RESEARCH ARTICLE10.1029/2017WR021992

Turbulence Links Momentum and Solute Exchangein Coarse-Grained StreambedsK. R. Roche1,2 , G. Blois3, J. L. Best4, K. T. Christensen3,5,6 , A. F. Aubeneau7 , andA. I. Packman1

1Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL, USA, 2Department of Civiland Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN, USA, 3Department ofAerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, USA, 4Departments of Geology,Geography and GIS, Mechanical Science and Engineering and Ven Te Chow Hydrosystems Laboratory, University ofIllinois at Urbana-Champaign, Urbana, IL, USA, 5International Institute for Carbon-Neutral Energy Research (I2CNER),Kyushu University, Japan, 6Department of Civil and Environmental Engineering and Earth Sciences, University of NotreDame, Notre Dame, IN, USA, 7Lyles School of Civil Engineering, Purdue University, West Lafayette, USA

Abstract The exchange of solutes between surface and pore waters is an important control over stream ecol-ogy and biogeochemistry. Free-stream turbulence is known to enhance transport across the sediment-waterinterface (SWI), but the link between turbulent momentum and solute transport within the hyporheic zoneremains undetermined due to a lack of in situ observations. Here, we relate turbulent momentum and solutetransport using measurements within a streambed with 0.04 m diameter sediment. Pore water velocities weremeasured using endoscopic particle image velocimetry and used to generate depth profiles of turbulence statis-tics. Solute transport was observed directly within the hyporheic zone using an array of microsensors. Soluteinjection experiments were used to assess turbulent fluxes across the SWI and patterns of hyporheic mixing.Depth profiles of fluctuations in solute concentration were compared with profiles of turbulence statistics, andprofiles of mean solute concentration were compared to an effective dispersion model. Fluorescent visualizationexperiments at a Reynolds number of Re � 27,000 revealed the presence of large-scale motions that ejectedtracer from the pore waters, and that these events were not present at Re 5 13,000. Turbulent shear stresses andhigh-frequency concentration fluctuations decayed greatly within 1–2 grain diameters below the SWI. However,low-frequency concentration fluctuations penetrated to greater depths than high-frequency fluctuations. Com-parison with a constant-coefficient dispersion model showed that hyporheic mixing was enhanced in regionswhere turbulent stresses were observed. Together, these results show that the penetration of turbulence intothe bed directly controls both interfacial exchange and mixing within a transition layer below the SWI.

Plain Language Summary Streams and rivers continuously exchange water with their underlyingsediments in a region called the hyporheic zone. This zone is a hotspot of transformation for many societallyrelevant chemicals, including carbon, nutrients, and contaminants. Accurate predictions for how muchtransformation occurs in the hyporheic zone requires an improved understanding of how reactive chemicalsare transported into, and within, this region of a riverbed. Although fluid turbulence can be the dominantprocess controlling surface-subsurface exchange in gravel-bed streams, its influence is poorly understooddue to the difficulty of measuring turbulent fluid velocities and concentrations within the streambed. In thisexperimental study, we show that turbulence strongly couples surface waters with hyporheic waters in athin layer where the water column and stream sediments meet. As a result, fluid transport and mixing areenhanced several centimeters into the hyporheic zone of gravel-bed streams. These findings support recenttheoretical arguments that surface and subsurface waters are not independent and must instead be treatedas a single unit to accurately model solute, particulate and pollutant transport in streams and rivers.

1. Introduction

Hyporheic exchange has long been recognized as a primary control of nutrient, carbon, and contaminantcycling in rivers and streams. Interactions between surface and hyporheic waters influence the fate of thesereactive constituents by controlling their fluxes to, and residence times within, bioreactive regions of the

Key Points:� High-frequency concentration

variability and enhanced mixing aredirectly linked to penetration ofturbulence into the hyporheic zone� Regions of enhanced mixing directly

correspond to the penetration depthof intermittent turbulent flowstructures� Low-frequency fluctuations in solute

concentration propagate deeper intothe hyporheic zone but do notenhance mixing

Supporting Information:� Supporting Information S1� Video S1

Correspondence to:K. Roche,kroche2@nd.edu

Citation:Roche, K. R., Blois, G., Best, J. L.,Christensen, K. T., Aubeneau, A. F., &Packman, A. I. (2018). Turbulence linksmomentum and solute exchange incoarse-grained streambeds. WaterResources Research, 54, 3225–3242.https://doi.org/10.1029/2017WR021992

Received 2 OCT 2017

Accepted 2 APR 2018

Accepted article online 10 APR 2018

Published online 2 MAY 2018

Corrected 18 JUN 2018

This article was corrected on 18 JUN

2018. See the end of the full text for

details.

VC 2018. American Geophysical Union.

All Rights Reserved.

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hyporheic zone (Boano et al., 2014; Jones & Mulholland, 1999; Lawrence et al., 2013). Assessment and pre-diction of overall stream function (e.g., net hyporheic metabolism, contaminant removal) therefore requiresa proper description of the mechanisms governing hyporheic transport. Although physical models for hypo-rheic transport have advanced substantially over the past two decades, current physical models only cap-ture transport associated with viscous flows that are governed by Darcy’s Law. They thus ignore fasterexchange processes associated with fluid turbulence that can control hyporheic exchange in high perme-ability streambeds (Chandler et al., 2016; Nagaoka & Ohgaki, 1990; Packman et al., 2004; Shimizu et al.,1990; Voermans et al., 2017). A motivating question for the current study is thus where, and to what extent,does turbulent transport enhance hyporheic exchange?

Current physical models of hyporheic exchange are rooted in experimental observations of advective anddispersive transport in the subsurface (Bottacin-Busolin & Marion, 2010; Hester et al., 2017; Huettel et al.,1996; Thibodeaux & Boyle, 1987). Advective transport is controlled by a combination of energy gradientsnear the sediment-water interface (SWI), properties of stream sediments, and large-scale interactions withunderlying aquifers (Boano et al., 2014; Fox et al., 2014). Roughness elements such as surface-exposedgrains, dunes, and riffles alter the near-streambed pressure field, and the resulting hydrodynamic forcesdrive water from high-pressure to low-pressure regions of the streambed (Blois et al., 2014; Cardenas & Wil-son, 2007; Sinha et al., 2017). This process of ‘‘advective pumping’’ is well understood to regulate hyporheicfluxes and residence times (Cardenas, 2015; Elliott & Brooks, 1997b). However, turbulence is commonlyassumed to influence such a thin region of the streambed that it can effectively be ignored (Cardenas & Wil-son, 2007; Tonina & Buffington, 2009).

The advective pumping model predicts limited or no exchange in streambeds with very small topographicfeatures. However, exchange rates in flat gravel beds have measured 2–4 orders of magnitude greater thanthose predicted by advective pumping or by basic diffusion (O’Connor & Harvey, 2008; Packman et al.,2004), and experimental evidence suggests that turbulent velocity fluctuations are a primary driver of soluteexchange (Nagaoka & Ohgaki, 1990). In these instances, exchange is typically described using a dispersionmodel with an effective coefficient at the SWI, Deff . This coefficient is determined from observations of netexchange between the water column and the streambed, based on changes in water column solute con-centrations (Elliott & Brooks, 1997a; Grant et al., 2012; O’Connor & Harvey, 2008; Packman et al., 2004; Rich-ardson & Parr, 1988). However, it is unclear how interpretations of this exchange are biased by this modelchoice when velocities and mixing rates vary spatially within the streambed.

Despite the absence of a mechanistic model, detailed experimental and numerical investigations of subsur-face flow have improved understanding of turbulent momentum transport within the hyporheic zone. Akey finding is that both stream flow and bed permeability affect the flow structure through the surface-subsurface continuum (Blois et al., 2013; Manes et al., 2011; Suga et al., 2010; Zagni & Smith, 1976). Flowsover permeable sediment beds exhibit higher overall flow resistance, deviations from the canonical loga-rithmic turbulent velocity profile, and modified shapes and intensities of the turbulent kinetic energy (TKE)profile compared to flows over impermeable beds with similar boundary topography (Breugem et al., 2006;Manes et al., 2009, 2011; Ruff & Gelhar, 1972; Zagni & Smith, 1976; Zippe & Graf, 1983). Further, turbulenteddies from the water column penetrate across the SWI, driving momentum below the interface (Bloiset al., 2012; Stoesser et al., 2007). Below the SWI, momentum is dissipated by drag forces around bed sedi-ment grains, resulting in a transition layer where velocities, turbulent stresses, and pressure fluctuationsdecrease rapidly to uniform values (Breugem et al., 2006; Vollmer et al., 2002). Simulations and experimentssuggest that these turbulent flow properties influence mass transport in the turbulent transition layer, withvelocity fluctuations inducing mixing in pore waters, and low-frequency pressure fluctuations inducing sub-surface advection without appreciable mixing (Chandesris et al., 2013; Packman et al., 2004).

A predictive understanding of turbulent solute exchange in coarse sediment beds is currently limited by alack of high-resolution observations in pore waters. Such observations are needed to evaluate the specificflow features that control hyporheic transport. To address this need, we conducted two series of experi-ments in laboratory channels with a bed composed of coarse spherical beads, which were used to enablenovel in situ observations of turbulent flow and solute transport. In the first set of experiments, an endo-scopic flow visualization system was used to quantify the fluid momentum and turbulent statistics throughthe bed by performing pore space measurements at different depths. In the second set of experiments,tracer mixing was observed in situ using a custom-constructed sensor array. Coordinated experiments were

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conducted over a range of matching flow conditions to assess momentum and mass transport with varyingdegrees of surface-subsurface flow coupling.

2. Materials and Methods

2.1. EPIV ExperimentsEndoscopic particle image velocimetry (EPIV) was used to directly measure pore water flow in a recirculatingflume in the Ven Te Chow Hydrosystems Laboratory, University of Illinois at Urbana-Champaign. Details ofthe EPIV experimental setup and calibration procedure are provided in (Blois et al., 2012). In brief, experi-ments were conducted in a flume with a 4.8 m L 3 0.35 m W 3 0.6-m H test section. The test section wasfilled with 0.04 m spherical beads fixed in a simple cubic packing, creating a 0.24 m streambed that wasnine beads wide and 6 beads high. The water depth was fixed at 0.16 m, and water was recirculated at threedifferent discharges as reported in Table 1.

Flow within the pore space was illuminated by a dual-cavity, Nd:YAG laser (New Wave, 120 mJ/pulse, ElectroScientific Industries, Portland, OR) passed through an endoscope that produced a thin sheet of laser lightoriented in the streamwise-wall-normal (x–z) plane and centered in the high porosity plane of the porethroat. The scattered light from neutrally-buoyant tracer particles (14 lm diameter hollow glass spheres)were imaged by a CCD camera via an 8 mm borescope, similar to that of Blois et al. (2012). However, ahigher-resolution camera (29 MP PowerView CCD, 6.6k 3 4.4k pixel, 12-bit frame-straddle CCD, TSI Inc.,Shoreview, MN) was used for the present experiments compared to Blois et al. (2012). The experimentalsetup provided a � 20 mm diameter circular field of view in the center of a pore throat. The low data acqui-sition rate of this PIV system (1 Hz) yielded ensembles of statistically independent instantaneous 2D flowfields across a vertical column of pore throats over the streambed depth, at elevations of z 5 20.04, 20.08,20.12, 20.16, 20.20, and 20.24 m, where z 5 0 represents the elevation of the SWI (top of uppermost sedi-ment grains). The ensemble of velocity fields acquired at each depth were then averaged into spatially vary-ing mean and instantaneous fluctuating components using standard Reynolds decomposition (Tennekes &Lumley, 1972):

u5u1u0 (1)

w5w1w0

where u is the instantaneous streamwise velocity decomposed into its mean u and fluctuating u0 compo-nents, and w is the instantaneous bed-normal velocity decomposed into its mean w and fluctuating w0

components. From these planar EPIV measurements, the turbulent Reynolds shear stresses, u0w0 , and thewall-normal Reynolds normal stresses, w0w0 , are reported in this study. The ensemble-averaged mean andturbulent stress fields were then spatially averaged within each pore space to generate a single data pointat a given depth.

Table 1Flow Conditions for all Experiments

Re 13,000 22,000 27,000 39,000 55,000 75,000Experiment Solute EPIV Solute EPIV Solute EPIV

Q (Ls21) 2.2 8.0 4.4 14.0 8.8 26.0H (m) 0.123 0.160 0.123 0.160 0.123 0.160Fr 0.09 0.11 0.18 0.20 0.38 0.37U (ms21) 0.10 0.14 0.20 0.24 0.41 0.47U p(ms21) 0.007 – 0.012 – 0.028 –dg (m) 0.038zbed (m) 20.224/ 1 – p/6 � 0.476k (m2) 3.21 3 1026

u� (ms21) 0.006 0.013 0.012 0.024 0.036 0.048Rek 10 23 21 42 64 86

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A similar experimental arrangement was used to measure velocities in the water column, except that thecamera borescope was replaced by a standard Nikon lens (60 mm focal length), which enabled the flowacross the entire water column to be captured, from the free surface down to the SWI.

The Reynolds number of the overlying (surface) flow was calculated as Re5UHt21, where U is the meanfree-stream velocity, and t is the kinematic viscosity of water, taken to be 1026 m2s21. The Froude numberwas calculated as Fr5U Hgð Þ21=2, where g is acceleration due to gravity. Shear velocity was calculated asu�5 u0w0max

� �1=2, where u0w0max is the maximum measured Reynolds stress, consistent with Voermans et al.

(2017). Permeability k was estimated using the Karman-Cozeny equation (Freeze & Cherry, 1979; O’Connor& Harvey, 2008):

k55:631023/3d2

g

12/ð Þ2(2)

where / is porosity. The permeability Reynolds number, which has been shown to be an important predic-tor of interfacial momentum and mass transport (Blois et al., 2013; Breugem et al., 2006; Grant et al., 2012;Voermans et al., 2017), is calculated as Rek5u�k1=2m21=2 :

2.2. Solute Transport Experiments2.2.1. Solute Transport Experiments: Laboratory Flume and Sediment BedSolute mixing experiments were conducted in a 2.5 m L 3 0.2 m W 3 0.5 m H recirculating flume in theEnvironmental and Biological Transport Processes Laboratory at Northwestern University. Water was recircu-lated from the downstream to the upstream end-well of the flume via a PVC pipe and pump. An in-line vor-tex-shedding flowmeter (Rosemont 8800) was used to measure the total flow rate. The flume slope wasadjustable via a manual jack.

The sediment bed was constructed from spherical PVC beads (Figure 1). The bed consisted of a 1 m inletsection that was randomly packed with 0.038 m and 0.064 m beads for flow conditioning, and a down-stream test section filled with 0.038 m beads in a simple cubic packing array of five beads W 3 6 beads H.These dimensions differ slightly from bed and flume dimensions in the EPIV experiment. However, the bedstructure was identical in both experiments, and in both streambeds the six bead bed depth was sufficientlylarge to capture the transition to uniform velocities in the subsurface. The cubic-packed bed was con-structed by stacking vertical columns of six beads onto a threaded 0.0032 m diameter stainless steel rod.Each column was fixed to a 0.0064 thick acrylic sheet, which was installed as a false bottom in the flume.The array of beads was fixed within the flume through insertion of two 0.0064 m thick acrylic sheetsbetween the bed and the flume sidewalls to maintain tight cubic packing. The streambed elevation, mea-sured from the SWI to the false bottom, was zbed 5 20.224 m.

xz*

*

P

PFlow

0.224 m

0.12 m

2.5 m

1.5 m

Slope

Recirc.Loop

InjectionSensorArray

Figure 1. Schematic of recirculating flume used for solute transport experiments, with bed composed of a flow-conditioning region of randomly packed beads and a test section composed of a cubic-close-packed array of beads.Image is not to scale. Injection location in the schematic corresponds to x�inj 5 3.5, z�inj5 22.15.

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To allow comparison between the results obtained from the two different facilities, the grain diameter andfree-stream velocity were selected as the characteristic length and velocity scales for normalization (i.e.,L�5L/0.038 m). For the solute transport experiments, streamwise distances x� are reported relative to thesolute injection location. Transverse distances are reported from the edge of the flume sidewall, withy�5 4.5 and y�5 2.5 representing the flume centerline for the EPIV flume and the solute transport flume,respectively. Depths are reported relative to the SWI, which is defined as the top of the first row of beadscomprising the bed, so that z�5 21 signifies the bottom of the first layer of beads, and thus the verticalcenter of the uppermost pore space.2.2.2. Solute Transport Experiments: Concentration MicrosensorsA cross-sectional array of beads in the test section was instrumented with high-frequency conductivity sen-sors for in situ observation of salt tracer concentrations (Figure 2). The sensors were 2.5 mm interdigitatedelectrodes (Synkera Technologies, Longmont, CO) with 100 lm spacing and gold conductors, wired into aresistor-capacitor-resistor integrated circuit. The small sensor size allowed pore waters to be sampled nearlyat-a-point without significantly perturbing the pore water flow field. Sensors were surface-mounted ontothe beads using high-resistivity epoxy. One sensor was implanted directly onto each of the 30 beads in a y–z cross section of the regular packed streambed, located x�5 20.5 downstream of the test section inlet.Each sensor was aligned with the centerline of the spherical bead in the x–z plane and placed 0.15 beaddiameters below the top of the beads in the upstream direction (i.e., sensor depth for the top layer of beadswas z�5 20.15). All wires were shielded and grounded to minimize noise, and unsheathed wire leads weresealed with electrically resistive wax to ensure only the sensor was exposed. Calibrations confirmed that the0.038 m sensor spacing in the array did not yield interference between measurements at adjacent sensors.Wires were run downstream from the sensors and along bead-to-bead contact points to minimize distur-bance of the pore water flow field.

Circuits were powered and sampled with a National Instruments PCI-6229 data acquisition board. Outputand input signals were controlled and recorded using LabView Signal Express 2013 software (NationalInstruments, Austin, TX). Circuits were powered in parallel by a 400 mV, 100 Hz AC waveform. The returningvoltage was bandpass filtered and recorded in LabView, and this file was exported to Matlab versionR2015a (Mathworks, Cambridge, MA) for further analysis. All waveforms were bias-corrected and sampled atthe peaks, yielding a 200 Hz sample rate.

Sensors were calibrated in situ. A known volume of reverse osmosis (RO) water was first pumped into theflume from a laboratory-grade reservoir, and flow was initiated. NaCl solution was then added to the flume.Once the solute was fully mixed with flume water, a one-minute conductivity time series was recorded. Athree-parameter calibration curve was used of the form

C5 exp V2a3ð Þ=a1ð Þ2a2; R2 � 0:995; � 9 dof (3)

Figure 2. Simple-cubic-packed sediment module with sensors installed (left). Sensors were 2.5 mm square interdigitatedelectrodes fixed to the sediment grains with epoxy and sealed with resistive wax (right).

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where C is NaCl concentration, V is voltage, and ai are constants. For all experiments, steady-state NaCl con-centrations were limited to 0–200 lmol L21, which yielded the greatest measurement sensitivity.2.2.3. Solute Transport Experiments: Flow Conditions and MeasurementsExperiments were performed over a range of flow conditions reported in Table 1. For each flow rate, theflume slope was adjusted to match the surface water slope to yield uniform flow conditions. The water sur-face elevation was measured with a digital point gauge attached to a rail-mounted carriage above theflume. Water column depth, H, was measured from the free surface to the tops of the sediment grains.2.2.4. Solute Transport Experiments: Free-Stream Velocity MeasurementsFree-stream velocities were measured using an acoustic Doppler velocimeter (ADV; SonTek 16MHz Micro-ADV, San Diego, CA) in the solute transport flume. The flume was seeded with 8 lm particles (SonTek, SanDiego, CA) to increase signal-to-noise ratio for velocity measurements. Spikes in the velocity time serieswere filtered using the phase-space thresholding algorithm of Goring and Nikora (2002) implemented inthe WinADV (v2.028) software package (Wahl, 2000). Three-dimensional velocities (u; v;w) were measuredin a vertical profile centered at the x-y location where equivalent EPIV measurements were recorded, start-ing from a location 0.05 m below the free surface and ending at the sediment bed. Velocities were recordedat 50 Hz for a minimum of 70 s, yielding second-order statistics within 5% of their convergent values (seesupporting information). Methods for calculating bulk flow properties u�; Re; Fr; k; and Rek were identical tothose used for the EPIV experiments (section 2.1). Similar dependence of u� on Re provided confidence thathydrodynamic conditions were comparable between the two flumes.2.2.5. Solute Transport Experiments: Pore Water Velocity MeasurementsIn addition to the EPIV measurements, mean pore water velocities were also estimated in the solute trans-port flume using a semiquantitative method based upon measuring solute concentration time curves anddetecting concentration peaks resulting from injection pulses. Short pulses (� 0.5 s) of solute tracer weremanually injected at multiple locations x� upstream of the sensor array at each depth. The concentrationtime series was recorded for all sensors at the injection depth, and mean fluid velocity was estimated fromeach sensor as u5x=tpeak , where x is the streamwise distance between the injection location and a sensorat the same elevation z� as the injection location, and tpeak is the time at which the peak concentrationpulse was recorded by a sensor. Velocities were then averaged over all injections to obtain the overall meanpore water velocity for each row of beads, Up zð Þ.

Injections were made via 3.1 mm silicon tubing that was inserted into the pore space, with the tubingaligned with the y-axis and aperture located at exactly y�5 2. This orientation ensured that: (1) the injectionwould minimally affect downstream momentum transport, and (2) the injection region would include fluidvolume in both the pore throat and any dead zones between sediment grains. To study the role of injectiondepth, independent injections were made at depths z�5 –0.15, 21.15, 22.15, 23.15, and 24.15.2.2.6. Solute Transport Experiments: Steady-State Solute InjectionsThe flume was filled with RO-purified water, and then a neutrally-buoyant NaCl solution was injected into porewater via a peristaltic pump using 3.1 mm silicon tubing. Flow pulsation from the pump was controlled byinserting a custom-constructed pneumatic pulse dampener into the injection line (see supporting information).An aquarium stone was installed onto the tubing outlet to diffuse the solution into the pore space and minimizedisturbance of the pore water flow field. Each injection solution was made neutrally buoyant by heating to theappropriate temperature, and dye-tracing injections confirmed that the solution was neutrally buoyant. Theinjection rate was set to ensure the injection did not alter the subsurface flow field (0.0046–0.0058 mL s21).Injections were performed at mid-width over a series of injection depths, z�inj , and were continued until salt con-centrations at the sensor array reached a statistical steady-state for at least 2 min. The injection concentrationwas adjusted in each experiment so that measured concentrations were within the calibration range of the sen-sor. A series of injections was performed until the background salt concentration reached �10 lmol L21, atwhich point the measured signal-to-background ratios became too low to fully capture the tracer injectiondynamics. The flume was then drained, flushed, and refilled with RO water for subsequent experiments.

Two sets of steady-state injections were performed at each of the three flow rates listed in Table 1. Injec-tions near the sensor array were used to capture detailed statistics of the tracer plume before it had mixedcompletely with pore water (x�inj 5 3.5, y�inj 5 2, z�inj5 20.15, 21.15, 22.15, 23.15). A second set of injectionswas made at three locations upstream of the sensor array (x�inj 5 3.5, 7.5, 12.5) to capture the larger-scaleplume spreading and average mass flux. All injections were performed at least x�5 7 downstream of theentrance to the test section to ensure that the flow within the bed was fully developed. Injections were

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repeated at and below the SWI (z�inj 5 20.15, 22.15), and at multiple transverse locations (y�inj5 2, 2.5, 3) toobtain ensemble statistics of plume spreading.2.2.7. Solute Transport Experiments: Data AnalysisSensor data were background-corrected. The background concentration was treated as a linear ramp toaccount for the steady increase in background concentration over the course of injections due to the recir-culating nature of the flume. Plume spreading was analyzed over the interval when measured concentra-tions were at a dynamic steady state. The resulting background-corrected time series were decomposedinto their frequency content by computing power spectral densities (PSD). For a real-valued concentrationtime series Cn of N samples, the PSD is defined as (Rodr�ıguez-Iturbe & Rinaldo, 2001):

P fð Þ5 2DtN

����XN21

n50

Cne2i2pfn

����2

(4)

where P fð Þ is the spectral power at frequency f and Dt51=f is the time between samples. PSDs were nor-malized by the signal variance, r2:

P fð Þnorm5P fð Þr2

(5)

r25

ð2 Hz

0:1 HzP fð Þdf (6)

The limits of integration in equation (6) correspond to the lowest common frequency measured across allexperiments, 0.1 Hz, and the frequency at which spectral power decayed beyond 1% of its maximum for allexperiments, 2 Hz. The upper limit of sampling frequency (2 Hz) also corresponds to the frequency at whichdifferences in P between experiments were no longer detectable. To compare across experiments, PSDswere integrated to determine the range of frequencies that accounted for 95% of the signal variance, r2

95:

r2955

ðf95

0:1 HzP fð Þdf (7)

where f95 represents the frequency below which 95% of signal variance is captured. An increase in f95

between experiments indicates an increasing contribution from higher frequencies.

Mean concentration, C zð Þ, was calculated for each sensor and then averaged over all sensors at each depth.Row-averaged values are reported as hCiy zð Þ. Root-mean-square concentrations, Crms5�r2, were normal-ized by the mean concentration measured across all sensors in the injection row where a non-zero concen-tration was recorded. Uncertainty estimates of Crms are based on convergence of the time series variance,and were between 2 and 6% in all experiments (see supporting information).2.2.8. Solute Transport Experiments: Whole Streambed AnalysisMass recovery was used to quantify the amount of injected solute that exchanged from the pore water tothe water column. Recovery, R; is calculated as the fraction of the total injected mass, minj , that is measuredpassing the y-z plane of the sensor array:

R5mmeas

minj(8)

mmeas51/

ð0

z 525:15dg

hCiy dz (9)

minj5Cinj Qinj

Up w(10)

where Cinj is the injection concentration, Qinj is the injection flow rate, / is bed porosity, Up is the mean porewater velocity (i.e., averaged over all depths), w is the flume width, and z 5 25.15dg is the location of the low-est row of sensors. Here, m is interpreted as a measure of mass per unit area in the x-y plane [M L22]. Notethat an implicit assumption of equation (9) is that solute is fully mixed over the unit cell comprising the porevolume surrounding each bead, and measurements at each sensor are representative of the concentrationwithin the unit cell. The integral in equation (9) was evaluated numerically using the trapezoid rule.

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2.2.9. Solute Transport Experiments: Effective Dispersion ModelA 1D vertical dispersion model was fit to subsurface injections (z�inj 5 22.15) to evaluate if the observedtracer transport could be adequately represented as an effective dispersion process:

@/hCiy@t

5Deff@2/hCiy@z2

(11)

/hCiy 0; tð Þ50

@/hCiy zbed; tð Þ@z

50

where t5x=Up is the travel time of the advecting plume from the injection point, and Deff is a spatially uni-form dispersion coefficient. Deff was obtained for each injection by fitting to the modeled profile of hCiy .The analytical solution to equation (11) is (with constant /):

hCiy z; xð Þ5 M

/ 4pDeff x=Up� �0:5 e

2z2zinjð Þ2

4Deff x=U p 2e2

z1zinjð Þ2

4Deff x=U p 1e2

z22zbed 1zinjð Þ24Deff x=U p

0@

1A (12)

where M=/ is a normalized mass, correcting for porosity. The last term on the right-hand side of (12) repre-sents the first term in an infinite series image solution that accounts for the no-flux boundary condition atzbed . Higher-order terms contributed less than 0.1% of overall mass observed in between [zbed; 0� and thuswere omitted. The validity of this approximation was confirmed experimentally, since solute was neverobserved at the lowest sensor (z 5 25.15dg). Two different normalization masses were tested:

M5minj (13)

M052/

ðzinj

z 525:15dg

hCiy dz: (14)

where z 5 25.15dg is the location of the lowest row of sensors. Equation (13) normalizes results using thetotal mass injected while equation (14) normalizes results based on integration over the concentration pro-file. Normalization based on equation (14) assumes that mixing is uniform below the injection location (i.e.,mixing is not enhanced by flow coupling). This normalization was insensitive to the effects of enhancedmass exchange and mixing at the SWI, which biased estimates of the dispersion coefficient based on nor-malization with equation (13) (See comparison of Deff and D0eff in section 3.2.2 and the supporting informa-tion). Fits for the dispersion coefficient based on M0 are denoted by D0eff .

D0eff fits obtained from each concentration profile were averaged to calculate ensemble-average estimatesof the effective dispersion coefficient at each flow rate, Dens. These values were then used to generate pre-dictions for ensemble concentration profiles from equation (12), with Dens in place of D0eff . Predicted massrecovery, defined as the fraction of injected mass retained in the streambed at downstream distance x, wasalso calculated from the analytical solution to equation (11):

Rpred5

ð0

21hCiy z; xð Þdz52erf

zinj

4Dens x=Up� �0:5

" #: (15)

where erf is the error function. Note that terms associated with the no-flux boundary condition @Cpred=@zzbed; tð Þ50 are not included in equation (15) since concentrations had decayed to a negligible concentra-

tion by zbed for all model fits and experiments used in the analysis of Dens. Mass recovery is plotted againstthe dimensionless timescale associated with vertical mixing over one grain diameter:

t�5ðx=UpÞDens

d2g

(16)

Because the experiments were conducted under steady conditions, t� also corresponds to the downstreamdistance required for vertical mixing over one grain diameter. Normalization by t� collapses all model pre-dictions onto a single curve.

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3. Results

3.1. Surface-Pore-Water Flow CouplingVertical profiles of the mean streamwise velocity and turbulent stresses, determined from the EPIV experi-ments, are presented in Figure 3. As expected, all profiles are characterized by a non-zero velocity at theSWI due to the relaxation of the no-slip condition. The vertical profiles of mean pore water velocities exhib-ited a minimum at z�5 21, which is consistent with prior studies of turbulent flows over simple-cubic-packed beds of beads (Manes et al., 2009; Pokrajac et al., 2007). Profiles of both Reynolds shear stress (u0w0 Þand the Reynolds normal stresses w0w0

� �reveal a transition layer where turbulence levels are elevated at

the SWI and exponentially decrease deeper in the subsurface. The magnitude of peak u0w0 stress was

2s-2m('w'u- )

0 0.2 0.4 0.6

-4

-2

0

2

4

z*

0 0.05 0.1-5

-4

-3

-2

-1

0

0 1 2

10-3

-4

-2

0

2

4

z*

0 2 4 6

10-4

-5

-4

-3

-2

-1

0

EPIV 22,000EPIV 39,000EPIV 75,000

0 1 2 3

10-3

-4

-2

0

2

4

z*

0 2 4 6

10-4

-5

-4

-3

-2

-1

0

EPIV 22,000EPIV 39,000EPIV 75,000

u (m s-1)

2s-2m('w'w ) 2s-2m('w'w )

2s-2m('w'u- )

u (m s-1)

EPIV 22,000EPIV 39,000EPIV 75,000

EPIV 22,000EPIV 39,000EPIV 75,000

EPIV 22,000EPIV 39,000EPIV 75,000

EPIV 22,000EPIV 39,000EPIV 75,000Solute 13,000Solute 27,000Solute 55,000

Figure 3. Left: Profiles of mean velocity and turbulent stresses for the EPIV experiments. Dotted rectangle representsregion shown in adjacent plots. Right: Same profiles, with only near-bed and subsurface shown. Colored profiles in upperright panel are subsurface velocity measurements for the solute transport experiments.

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greatest at the SWI for all Re. u0w0 stresses decayed to 1% of their peak value by z�5 21 for the lower Reyn-olds numbers considered (Re 5 22,000 and 39,000), whereas for the higher Reynolds (Re 5 75,000) a similardecay was reached by z�5 22, indicating an increased depth of turbulence penetration. Similarly, the pene-tration depth of w0w0 stresses increased with increasing Re, with values decaying to 1% of their peak valuesby z�5 23 for Re 5 22,000, and by z�5 24 for Re 5 22,000. w0w0 stresses were above 1% of their peak val-ues for all elevations at Re 5 75,000 and measured 2% at the lowest measurement elevation z�5 25.

3.2. Solute Transport Results3.2.1. Flow Visualizations and In Situ Concentration MeasurementsFlow visualizations from subsurface injections (z�inj 5 22.15) show rapid mixing at the SWI (Figure 4, videoms01). The large sediment beads act as roughness elements that protrude into the bulk flow, causing rapidvelocity fluctuations at the SWI. Additionally, larger-scale interactions between the water column and porewaters are visible to a depth of at least two beads below the SWI for Re 5 27,000 and 55,000, confirming tur-bulence penetration into the bed. Interactions appear as intermittent bursts of flow that drive high-concentration pore fluid into the high-momentum free flow (Figure 4). These qualitative observations areconsistent with recent measurements (Blois et al., 2013; Kim et al., 2017), and the topology of subsurfaceflow structures is detailed in Blois et al. (2013). Their presence suggests that coherent motions in the watercolumn of size l � 2dg control transport across the SWI, within the subsurface region where turbulent veloc-ity fluctuations are present. Ejections did not occur at Re 5 13,000, but were observed at Re 5 27,000, andincreased in frequency and intensity from Re 5 27,000 to Re 5 55,000, reflective of enhanced turbulentactivity.

In situ solute measurements show that energetic, high-frequency fluctuations dominate the time seriesnear the SWI (Figure 5), with concentration fluctuations being most intense at the SWI. As expected, highfrequency fluctuations decay with depth in the bed, while lower-frequency fluctuations persist at deeperlocations (Figure 6a), confirming results from Vollmer et al. (2002) and Kim et al. (2017), who showed thatthe bed acts as a low-pass filter of pressure and velocity fluctuations. These trends are also observed inpower spectral density and f95 plots (Figures 6a and 6b). An asymptotic limit in f95 was reached within onegrain diameter for Re 5 13,000 and 27,000, but f95 decays more slowly, and to a higher asymptote, forRe 5 55,000. These trends are coincident with the second-order turbulence statistics reported in Figure 3,which show rapid decay of u0w0 and w0w0 stresses over roughly one grain diameter for Re 5 22,000 and39,000, but greater turbulence penetration to a depth of �2 grain diameters at Re 5 75,000.

Overall concentration variability, quantified by normalized Crms values, is presented in Figure 6c. These pro-files differ from profiles of f95 and turbulence statistics by exhibiting a peak concentration below the SWI,which moves deeper into the streambed with increasing flow rate. Peak Crms at Re 5 27,000 and 55,000 alsocorresponds to the position at, or below, the position where u0w0 stresses have decayed to <1% of theirmaximum for EPIV experiments at similar Re (39,000 and 75,000, respectively). This suggests that the loca-tion of peak Crms is found at, or below, the streambed depth where turbulent shear stresses affect solutemixing. The location of peak Crms was observed at the SWI for Re 5 13,000, which indicates that solute trans-port was not influenced by turbulent shear stresses beyond one grain diameter for this flow rate. This resultis supported by the similarity of the u0w0 stress profile at Re 5 22,000 (Figure 3) and the CRMS profile at Re 5

13,000 (Figure 6c), which both approach zero within the first bead diameter of the bed.

Figure 4. Ejection event during a subsurface injection (z�inj 5 22.15) at Re 5 55,000. Images at 0.75 s and 1.25 s show thatthe event is at least two sediment beads wide. Sediment beads are 0.038 m in diameter.

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3.2.2. Upscaled Solute Transport PropertiesMean concentration profiles for subsurface (z�inj 5 22.15) injections were used to calculate an effective verti-cal dispersion coefficient Deff for each flow rate. Example fits based on the two mass normalizations M andM’ (equations (13) and (14), respectively) are shown in Figure 7a. Fits based on the injection mass (M5minj ,solid line) resulted in substantial overestimation of the effective dispersion rate, as the model attempted tocompensate for the large fraction of input mass that was lost to the water column. These fits predictedtracer propagation and accumulation at the flume bottom, which was not observed in any experiments.Model performance, measured by R2 values, also showed a clear dependence on overall mass recovery R(see plot of R2 versus mass recovery, supporting information Figure S4). In contrast, model fits using normal-ization mass M0 provided reasonable predictions at all locations below the injection point. Values of D0eff ,based on the normalization M0(equation (14)), were therefore used to generate ensemble-averaged valuesof the effective dispersion coefficient, Dens (Figure 7b). Dens values show a monotonic increase with flowrate, although the estimated values are not significantly different between Re 5 13,000 and 27,000. Allresults are normalized against molecular diffusion, taken here as Dm 5 1.5 3 1029 m2 s21, and plottedagainst Rek5u�k1=2m21=2.

Calculated Dens values are compared to subsurface Deff results from Nagaoka and Ohgaki (1990) and Chan-dler et al. (2016) in Figure 7b. Nagaoka and Ohgaki (1990) used an experimental streambed consisting ofhexagonally packed spheres (dg5 0.019 m or 0.041 m) to measure depth-dependent hyporheic mixing. Thewater column of the recirculating flume was loaded with a uniform concentration of NaCl solution(0–200 mg L21), which subsequently penetrated into the (initially solute-free) streambed. Time series ofincreasing solute concentration were observed at various depths using embedded conductivity sensors.Deff values were inferred from the concentration time series by assuming Fickian mixing with a depth-dependent Deff 5 Deff zð Þ. Since Dens from the present study represents a uniform dispersivity belowz�5 22.15, we compare our results to the parameter (K4) from Nagaoka and Ohgaki (1990) that equals thecalculated Deff for all depths below z�5 24. Values were of a similar order to Dens calculated from this study,but they were consistently higher and showed a stronger dependence on Rek : The cause of these differ-ences is likely due to the use of neutrally buoyant solutes in this study. Although relatively low concentra-tions (0–200 mg L21) of NaCl tracer were used in Nagaoka and Ohgaki (1990), hyporheic mixing in highly-permeable sediments may still have been influenced by buoyancy-driven convection; the median

Figure 5. Time series observations of solute concentrations for an injection at location x�inj ; y�inj ; z�inj

� �5 (3.5, 2.5, 20.15)

under a flow rate of 8.8 Ls21 Re 5 55,000). Location of the injection and observation points over a cross-section of thebed are shown on the right. Flow is into the page, yellow dot indicates the injection location, and the monitoring loca-tions are indicated in blue.

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concentration 100 mg L21 from that study corresponds to a Rayleigh number of 6 3 103, which is in therange of conditions where buoyancy-driven convection increases hyporheic exchange by a factor of 2–3(Boano et al., 2009).

Results also show a weaker dependence on Rek compared to the empirical scaling relation for Deff derivedin Chandler et al. (2016), who used a similar experimental and identical modeling approach to Nagaoka andOhgaki (1990). In their study, Chandler et al. (2016) calculated depth-dependent values of Deff for randomlypacked sediment beds over a range of grain diameters and shear velocities. The following scaling relationwas found to best fit their results:

Deff 53:1531011k1:32u3:11� e55z : (17)

10-2 10-1 100

Frequency (Hz)

-50

-40

-30

-20

-10

0

10

20

dB

z*inj

= -0.15

z*inj

= -3.15

0 0.2 0.4 0.6 0.8f95 (Hz)

-4

-3

-2

-1

0

z*

Re 13,000Re 27,000Re 55,000

0 0.2 0.4 0.6 0.8 1Normalized Crms

-4

-3

-2

-1

0

a

b c

f95 f95

Figure 6. (a) Power spectral densities for two injections at x�inj 5 3.5, y�inj 5 2 and Re 5 55,000, based on concentration time series.High-frequency power is filtered within the streambed, while power at low frequencies is similar at all depths. (b) Profiles of f95:

Each data point represents an individual experiment at x�inj 5 3.5, y�inj 5 2, with measurements taken only for sensors at thesame elevation as z�inj . f95 values, derived from power spectral densities using equation (7), capture the shift to concentrationvariability dominated by lower frequencies. Higher frequencies contribute to concentration variability at higher flow rates, andhigh frequency content decreases to asymptotic values at similar rates as the decay of turbulent stresses, shown in Figure 3.(c) Normalized Crms values for the same experiments as (b). Location of peak Crms propagates deeper into the streambed as flowrate increases.

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Equation (17) was used to calculate the average Deff for z 5 [–0.224 m, 20.082 m], which represents thedepths over which Dens was calculated for this study. Similar to comparison with Nagaoka and Ohgaki(1990), the trend predicted by equation (1) shows a stronger dependence of Deff on Rek compared toour results. Buoyancy effects did not accelerate mixing in Chandler et al. (2016), as their experimentsinvolved the upward mixing of tracer from the bed into the water column. Differences are most likelyrelated to the chosen definitions of u� and k. Nonlinearity in Reynolds stress measurements, which areused to calculate u� in both studies, is most pronounced when measurements are made at the locationof peak stress (Figure 3). The definition of u� used in Chandler et al. (2016) was based on Reynoldsstress measurements at a constant elevation. This choice may have reduced the nonlinear dependenceof u� on flow conditions, which would result in a greater dependence of Deff on Rek . Measurements of kin the present study were based on equation (2), which does not account for the effects of flowunsteadiness. We expect increasing unsteadiness of subsurface flows to have biased estimates awayfrom equation (2) (Bear, 1972; Chaudhary et al., 2013), which may have resulted in a narrower range ofk and a greater influence of Rek on Deff .

Figure 8 shows modeled concentration profiles based on Dens, compared to the measured profiles of hCiy .Enhanced mixing at depths 22.15� z� �20.15 is most visible at Re 5 55,000, evidenced by tracer propa-gating away from the injection location much faster than model predictions (Figures 8a, 8b, and 8d). Asym-metry of observed concentrations about the subsurface injection point is due to the combined effect ofrapid solute propagation near the SWI, which dominates at early times (Figure 8a), and enhanced mass lossto the water column, which dominates at late times (Figure 8e). Rapid mixing at 22.15� z� �20.15 alsoresults in greater mass exchange than the model predicts with uniform Dens, which is indicated by the lowerobserved mass recovery for all but one experiment in Figure 9.

Plots of mass recovery, R, show the fraction of injected mass measured in the hyporheic zone at the sensorarray (Figure 9). Predictions of mass recovery from the effective dispersion model are independent of flowrate when normalized by t�5 x=U p

� �Deff=d2

g; as illustrated by the dotted lines in Figure 9. Observed devia-tions from this prediction are expected to also collapse onto a single curve if subsurface transport scalesdirectly with Re: For experiments at Re 5 27,000 and 55,000, R decreases more rapidly than predictions fromthe dispersion model, and all experiments collapse onto a single trend (Figure 9). In contrast, experimentsat Re 5 13,000 show that approximately 50–100% more time was necessary for mass to be transported outof the streambed compared to experiments at higher Re (e.g., mass recovery is 0.7 at t� � 0.4 for intermedi-ate and high flows but does not reach this value until t� � 0.7 for the low flow condition in Figure 9a).

0 5 10 15 20 25C ( mol L-1)

-5

-4

-3

-2

-1

0

z*

ExpD

eff

D'eff

ba

100 101 102

Rek

104

105

Def

f/Dm

This StudyN&O 1990Equation (17)

Figure 7. (a) Comparison of observed (squares) and fit (lines) downstream concentration profiles C(z*) for an experimentwith Re 5 27,000, x�inj 5 12.5, z�inj 5 22.15. Fits normalized to mass below the injection point (dashed line) better representobserved concentrations at all bed depths. (b) Ensemble average of all best-fit effective dispersion coefficients at eachflow rate, based on D0eff . Error bars show one standard deviation. Values are normalized by molecular diffusion and plottedagainst Rek5u�K 0:5m21.

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Evidence from flow visualizations (Figure 4) and concentration timeseries (Figure 5) suggests that this difference is due to the emergenceof coherent surface-subsurface interactions of size l � 2dg byRe 5 27,000, which enhance mixing from 22.15� z� �20.15 com-pared to flows at lower Re. The large-scale flow structures consist ofinjections, commonly called sweeps, of high-momentum, low-concen-tration surface water into the streambed, and ejections of high-concentration, low-momentum pore water into the water column(Figure 4) (Blois et al., 2013; Suga et al., 2011). Note that two values atRe 5 13,000 (x�inj; z�inj 5 3.5, 22.15, and 7.5, 22.15) and one value atRe 5 27,000 (x�inj; z�inj 5 3.5, 22.15) are not plotted in Figure 9 due toincomplete mixing of the slowly spreading solute plume (i.e., plumewidth< dg), resulting in R > 1.

4. Discussion

The open pore geometry of coarse-grained sediment beds allows turbu-lent transport of both momentum and mass across the SWI, therebycoupling surface and pore water flows. This coupling modifies the flowstructure across the surface-subsurface continuum, thus affecting themechanisms controlling transport of solute. Our results suggest that theturbulent transition layer, or the extent of the region affected by suchmodifications, depends on the flow Reynolds number. Subsurface trans-port appears to be relatively unaffected by flow variability atRe 5 13,000, with small-scale (<0.5dg) recirculations visible only on theleeside of sediment beads. In contrast, transport at Re 5 27,000 and55,000 is clearly influenced by the presence of intermittent ejections ofpore water originating from depths 22.15� z� �20.15 (Figure 4).

Pore water hydrodynamics (i.e., turbulent fluctuations) directly con-trolled solute transport and mixing over the full range of flow ratestested. Reynolds stresses and f95 both decreased rapidly below theinterface to constant values by z�5 21.15 for Re� 39,000 (Figures 3and 6a, respectively), but both metrics decreased more gradually to

0 2 4 6 8

-5

-4

-3

-2

-1

0

z*

a

C ( mol L )-10 10 20 30

-5

-4

-3

-2

-1

0

z*

b

0 5 10 15 20 25

-5

-4

-3

-2

-1

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z*

c

0 5 10 15 20 25

-5

-4

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d

0 20 40 60

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-2

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0

z*

e

0 2 4 6 8 10

-5

-4

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-2

-1

0

z*

f

x* =

12.

5, t

* =

0.7

Re

= 13

,000

x* =

12.

5, t

* =

0.4

Re

= 55

,000

x* =

3.5

, t*

= 0.

1R

e =

55,0

00

zinj* = -2.15 zinj* = -0.15

C ( mol L )-1

C ( mol L )-1

C ( mol L )-1

C ( mol L )-1

C ( mol L )-1

Figure 8. Comparison of ensemble-averaged mean concentrations profilesobserved in experiments (markers) with constant-coefficient dispersion modelfits and an absorbing boundary condition at z�5 0 (solid lines). The model bestdescribes transport at depths below z� � -2.15 but does not adequatelydescribe enhanced mixing at depths 22.15� z� �20.15.

R

a

0 0.2 0.4 0.6 0.8 1

t*

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8 1

0.4

0.6

0.8

1

1.2

t*

R

bzinj* = -2.15 zinj* = -0.15

pred

Figure 9. Observed mass recovery in the streambed (markers) compared with the upscaled best-fit effective dispersionmodel (equation 15, dotted lines). (a) z�inj 5 22.15, (b) z�inj 5 – 0.15. Note the change in y-axis scales. Experiments atRe 5 27,000 and Re 5 55,000 follow a similar trend that deviates from the predicted retention curve. Experiments atRe 5 13,000 follow a distinct trend with greater mass recovery. Error bars showing one standard deviation are providedfor experiments with more than one replicate.

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z�� 22.15 for Re� 55,000. The relation between Reynolds stresses and f95 values suggests that solute waspredominantly transported by turbulent velocity fluctuations near the SWI, and these fluctuations con-trolled the high-frequency concentration variability in the subsurface (f�� 0.2 Hz, Figures 6a and 6b).

Profiles of root-mean-square concentrations (Crms) were distinct from profiles of Reynolds stresses. The loca-tion of maximum concentration variability, indicated by a peak in the Crms profile, was found deeper in thebed under higher flow rates (Figure 6c). The location of peak Crms corresponds to the location at, or below,where the turbulent shear stresses had decayed to <1% of their maximum measured values. Low-frequency concentration fluctuations were also observed at this location in flow visualizations and solutetime series (Figures 4, 5, supporting information video ms01). Low-frequency fluctuations have beenobserved previously in gravel beds and are related to damping of dynamic pressure oscillations associatedwith dissipation of kinetic energy due to fluid-grain interactions (Packman et al., 2004; Vollmer et al., 2002).The streambed acts as a low-pass filter for turbulent velocity and pressure fluctuations, allowing low-frequency fluctuations to propagate to greater depths than high-frequency fluctuations (Breugem et al.,2006; Kim et al., 2017). The numerical results of Chandesris et al. (2013) suggest that these pressure fluctua-tions contribute to advection but not to enhanced mixing within pore waters, resulting in high concentra-tion variability and low dispersion in this region. This hypothesis is supported both by the flowvisualizations presented here (Figure 4 and supporting information video ms01), which show evidence oflow mixing at the location of peak Crms, as well as by observed concentration profiles (Figure 8), which showthat concentrations below z� � –2.15 are well described by a spatially invariant dispersion coefficient.

Enhanced mixing is evidenced above z� � –2.15 by the rapid propagation of tracer away from the injectionlocation and by the rapid decay of the concentration peak, relative to the spatially-invariant dispersion model(Figures 8a–8d). Differences between modeled and observed concentrations were smaller for Re 5 13,000,compared to higher flow rates (Figures 8e and 8f). Together with near-zero u0w0 and w0w0 stresses below theSWI at Re 5 13,000 (Figure 3), this result suggests that surface-subsurface flow coupling weakens at lower Redue to the dampening of turbulence by viscosity (Ghisalberti, 2009), and subsurface mixing approaches astate that is adequately described by a constant-coefficient dispersion model (Voermans et al., 2017). Further,plots of normalized mass recovery illustrate that flow coupling enhances hyporheic exchange, since mass waslost more quickly to the water column for flows exhibiting large-scale ejection events Reð � 27,000, Figure 9).

Our results emphasize that flow coupling controls vertical mixing patterns and near-surface variability in sol-ute concentration, particularly for streambeds with high permeability near the SWI. For example, coarse-grained, high-permeability armor layers develop at the SWI in gravel rivers, due to grain sorting and to pref-erential entrainment of smaller particles (Ferdowsi et al., 2017; Hassan & Church, 2000). Presence of anarmor layer accelerates hyporheic exchange at sub-hourly timescales and can modify exchange rates acrossall timescales (Marion et al., 2008). Our findings show that mixing and overall exchange also depend on thedistribution of turbulent stresses within the armor layer. Specifically, mixing intensities will vary stronglybelow the SWI when the armor layer depth exceeds the depth over which turbulent stresses penetrate thesubsurface. These findings also extend to systems where high interfacial permeability is a common charac-teristic, such as high-gradient alluvial streams (Lamb et al., 2017; Montgomery et al., 1999; Tonina & Buffing-ton, 2007), actively bioturbated systems (Montgomery et al., 1996; Nogaro et al., 2006; Xie et al., 2018), andlow-gradient streams with substantial reach-scale substrate heterogeneity (O’Connor et al., 2012).

5. Conclusions and Implications

Our results show that high-frequency variability in solute concentration and enhanced mixing are directlylinked to penetration of turbulence into the hyporheic zone. Turbulent stresses and high-frequency concen-tration fluctuations decay similarly with depth in the bed. Interactions between the turbulent free streamand porewaters also influence solute transport beyond the depth where shear stresses penetrate, manifest-ing as low-frequency oscillations deeper into the bed. The decay of turbulence in the bed therefore controlsboth spatial and temporal variability in solute concentration in the turbulent transition layer.

The simple cubic packing of sediments utilized in the present study represents an endmember case, whoseopen geometry allows for high penetration of coherent flow structures from the water column. Streambedswith smaller sediments, closer packing, or heterogeneous grain size mixes are expected to obstruct penetra-tion of these structures and may alter the hydrodynamic conditions at which they emerge. Additional

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experiments for depth-dependent turbulent mixing and overall exchange fluxes are expected to dependboth on streambed attributes, such as sediment permeability, and on measures of interfacial turbulence,such as shear velocity (Grant et al., 2012; Voermans et al., 2017).

The direct correspondence between profiles of turbulent velocity fluctuations in the pore space and regions ofenhanced hyporheic mixing suggests that mechanistic predictions of the distribution of turbulent stresses acrossthe surface-subsurface continuum may also be predictive of enhanced hyporheic mixing. Results from the pre-sent study show that vertical mixing within flat, coarse-grained streambed can be represented as an effective,constant-coefficient dispersion process if inertial effects are weak compared to viscous effects. In contrast, flowat high Reynolds number is dominated by coherent flow structures (large-scale sweep and ejection events) thatepisodically pulse solutes across the SWI and deliver pulses of stream water into the bed. These findings supportrecent research that shows momentum transport over high permeability streambeds can be described by a sin-gle set of scaling relations that captures the transition from laminar flows to flows dominated by turbulentsweeps and ejections (Voermans et al., 2017). To strengthen the link between turbulent momentum and masstransport in streambeds, future research is needed to expand the range of flow rates and bed geometries whereturbulent hyporheic mixing and mass transport are measured. The mass exchange associated with individualsweep and ejection events must also be quantified to establish the importance of this mechanism relative toothers, such as mixing induced by roughness elements at the SWI or mechanical dispersion in the streambed.Experiments that simultaneously measure momentum and mass transport across the surface-subsurface contin-uum will provide the most unambiguous evidence for this linkage.

A physically based model for turbulent hyporheic mass transport will also improve the interpretation of reach-scale mass transport in coarse-grained streams by capturing finer scales than those currently considered. Mecha-nistic reach-scale models for hyporheic transport are presently capable of relating upscaled measures of soluteresidence times to physical stream features ranging from dunes to meanders, provided pore water flows are vis-cous (Boano et al., 2007; Cardenas, 2009; Gomez-Velez and Harvey, 2014; Stonedahl et al., 2012). A new physi-cally based model will extend the range of spatial and temporal scales that can be resolved within the streamreach. Such a model will inform proper selection of field-based measurements by identifying the locations andconditions where turbulent hyporheic exchange is expected to control transport. It will also improve our abilityto distinguish turbulent hyporheic exchange from other solute retention processes that operate at similar time-scales, such as exchange with side pools, benthic biofilms, and in-stream structures (Battin et al., 2003; Bottacin-Busolin et al., 2009; Ensign & Doyle, 2005; Gooseff et al., 2005; Jackson et al., 2013; Orr et al., 2009; Uijttewaalet al., 2001). Independent parameterization of all retention mechanisms active at fast timescales will improveassessment of biogeochemical transformation from whole-stream tracer injection experiments, since they willexplicitly account for the distinct transport processes and reaction kinetics associated with each region of thestream (Aubeneau et al., 2015; Boano et al., 2014; Jones & Mulholland, 1999; Li et al., 2017).

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underlying a unidirectional turbulent boundary layer: A review and some new experimental results. In Coherent flow structures at earth’ssurface (pp. 43–62). John Wiley & Sons, Ltd.

Blois, G. L., Best, J. L., Sambrook Smith, G. H., & Hardy, R. J. (2014). Effect of bed permeability and hyporheic flow on turbulent flow overbed forms. Geophysical Research Letters, 41, 6435–6442. https://doi.org/10.1002/2014GL060906

Blois, G. L., Sambrook Smith, G. H., Best, J. L., Hardy, R. J., & Lead, J. R. (2012). Quantifying the dynamics of flow within a permeable bedusing time-resolved endoscopic particle imaging velocimetry (EPIV). Experiments in Fluids, 53, 51–76.

Boano, F., Harvey, J. W., Marion, A., Packman, A. I., Revelli, R., Ridolfi, L., & W€orman, A. (2014). Hyporheic flow and transport processes: Mech-anisms, models, and biogeochemical implications. Reviews of Geophysics, 52, 603–679.

Boano, F., Packman, A., Cortis, A., Revelli, R., & Ridolfi, L. (2007). A continuous time random walk approach to the stream transport of sol-utes. Water Resources Research, 43, W10425. https://doi.org/10.1029/2007WR006062

Boano, F., Poggi, D., Revelli, R., & Ridolfi, L. (2009). Gravity-driven water exchange between streams and hyporheic zones. GeophysicalResearch Letters, 36, https://doi.org/10.1029/2009GL040147

Bottacin-Busolin, A., & Marion, A. (2010). Combined role of advective pumping and mechanical dispersion on time scales of bed form–induced hyporheic exchange. Water Resources Research, 46, W08518. https://doi.org/10.1029/2009WR008892

Bottacin-Busolin, A., Singer, G., Zaramella, M., Battin, T. J., & Marion, A. (2009). Effects of streambed morphology and biofilm growth on thetransient storage of solutes. Environmental Science & Technology, 43, 7337–7342.

AcknowledgmentsWe thank Marcelo Garc�ıa for use offacilities at the Ven Te ChowHydrosystems Laboratory and ScottSimpson, Nick Marchuk, MichaelPeshkin, Andrea Salus, Duanding Yuan,Wu Heng, Carlo Zuniga Zamalloa, andDiogo Bolster for assistance withexperiments and analysis. KRR wassupported by an NSF GraduateResearch fellowship. We also thankStanley Grant and two anonymousreviewers for constructive commentsthat helped improve the manuscript.The research effort was supported byNational Science Foundation grantEAR-1215898 and the Department ofthe Army, U.S. Army Research Officegrant W911NF-15-1-0569. Supportingdata is available at DOI: 10.6084/m9.figshare.4244405. The authorsdeclare no conflicting interests.

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Erratum

In the originally published version of this article, Equation (16) was incorrectly labeled as Equation (1). Theerror has been corrected and this may be considered the official version of record.

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