case 2, Figure S2). This hydraulic divide is due to an underflow caused by a pressure/head drop along the flume, as explained in previous studies [Cardenas and Wilson, 2007; Jin et al., 2010]. The fundamental difference between the variable- and constant-density flows has ramifications for solute transport in the streambed and exchange across the sediment-water interface.

[18] As shown in Figure 1, the solute concentration in the overlying stream water decreased with time as the solute was transported into the bed. The concentration reduction at the beginning of the flume experiment and simulations (0–100 min) was rapid, corresponding to the initial fast transfer of solute from the overlying water to the shallow streambed area, where the pore water flow velocity was relatively large mainly under the influence of hydraulic head gradients at the sediment-water interface. The flow in the shallow area was less affected by the density/concentration variations (26 and 180 min, Figure 3). Thus, all models with and without the density effect predicted similarly well the initial decrease of the solute concentration in the stream water (Figure 1).

[19] The further reduction of the stream water solute concentration in the second phase (100–1100 min, Figure 1) was more gradual. During this stage, solute transport continued downward towards the deep area of the bed. The density gradient due to the concentration variation started to affect the flow as simulated in case 4 (Figure 3). This resulted in a considerable increase of the flow rate and significant changes in the flow pattern. After an elapsed time of 400 min, the circulation initiated from the sediment-water interface extended to the bottom boundary of the bed. This is in contrast with the separation of the upper and lower flow zones in the constant-density flow simulations (case 1, Figure 3 and case 2, Figure S2). The density effects on the flow led to a more rapid solute transfer to the deep area, particularly in the area close to the bottom boundary of the bed. Again, this bottom area would be separated from the upper circulating zones if the density effect was not considered as in cases 1 and 2 where the solute transfer across the hydraulic divide to the bottom area was due to solute diffusion – a very slow process. These manifestations of the effects of density on hyporheic flow are evident in the experimental results.

[20] The density effects enhanced solute exchange across the sediment-water interface, which led to a relatively rapid decrease of solute concentration in the stream water. Without such effects taken into account, the constant-density flow and solute transport model failed to reproduce the rapid solute concentration change observed in the laboratory experiment (case 1 in Figure 1). More importantly, the constant-density model, unable to provide a relatively fast, advective transport mechanism for the bottom area of the bed, would not predict an asymptotic concentration, which was evident in the experiment over a relatively short period. This asymptotic concentration represents a steady state condition with no net exchange between the overlying stream water and pore water in the bed. In this condition, the solute concentrations in both waters become the same, equal to C0Vs/(Vs + Vp) [Jin et al., 2010], where Vs is total volume of water in the flume system excluding pore water and Vp is the total volume of the pore water in the streambed. The experimental results show that the concentration in the stream water reached a relatively steady level after an elapsed time of 1300 min. Even with a five-fold increased hydraulic conductivity, the model without the density effects included still failed to predict the approach of the asymptotic state despite over-prediction of the earlier decrease of the solute concentration (case 2 in Figure 1).

[21] With the density effects included, the variable-density model was able to replicate the observations from the experiment. Although adjustment of the hydraulic conductivity from the measured value (4.35 × 10−3 m s−1) to 2.5 × 10−3 m s−1 was necessary for the model predictions to match the experimental results (case 4, Figure 1), the prediction of the asymptotic condition (including case 3) indicated the important role played by the density-driven flow in hyporheic exchange. The adjustment by a factor less than 2 is likely to be within the range of uncertainty with the hydraulic conductivity measurement.

[22] Further evidence of the density effects on the hyporheic flow and solute transport is provided by the measurements of the pore water solute concentrations at the two arrays of sampling points (Figure 2). Again, without the density effect included, the constant-density model was unable to predict the downward movement of the solute front as shown by the measured concentration profiles. With no adjustment of the hydraulic conductivity, the model under-predicted the solute front movement except for the early time when the front was near the sediment-water face and the density effect was relatively insignificant. The model failed to predict the movement of the solute through into the bottom area of the bed (>575 min in Figure 2 even with a five-fold increased hydraulic conductivity and at the cost of over-predictions for early times. As discussed above, this failure is due to the confinement of the upper circulations by the hydraulic divide, which persists in the constant-density flow simulation. In contrast, the variable-density model, with density effects accounted for, simulated the behavior of the solute front as observed in the experiment, especially in the area near the bottom of the bed.

4. Concluding Remarks

[23] Small density variations between the stream water and pore water in the streambed exist commonly in natural streams. Such variations also occur in laboratory experiments on hyporheic exchange, which typically release solutes to the stream water at low concentrations as tracers for studying the hyporheic exchange processes. The effects of small density variations on hyporheic flow and solute transport have been assumed to be of little importance compared with other forcing factors such as hydraulic gradient due to stream flow and bed form interactions. Using well-controlled laboratory experiments and numerical simulations, we have demonstrated that even small density variations can influence the hyporheic flow and solute transport in the streambed with the presence of periodic bed forms.

[24] The density effect leads to alteration of the flow rate and patterns as the solute front moves downward. The main difference is that the density-induced head gradients drive the circulating flow below a hydraulic divide that would exist without the density influence. The modified hyporheic flows provide a relatively fast solute transport mechanism and enhanced the overall mass exchange between the stream and bed. These findings will have important implications for studies of river ecosystems including hyporheic zones.

[25] The experimental set-up used here is one that has been adopted in many previous studies [Elliott and Brooks, 1997; Marion et al., 2003; Boano et al., 2009; Jin et al., 2010]. While the findings highlight the importance of small density variations as a driving factor of hyporheic exchange processes, further investigation should be conducted to examine the density effects on hyporheic flow and solute transport under different conditions such as a pulse input of solute to the stream, large solute concentrations in the stream water and downward density gradients (solutes initiated from the bed).

Acknowledgments

[26] This research has been supported by the Natural Science Foundation of China (50925932, 51109059), the Special Fund of State Key Laboratory of China (2011585612, 2011585112), the Natural Science Foundation of Hohai University (2009422211), the Fundamental Research Funds for the Central Universities (2009B09514, 2010B21914), Australian Research Council (DP0988718), Basic Research Programs (Natural Science Foundation) of Jiangsu Province (BK2011749), and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. The authors acknowledge the assistance provided by Xiaoquan Yang, Ming Chen and Kai Xie during the experiments.

[27] The Editor thanks an anonymous reviewer for assistance in evaluating this paper.

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