Gravity-driven water exchange between streams and hyporheic zones

Authors


Abstract

[1] The exchange of water and nutrients between rivers and hyporheic zones has been recognized as a very important process for the stream ecosystem. This water exchange is generally explained by pressure gradients on the riverbed that are induced by fluvial geomorphological features or by turbulent coherent structures. In this work we discuss a different exchange mechanism due to density gradients between the in-stream and the hyporheic water. We present laboratory results that show how weak density gradients are able to induce significant hyporheic fluxes. This gravity-induced exchange is expected to play a major role in streams with low-permeability sediments or with small topographic features.

1. Introduction

[2] The exchange processes of stream water with the hyporheic zone – the sediment zone where surface and subsurface waters mix – are known to exert a strong influence on the biochemical characteristics of both surface and subsurface waters [Jones and Mulholland, 2000; Boulton and Hancock, 2006]. The hyporheic fauna relies on the dissolved oxygen, chemicals, and nutrients carried by the stream, while the metabolic activity of the hyporheic microbial communities has a strong impact on the in-stream water quality dynamics [Hayashi and Rosenberry, 2002; Battin et al., 2008].

[3] The fundamental hydrodynamic mechanism that has always been invoked to explain the hyporheic fluxes is the presence of pressure gradients on the streambed surface that are able to induce flow within the fluvial sediments. These pressure gradients are generally caused by the interaction between the free-surface stream and geomorphological features like bedforms [Elliott and Brooks, 1997; Packman and Brooks, 2001; Marion et al., 2002; Boano et al., 2007], point bars [Cardenas et al., 2004; Boano et al., 2006; Revelli et al., 2008], pool-riffle sequences [Tonina and Buffington, 2007; Zarnetske et al., 2007], and changes in the bed slope [Harvey and Bencala, 1993]. Moreover, hyporheic exchange also arises because of pressure gradients that are caused by large-scale regional groundwater flows [Wroblicky et al., 1998; Storey et al., 2003; Wörman et al., 2007; Cardenas, 2007; Boano et al., 2008, 2009] and by local-scale turbulent coherent structures [Packman et al., 2004; O'Connor and Hondzo, 2008].

[4] In this work, we discuss a further mechanism that is potentially able to drive hyporheic exchange in streams and that is related to gradients of water density between in-stream and subsurface water. Even though this mechanism is known to represent an important exchange process in estuaries [Smith and Turner, 2001; Robinson et al., 2007] and lakes [Wooding et al., 1997a, 1997b; Golosov and Ignatieva, 1999; Wooding, 2007], its role in driving water exchange in rivers has not received the same attention. Temperature-based methods are becoming common approaches for the evaluation of surface-subsurface exchange [Constantz, 2008]. However, these approaches often consider temperature fluctuations as a passive result of water exchange, neglecting the active role of temperature differences in driving convective water fluxes. Measurements of hyporheic exchange also rely on the injection of ionic or dye tracers in streams [Harvey and Wagner, 2000]. While these tracers are known to alter water density and thus to represent a potential source of density-driven exchange, no attempt is usually made to quantitatively assess this effect, with the possible outcome of overestimating the exchange flux.

[5] We have performed a series of laboratory experiments in a flume with a flat sand bed demonstrating that small density gradients are able to induce significant exchange fluxes. Similar density gradients are common in streams because of differences in water temperature and chemistry between surface water and subsurface water. Therefore, we argue that this mechanism is widespread in natural streams and plays a significant role along with the exchange processes caused by pressure gradients.

2. Experimental Facility and Measurements

[6] The gravity-induced exchange process between the free-surface flow and the porous medium was investigated using a small recirculating flume at the Giorgio Bidone Hydraulics Laboratory, DITIC, Politecnico di Torino. Here, a brief description of the experimental setup and is provided. A scheme of the flume (Figure S1) and a more detailed description of the experimental procedure are given in the auxiliary material. The flume has a 9 m long, a 0.3 m wide, and a 0.3 m deep working section, and a recirculating flow rate up to 15 l s−1. The channel sides are made of glass to permit optical access [Poggi et al., 2002, 2004]. The 8.5 m long test section covering the entire width started 0.5 m from the entrance of the flume. Sand was used as the bed sediment. Sieve analysis indicated that our sand has a mean diameter (d50) of 0.8 mm and a standard deviation of 1.2.

[7] Density gradients can result from variations of either water temperature or concentration of solutes and suspended solids. In this work, sodium chloride (NaCl) was used as a conservative tracer to assess mixing between the stream and pore water. A concentrated NaCl solution was prepared using 20 l of water and a variable amount of salt. This solution was then slowly injected in the downstream reservoir over approximately one recirculation period. The NaCl concentration in the stream water was then measured with calibrated conductivity meters until it reached a stationary value.

3. Results

[8] The main characteristics of the performed experiments are reported in Table 1. All the experiments are characterized by the same height of the sand layer ds = 0.1 m. The experiments are divided in 9 runs (A-I). In each run the flow properties were kept constant, and a variable number of salt injections were performed in order to explore different ranges of tracer concentrations. A total number of 31 experiments was thus performed.

Table 1. Summary of the Experimental Parameters and Resultsa
 Q (l s−1)h (m)U (m s−1)Fr (−)Re (−)Re* (−)Pek (−)ΔC (g l−1)q (cm h−1)
  • a

    Values of the dimensionless parameters Fr = U(gh)−1/2, Re = 4Uhν−1, Re* = u*d50ν−1, and Pek = u*k1/2Dm−1 are also reported. The experiments within each run A-I were characterized by the same hydrodynamic conditions.

A19.00.120.252.3 · 10−11.1 · 10513.31.4 · 1032.841.15
A29.00.120.252.3 · 10−11.1 · 10513.41.4 · 1032.931.19
B15.20.090.192.1 · 10−17.1 · 10413.41.2 · 1032.901.03
B25.20.090.192.1 · 10−17.2 · 10413.51.2 · 1032.740.99
B35.20.090.192.1 · 10−17.1 · 10413.31.2 · 1033.221.11
B45.20.090.192.1 · 10−17.1 · 10413.31.2 · 1033.141.08
C11.50.030.162.8 · 10−12.2 · 1048.77.1 · 1022.150.87
C21.50.030.162.8 · 10−12.2 · 1048.57.1 · 1023.491.41
C31.50.030.162.8 · 10−12.2 · 1048.57.1 · 1024.641.49
C41.50.030.162.8 · 10−12.2 · 1048.47.1 · 10211.453.90
D12.00.040.193.3 · 10−12.9 · 1048.77.4 · 1022.100.63
D22.00.040.193.3 · 10−13.0 · 1049.07.4 · 1024.211.38
D32.00.030.224.1 · 10−13.0 · 1048.46.9 · 1025.441.78
D42.00.030.224.1 · 10−13.0 · 1048.46.9 · 1024.751.55
E12.10.090.089.0 · 10−23.4 · 10415.31.2 · 1030.440.25
E22.10.090.089.0 · 10−23.5 · 10415.61.2 · 1030.430.27
E32.10.080.099.9 · 10−23.5 · 10415.21.1 · 1030.600.36
E42.10.080.091.0 · 10−13.5 · 10415.01.1 · 1030.780.36
E52.10.080.091.0 · 10−13.5 · 10415.01.1 · 1030.970.46
F10.50.060.034.0 · 10−26.9 · 10310.59.6 · 1023.580.75
F20.50.060.034.0 · 10−27.3 · 10311.09.6 · 1022.640.58
F30.50.060.034.0 · 10−27.2 · 10310.99.6 · 1021.410.45
G10.50.060.034.1 · 10−26.7 · 10310.19.5 · 1025.751.26
G20.50.060.034.1 · 10−27.4 · 10311.09.5 · 1028.442.80
G30.50.060.034.1 · 10−27.4 · 10311.19.5 · 1026.871.71
H13.00.070.131.6 · 10−14.1 · 10412.21.1 · 1039.622.47
H23.00.070.131.6 · 10−14.3 · 10412.81.1 · 1037.002.15
I12.80.070.131.5 · 10−13.5 · 10411.11.1 · 10310.502.86
I22.80.070.131.5 · 10−13.8 · 10412.01.1 · 10311.392.99
I32.80.070.131.5 · 10−13.7 · 10411.91.1 · 1036.101.66
I42.80.070.131.5 · 10−13.7 · 10411.81.1 · 1036.151.62

[9] In order to facilitate the comparison of the data from different experiments, the stream concentration is replaced by the corresponding dimensionless concentration equation image = (CCf)/(ΔCCf), where ΔC is the initial difference between surface and subsurface concentrations and Cf is the in-stream concentration at the end of the experiment. This definition ensures that equation image ∈ [0,1]. Figure 1 shows three series of salt concentration data in the free-surface flow. The exchange of water between the stream and the sediments causes a progressive dilution of the stream solute concentration, as reflected by the monotonic decaying behavior of the curves in Figure 1. Despite the presence of some scattering due to difficulty to measure low concentrations, it is important to notice that the plots of log(equation image) versus t fall on straight lines, which implies that the concentrations decrease exponentially with time.

Figure 1.

Examples of three data series of dimensionless in-stream concentration.

[10] An exponential decay of solute concentration could be the result of a steady advective exchange of water. For such an exchange, variations of surface and subsurface concentrations are in fact given by

equation image

where C and Cs are the salt concentration in the surface flow and in the sediments, respectively, W is the volume of water in the surface system (including tanks and pipes), Ws is the volume of water in the sediment pores, and q is the exchanged flux per unit bed area Ω. Equation (1) can be also written as

equation image

where α = q/d is the rate of surface-subsurface exchange, ε = Ws/W = n · ds/d is the ratio between the volumes of subsurface and surface water, n is the sand porosity, and d = W/Ω is the effective stream depth, which is higher than the real stream depth h. The initial conditions associated with equation (2) are C(t = 0) = ΔC + Cback and Cs(t = 0) = Cback, where Cback is the possible background concentration before the salt injection. As equation (2) is only affected by the differences of concentration, the value of Cback has no practical relevance and it is set equal to zero for the sake of simplicity.

[11] The solution of the system of equation (2) in terms of equation image is

equation image

where T = α−1ε/(1 + ε) represents the characteristic timescale of the exchange. Equation (3) shows that the observed exponential decay of stream concentration is consistent with the advective exchange of water described by equation (1). It is not completely clear why the observed exchange flux was steady and why the progressive dilution of the concentrations did not result in a time-decaying flux. Unfortunately, it is very difficult to propose an explanation for this process without measuring the concentrations within the sediments. However, equation (3) has proved to provide an excellent fit to the observed concentrations, and it was thus adopted for the data analysis.

[12] For each experiment, the normalized concentrations equation image were evaluated from the experimental data and they were then fitted to the exponential solution given by equation (3). The fitting procedure allowed to evaluate the characteristic timescale of the exchange T = α−1 ε/(1 + ε), from which the exchange flux q = α · d could be obtained. The values of the exchange flux q for the different experiments are reported in Table 1, and show a strong correlation with the corresponding differences between surface and subsurface concentrations, ΔC.

[13] In order to better show the relative role of the density-induced buoyancy forces, we introduce the Rayleigh number

equation image

which represents the ratio between the timescales of the mass transport due to molecular diffusion and convection, respectively. In equation (4)g is the gravity acceleration, k is the sediment permeability, Dm is the molecular diffusion coefficient of the solute in the sediments, ν is the kinematic viscosity of water, β = ρ−1ρ/∂C is the water expansion coefficient due to solute concentration, ρ is the water density, and K is the hydraulic conductivity. Since ρ is given by the sum of the solute-free water density and the solute concentration, the expansion coefficient is simply β = ρ−1. In our experiments the value of the Rayleigh number range between 5 · 102 and 104, which means that convection in the pore water was always much greater that molecular diffusion.

[14] The dimensionless fluxes q/K are then plotted in Figure 2 against the corresponding Rayleigh number. The strong linear correlation q/K = 3.83 · 10−7Ra (R2 = 0.92) in Figure 2 clearly shows that the variations of the flux between the experiments are mainly due to the difference of density between surface and subsurface water. Moreover, the exchange fluxes did not exhibit any correlation when plotted against other experimental variables, like the stream discharge, the mean velocity, and the width-to-depth ratio. These results demonstrate that the most important factor that controlled the exchange of water in our experiments is the vertical gradient of water density induced by the differences of solute concentration. This effect was still observable for relative variation of water density Δρ/ρ = 4 · 10−4, which represents the lower limit that was considered in our study.

Figure 2.

Dimensionless exchange flux against Rayleigh number. The dashed line represents the linear regression of the data, q/K = 3.83 · 10−7Ra, and has R2 = 0.92.

4. Discussion and Conclusions

[15] In the laboratory experiments here presented, a net exchange of water between the surface flow and the subsurface sediments was observed, as testified by the asymptotic decrease in the tracer concentrations of the surface stream. The exchange was essentially driven by density gradients, as confirmed by the strong correlation that was found between the dimensionless exchange and the Rayleigh number. In particular, a simple linear relationship was found to provide an excellent fit to the experimental data. There are some aspects, such as the geometry of the experimental domain and the sediment granulometry, whose influence on the exchange is not clear yet and that will require additional tests in the future. However, the clarity of our findings supports our opinion that these results can be generalized to provide a quantitative description of the exchange even in more complex and realistic settings.

[16] An interesting result of our analysis is that the exchange did not appear to be influenced by the hydrodynamic properties of the free-surface flow. The dimensionless fluxes were not significantly correlated either to Reynolds or Froude number, nor to any other variables related to the surface flow. This lack of correlation depends on the particular experimental setting used in our tests, in which water was flowing on a flat bed of sandy sediments. In the case of gravel beds, it has been observed that turbulent flow structures penetrate into the upper layers of the permeable sediments, and that the resulting exchange shows a marked dependence on the Reynolds number of the surface flow [Packman et al., 2004]. In our experiments, the low permeability of sand precluded the turbulent diffusion of salt within the sediments, and therefore no influence of the Reynolds number on the exchange could be observed. The presence of bedforms on the streambed also results in an exchange flux that is tightly related to the stream flow properties through the Froude number [Elliott and Brooks, 1997], but there is no reason for a Froude dependence for the case of a flat bed. A recent study by O'Connor and Harvey [2008] has proposed a scaling law (with Re* and Péclet Pek numbers) that considers the aforementioned hydrodynamical exchange process. However, this law predicts an effective diffusion coefficient De that is only one order of magnitude higher than molecular diffusion. This means that the diffusive timescales ds2/De would be of the order of ten days, which is too slow to explain our results. This fact further confirms that the hydrodynamic factors played a negligible role in our experiments.

[17] Even though it is universally recognized that high concentrations of ionic solutes can modify the density of water and induce convective motions, this fact has received little attention in previous studies of surface-subsurface interactions. Here, we stress that vertical density gradients represent a potential mechanism of hyporheic exchange that is different from the ones related to river morphology. Our experiments have shown that the density gradients represent a factor that can generate a flux of solutes from the water column to the stream sediments and thus contribute to the overall exchange of water between the stream and the hyporheic zone, particularly in streams with sandy beds or with small topographic features. This gravity-driven flow can be an important exchange process in the case of a release of heavy metals or cyanides, such as those that result from accidental mine spills. Density-induced exchanges can also result from variations of the stream temperature due to anthropic releases of wastewater or to diel natural fluctuations. Temperature fluctuations of 4–5°C are commonly observed in streams [e.g., Burkholder et al., 2008] and can be associated with Rayleigh numbers and exchange fluxes similar to those observed in our experiments. In streams with more permeable sediments, the same temperature fluctuations would result in higher exchange rates because of the definition of the Rayleigh number in equation (4). Our results also suggest that cautions should be adopted when stream tracer tests are performed to evaluate the surface-subsurface exchange in order to avoid the overestimation of the exchange due to unexpected gravity effects.

Acknowledgments

[18] The authors would like to thank A.I. Packman for his careful review of the manuscript, and A. Lovera and L. Viada for their help with the laboratory experiments.

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