沉积物层中混合度检测方案(粒子图像测速)

智能文字提取功能测试中

@AGUPUBLICATIONS @AGUWater Resources Research10.1002/2015WR018274 Water Resources Research RESEARCH ARTICLE 10.1002/2015WR018274 Key Point： ·Sediment-water exchange， laboratorystudy， mixing coefficients Citation： doi：10.1002/2015WR018274. Accepted 11 APR 2016 Accepted article online 19 APR 2016 Published online 7 MAY 2016 ◎ 2016. The Authors.This is an open access article under theterms of the Creative CommonsAttribution License， which permits use，distribution and reproduction in anymedium， provided the original work isproperly cited. Vertical variation of mixing within porous sediment bedsbelow turbulent flows I. D. Chandler1，I.Guymer2，J. M. Pearson2，and R. van Egmond3 1HR Wallingford， Wallingford， UK， ’School of Engineering， University of Warwick， Coventry， UK， Unilever Safety andEnvironmental Assurance Centre， Colworth Science Park， Sharnbrook， UK Abstract River ecosystems are influenced by contaminants in the water column， in the pore water andadsorbed to sediment particles. When exchange across the sediment-water interface (hyporheic exchange)is included in modeling， the mixing coefficient is often assumed to be constant with depth below theinterface. Novel fiber-optic fluorometers have been developed and combined with a modified EROSIMESSsystem to quantify the vertical variation in mixing coefficient with depth below the sediment-waterinterface. The study considered a range of particle diameters and bed shear velocities， with the permeabilityPeclet number， Pek between 1000 and 77，000 and the shear Reynolds number， Re， between 5 and 600.Different parameterization of both an interface exchange coefficient and a spatially variable in-sedimentmixing coefficient are explored. The variation of in-sediment mixing is described by an exponential functionapplicable over the full range of parameter combinations tested. The empirical relationship enablesestimates of the depth to which concentrations of pollutants will penetrate into the bed sediment， allowingthe region where exchange will occur faster than molecular diffusion to be determined. 1. Introduction The impact of chemical pollutants on the environment， particularly aquatic ecosystems， has been thefocus of much research in recent years. River ecosystems include the macro-invertebrate benthic com-munities which may be strongly influenced by contaminant concentrations， both in the pore water andadsorbed to fine sediment particles [Bottacin-Busolin et al.， 2009]. Different modeling approaches havebeen proposed including transient storage， Runkel [1998] and risk assessment models based on the"impact zone" concept [McAvoy et al.， 2003]. A knowledge of the movement of soluble chemical pollu-tants from the water column across the sediment-water interface， and then into the sediment bed， or viceversa， may be required. This process of mass transfer across the sediment-water interface is referred to ashyporheic exchange. Boano et al.[2014] provide a comprehensive overview of the hyporheic zone as oneof the key elements of river corridors where water exchange is characterized by a wide range of spatialand temporal scales. The review discusses the transport of water， heat， dissolved and suspended com-pounds. Models， currently employed [Technical Guidance Document (TGD)， 2003] to predict exposure insediments， are based on an assumption of equilibrium partitioning between dissolved and suspended-particle-sorbed phase in the water column. The bed sediment is assumed to consist of deposited sus-pended solids (with associated sorbed chemicals). Direct solute interactions with the bed， via diffusive oradvective transfer from the water column to sediment pore water， are not taken into account. When anexchange coefficient has been included in modeling [Fries， 2007]， it has been assumed to be constantwith depth below the sediment-water interface. Numerous studies [Marion et al.， 2002； Packman et al.， 2004； Tonina and Buffington， 2007； Rehg et al.， 2005；Ren and Packman， 2004] have shown significant mass transfer across the sediment-water interface into thehyporheic zone. These studies investigated the interface exchange and not the variation in mixing withdepth. Hester et al.[2013] numerically investigated the mixing zone thickness， in particular the mixing-defined hyporheic zone on river beds and conclude that dispersivity is a critical parameter for which dataare needed for shallow sediments. Nagaoka and Ohgaki [1990] and Shimizu et al. [1990] both showed areduction in mixing with depth below the sediment-water interface， but the studies were limited to depthsof a few particle diameters below the interface. Previous laboratory studies have used recirculating flumes to investigate hyporheic exchange. These allowthe effect of bed forms to be studied， however they generally require large volumes of sediment and anextensive setup period， which restrict the range of conditions that can be tested in one series. Smaller vol-umes of both sediment and water would significantly reduce the time required， however this is difficult toachieve in a laboratory flume whilst maintaining a realistic physical scale. This paper explores the potentialof utilizing an experimental tool to examine some of these processes. The EROSIMESS System (shortened to erosimeter) is an instrument designed to generate realistic scaleboundary shear and turbulence to investigate critical bed shear stress of sediment beds [Liem et al.， 1997；Spork et al.， 1997]. The erosimeter was originally developed at The Institute of Hydraulic Engineering andWater Resources Management， Aachen University of Technology in Germany (IWW， RWTH) and has beenmodified previously to study the effect of sediment resuspension on dissolved oxygen content of riverwater [Jubb et al.， 2001] and to quantify hyporheic exchange coefficients [Chandler et al.， 2012]. This paperdescribes further developments， to include both in-flow and in-bed fluorometric measurements. Theerosimeter was then employed to record temporal concentration variations， both above and within-bed，from an initial concentration of interstitial bed fluid， subject to a range of applied shear stresses. Newresults quantifying both an interface exchange coefficient and the vertical variation in mixing withinporous sediment beds below the sediment-water interface are presented and empirical scaling relation-ships explored. 2. Previous Work Several different approaches have been taken to predict and/or model the interface exchange betweenflowing water and a porous sediment bed， the hyporheic exchange. Conceptual physical models havebeen studied， such as： a pumping model [Elliott and Brooks， 1997； Tonina and Buffington， 2007]， slip flowmodel [Fries， 2007]， a transient storage [Hart， 1995； Runkel， 1998； Johansson et al.， 2001； Worman， 2000；Jonsson et al.， 2003； Marion et al.， 2003] and a 1-D vertical diffusion model [Worman et al.， 2002； Packmanet al.， 2004； Habel et al.， 2002]. Additionally empirical scaling relationships [Richardson and Parr， 1988；Packman and Salehin， 2003； O'Connor and Harvey， 2008] have provided useful insights into the relativemagnitude of contributing parameters. This approach will be taken here to investigate the spatial varia-tion of in-sediment mixing. The following sections describe the basic properties and parameters previ-ously employed in estimating hyporheic exchange， how these parameters have been combined withinempirical relationships to estimate the sediment-water exchange coefficient and finally， how in-bed mix-ing processes， driven by turbulence generated at the sediment-water interface， have been quantifieduing a Fickian analogy. 2.1. Fundamental Parameters Previous studies investigating hyporheic exchange have shown that permeability (K)， bed shear velocity(ux) and roughness height (k，) are important parameters affecting hyporheic exchange. There are severalformulae available to predict permeability. The Kozeny-Carman equation [Carman， 1937]， cited [Freeze andCherry， 1979] gives where Kc is the hydraulic conductivity， pw is the density of the fluid， g is gravitational acceleration， u isdynamic viscosity，0 is porosity and dg is the mean grain diameter. Hydraulic conductivity can be converted to permeability (2)， which when combined with (1)， results in (3)that can predict the permeability of a sediment [O'Connor and Harvey， 2008]. where v is the kinematic viscosity (v=p/pw). Equation (1) is derived from Darcy's law and the packing of spheres， with the addition of an experimentallyderived constant [Bear， 1972]. Carman [1937] states that (1) is valid for nonspherical particles in the stream-line (laminar) flow region with an error of 10-20%. Equation (3) is used by OConnor and Harvey [2008] toderive their scaling relationship when the permeability was not stated in previous studies. It has been usedin this study to validate the in situ permeability measurements. To provide an assessment of potential sub-seafloor pore water advection， Wilson et al. [2008]， investigated the potential for employing grain size as apredictor of permeability in coastal marine sand and recommend permeability-grain size relationships maybe useful， but that a larger database is required. The bed shear velocity， ux is defined [Fischer et al.， 1979； Tennekes and Lumley， 1972] as where t is the bed shear stress， which combined with (5)， derived from the rate of interchange of momen-tum in the Reynolds stress model of turbulence [Tennekes and Lumley， 1972]， gives where u'and v'are the instantaneous velocity fluctuations in the horizontal and vertical directions respec-tively. Tennekes and Lumley [1972] state that if viscous effects are negligible， the velocity fluctuations arecorrelated and the average vertical flow at the sediment-water interface is zero， then (6) is valid at any verti-cal position within the flow. The roughness height， k， is a function of both the sediment grain diameter and any bed-forms present. Itallows comparison， through a single parameter， of experiments that have flat beds with those where bed-forms were used. van Rijn [1984] defined the roughness height as where dgo is the particle size such that 90% of the particles are finer，A is the bed-form amplitude and 2 isthe bed-form wavelength. For flat-bed experiments， A=0 and (7) reduces to 2.2. Interface Exchange Studies Several studies have been conducted to derive empirical scaling relationships to describe the soluteexchange at the sediment-water interface. All studies use the same general methodology， based on Fick'ssecond law in one dimension where C is the solute concentration， t is time，D mixing coefficient and y is the vertical coordinate. Richardson and Parr [1988] conducted flume experiments with glass beads for three flow depths， four veloc-ities and five bead diameters， representing fine to very coarse sands. For an initially saturated bed， theymeasured the tracer concentration at the effluent weir throughout the 30 min experiments. From thesetemporal concentration measurements， after an initial non-Fickian phase， they showed that where D is the effective interface mixing coefficient，Dm is the molecular diffusion coefficient through thesediment pore water and Pek is the permeability Peclet number Packman and Salehin [2003] used seven published data sets to derive a scaling relationship， covering amuch wider range of sediment and flow conditions than those used by Richardson and Parr [1988]. Theyproposed two scaling relationships， the first combining the permeability， the dynamic pressure head andthe sediment porosity was found to be appropriate for larger diameter material and fitted data over morethan three orders of magnitude. It did not however hold for fine sands and so they reported an alternativescaling relationship，which holds for almost five orders of magnitude where Re is the stream Reynolds number Re=h where U is the average velocity in the main stream and h isthe flow depth. A practical method for predicting exchange coefficients across the sediment-water interface over a widerange of sediment and flow conditions is the scaling relationship proposed by OConnor and Harvey [2008].It is derived from 11 previously published data sets covering numerous different sediment characteristics，flow parameters and topographies. OConnor and Harvey [2008] proposed where Re is the shear Reynolds number， Re，=u and the inverse of the scaling constant (5 x 10-4) pro-vided a threshold value in transport conditions (Re，Pe/5=2000)， below which transport was governed bymolecular diffusion， resulting in De/D=1. A limitation of this approach， when investigating fundamentalrelationships， is that both the nondimensional numbers， the shear Reynolds number， Re， and the permeabilityPeclet number，Pek consist of independent variables， as both are functions of the bed shear velocity， u*. The data collated by O'Connor and Harvey [2008] resulted from different experimental setups. All the studiesused recirculating flumes， but the initial location of the solute tracer and the sampling location (either in-bed or water column) was different. This resulted in different equations being used to analyze the data. Fora temporal concentration profile obtained from an instrument positioned within the water column andtracer initially located in the sediment pore water (in-bed)， O'Connor and Harvey [2008] calculated theexchange coefficient across the sediment-water interface from where Co.s is the initial solute concentration within the sediment pore water， dMw/d(t1/2) is the "initialslope" taken from the temporal concentration profile， where Mw is the accumulated mass of solute tracer inthe water column and t1/2 is the square root of time. However， OConnor and Harvey [2008] do not specifywhat portion of the profile corresponds to the"initial slope."Similar approaches have been adopted byPackman et al. [2004]， Chandler et al. [2012]， and others. 2.3. In-Bed Studies A few studies have measured temporal concentration profiles within the bed sediment. Liu et al. [2014] pro-vide a review of recent advances in the measurement of the diffusive flux of chemicals at the sediment-water interface， describing a new sampler [Liu et al.， 2013] which， unlike a conventional benthic chamber，does not need to assume a linear concentration gradient， though an estimation of the chemical diffusioncoefficient in the overlying water is still required. Cho et al. [2010] employed temperature as a tracer andstudied the advective pore water movement in the top 0.60 m sediment layer in marine mudflat sediments.In the limiting case， with no net advection， they report the best-fit depth-averaged mechanical dispersioncoefficient was 2.2.10-7m²/s， with a range between 0.9 and 5.6.10-7m²/s. Nagaoka and Ohgaki [1990] and Shimizu et al. [1990] showed a reduction in mixing coefficient with depth，over a few particle diameters below the interface. They employed large diameter glass spheres (geometricmean particle diameter， dg≥17 mm) for the sediment bed. Neither study quantified the variation in mixing coefficient with depth， as the primary focus of both papers was on understanding the flow through porousmedia. Nagaoka and Ohgaki [1990] and Shimizu et al.[1990] used different analysis techniques to obtainmixing coefficients from the in-bed concentration profiles. Shimizu et al. [1990] use the time at which themeasured concentration equals 1/e of the equilibrium mixing concentration (where e is the base of the nat-ural logarithm) to fit an analytical solution of Fick’s second law (13)， thus obtaining a mixing coefficientfrom one in-bed profile. This technique is susceptible to experimental noise， as only one point is used and itdoes not account for variations in the mixing coefficient depth. Nagaoka and Ohgaki [1990] also used an analytical solution to Fick’s second Law (9). They solved this usinginitial and boundary conditions： where L is the vertical distance between sensors. This corresponds to the scenario where two differentlayers， with different mixing coefficients (D in the upper and D2in the lower) are acting at y=-L. Theupper layer is from y=0 to y=-Land the lower layer is from y=-L to y=-oo. Substituting y=-L into theanalytical solution to Fick’s second law， Nagaoka and Ohgaki [1990] obtained the concentration change atthe interface between the two layers， C as Equation (22) expresses how the concentration at the interface between the two layers changes when theconcentration at the upper edge of the upper layer， f(t)， changes. This equation can be applied if thechange in concentration at the top of the upper layer and both mixing coefficients are known. To analyzeexperimental data， the calculated profile can be optimized to give the best fit to the measured data by vary-ing D1.D2 can be fixed from analysis of the region below that currently being studied. Applying this to several layers creates a challenge with analyzing the lowest region， because D2 is notknown and cannot be obtained from the analysis of a lower region. However taking the limit Di →D2，Nagaoka and Ohgaki [1990] defined another function Here the assumption is that the mixing coefficient for the upper layer is the same as that in the lower layer.The analysis methodology therefore starts by optimizing D1 in (23) so that the closest match is foundbetween the predicted profile and measured concentration profile from the lowest instrument position.Once D is obtained between the lowest pair of instruments， it can be used as D2 in (22)， and Di can beoptimized between the next lowest instrument pair. 3. Experimental Setup An erosimeter was modified to improve the placement of sediment， provide side access for instrumentationin the base section and to incorporate an in situ permeability test. Figure 1 shows the redesigned erosimeter， with a flanged con-nection between the main sec-tion and base at the sediment-water interface， and outlet in thebase for the permeability testing. The main section is 300 mmhigh with an internal diameterof 96.2 mm. A Turner DesignsCyclops 7 fluorometer and a tem-perature sensor were positionedon opposite sides 60 mm belowthe top. The 200 mm tall basesection had the same diameteras the main section. Fiber -opticfluorometers were aligned verti-cally at -0.015，-0.049，-0.083，-0.117， and -0.151 m belowthe top of the base section， thesediment-water interface. Figure 1. Schematic of Erosimeter Experimental Set-Up. A motor sits on top of the mainsection with a 260 mm longshaft bringing the 20 mm diam- eter tri-bladed propeller to 40 mm above the sediment-water interface. Six baffles around the circumference，at the height of the propeller， create a uniform bed shear stress at the sediment surface [Liem et al.， 1997]. The propeller speed is calibrated to the bed shear velocity (u) through observing the onset of sedimentmotion， where "the grains roll over the sediment surface， being moved a significant distance" for single sizesediments. Thereby obtaining the critical bed shear stress which is used to estimate bed shear velocitythrough the van Rijin [1984] criteria，as used by Jubb et al. [2001]. 3.1. Experimental Procedure Each test consisted of five main stages. The first stage was to place a homogeneous concentration ofRhodamine throughout the bed into the base section and take a calibration reading for the fiber optic fluor-ometers. Next， the main section was placed and filled with clean de-aired water. The motor was theninstalled， switched on and the tracer experiments allowed to run. Once the tracer experiment was completethe motor was stopped and replaced by the constant head permeability test apparatus. The permeabilitytest was then conducted on the in situ bed sediment. The test series consisted of five different bed shear velocities and five different sediment diameters in variouscombinations which are given in Table 1， along with the number of tests conducted for each parameter com-bination. Some combinations could not be tested without causing sediment motion，which was undesirable inthis study， and are indicated with a "-"in Table 1. The sediment consisted of single size solid soda glass sphereswith a quoted density of 2530 kg/m. The range of particle diameters， including the mean particle diameters，is given in Table 2. The solute tracer used was Rhodamine WT， a fluorescent tracer developed in the 1960s (USpatent 3， 367.946) and was initially placed in the interstitial fluid， with clean water in the water column. 3.2. Particle Image Velocimetry To confirm the flow field within the erosimeter， particle image velocimetry (PIV) measurements were under-taken. The aims were to qualitatively asses the flow field within the system， to establish the uniformity ofthe flow field at the sediment-water interface and to relate the velocity field to the bed shear velocity (ux)obtained during the sediment motion calibration. Two experimental setups were employed： the first with avertical light sheet (VLS) and the second with a horizontal light sheet (HLS). Further information on the PIVsetup can be found in Chandler [2012]. Five different propeller speeds were investigated， which correspond to the bed shear velocities employedin the dye tracing experiments. Horizontal light sheets at 3 mm， 13 mm and 23 mm above the fixed bed Propeller Mean Particle Diameter，dg(mm)Bed Shear Velocity us(m/s) Speed (rpm) 5.000 1.850 0.625 0.350 0.150 Calibrated PIV (19) 440 3 - - - - 0.0406 0.0427 329 2 2 - - - 0.0296 0.0266 226 2 2 - 一 0.0194 0.0166 179 2 2 2 1 - 0.0147 0.0147 124 2 2 2 1 1 0.0093 0.0091 were used， along with one vertical light sheet position， across the centre of the erosimeter between thebed and the propeller， for both fixed and mobile beds. Raw images were processed using DaVis 7.2 (a LaVision product) to produce velocity vector fields. Fromthese， temporal average vector fields were generated and the instantaneous velocity fluctuations calcu-lated. The velocity components for each point within the vector fields were averaged using where u is the temporally averaged velocity in the x-direction and N is the number of vector fields. The vec-tor fields already account for the time step between images， so time is not explicitly used in the averaging，only the number of vector fields. The same equation was also used for the vertical velocities (v) and theother horizontal component (w) in the z-direction. The vertical light sheet data contain components w and v， whilst the horizontal light sheet data containcomponents u and w. As discussed in 2.1， the bed shear velocity can be calculated from the velocity fluctua-tions. In the coordinate system imposed here， and given the flow field discussed below， (6) becomes This requires simultaneous velocity components from both the horizontal and vertical light sheets， at theline across the erosimeter where the sheets would intersect. However， as the measurements were not con-ducted simultaneously， the instantaneous fluctuations in the z and y directions are not concurrent. Bed shear velocity is often used as a measure of turbulent intensity and is taken as indicative of turbulencein all directions if turbulence is assumed to be homogeneous. Given the flow field above the bed in theerosimeter shown in Figure 2， the wall shear around the edge of the erosimeter should be similar to thebed shear， assuming that the turbulence is homogeneous. Therefore the assumption has been madethat the bed shear velocity can be calculated from the velocity fluctuations in the x and z directions usingthe horizontal light sheet data from 3 mm above the bed. Therefore (25) becomes 3.3.Fluorometry In-bed concentration measurements were taken using fiber-optic fluorometers. The fiber-optic fluorometershad a head diameter of 4 mm. A mesh cover (30 mm long by 4 mm) was positioned over the end of the Table 2. Sediment Properties Mean Particle 90% Larger， 90% Smaller， Permeability， K(10-1m) Diameter，dg(mm) d10(mm) d90(mm) Measured Calculated (3) 5.000 4.700 5.300 223 107 1.850 1.700 2.000 30.6 20.4 0.625 0.500 0.750 3.12 3.18 0.350 0.300 0.400 0.98 1.38 0.150 0.100 0.200 0.18 0.46 Rh fiber to create a measure-ment volume ofapproxi-mately 0.23 ml. The excitationsource： wass a green laserdiodeandthe emissionsdetector was a photo multi-plier tube (PMT) with appro-priateeoptical filters； forRhodamine WT. The signal x direction (mm) Figure 2. Time averaged horizontal light sheet vector fields at different heights above the bed. from the PMT was passed through a low pass filter， with a cut off frequency of 30 Hz， to reduce noise from themains power supply， whilst still capturing the expected rate of concentration change. The fiber optic fluorometers were calibrated in situ for each test using a two point calibration， whilst theCyclops 7 fluorometer， used for water column concentration measurements， was calibrated before and afterthe test series. All the fluorometers had an accuracy of 1 ppb or better. 3.4. Permeability Test The base section of the erosimeter includes a drain so that a constant head permeability test can be con-ducted [British Standard， 1990， 1377-5]， in situ， after solute trace experiments had been undertaken. A cap，connected to the constant head source， is placed on top of the main section， replacing the motor and hous-ing. Manometer gland points， 140 mm apart in the base， are used to measure the hydraulic gradient (l)within the sediment bed. This gradient is used to calculate hydraulic conductivity of the sediment using where Q is flow rate (ml/s)， / is hydraulic gradient (h/y) with h the difference in manometer level (mm) andy the distance between manometer gland points (mm)， Rr is the temperature correction factor obtainedfrom British Standard [1990] 1377-5 and A， is the cross-sectional area of the sample (mm). The hydraulicconductivity is converted into a permeability using (2). Figure 3. Time averaged vertical light sheet vector fields over fixed and mobile bed. The permeability measurements taken after the tracer experiments show good agreement with the calcu-lated permeability using(3)， shown in Table 2. The higher than expected permeability for large diameterspheres could be due to nonlaminar flow conditions within the permeability tests. This would invalidate theassumption of Darcy flow in the derivation of (3) and lead to the discrepancy. The difference betweenthe measured and calculated permeability for the small diameter sediment is within the 10-20% boundsuggested by Carman [1937]. 4. Results 4.1. PIV Experiments The flow field within the erosimeter is complex and changes with height above the bed. However， the spa-tial velocity distribution is independent of propeller speed， which only changes the magnitude of the veloc-ities. The field is relatively uniform at the bed with slightly higher velocities in the centre and lowervelocities around the outside near the wall. The velocities obtained from the PIV data are comparable tothose reported by Liem et al.[1997]. Example time averaged horizontal light sheet vector fields at three heights above a fixed bed for propellerspeed 440 rpm are shown in Figure 2. Raw images were recorded at 1000 fps for 3.2 s for each propeller speed.Close to the bed， 3 mm above in Figure 2c， the flow is rotational， without any inward motion that is seen at23 mm above the bed， Figure 2a. There are higher velocities in the centre and lower ones around the edge atthe bed. The mean velocity is 0.11 m/s， with most velocities within ±40% of the mean. Figure 2 suggests anapproximately uniform circulating flow field at the bed， which has similar velocities at the wall to those seen atthe bed in vertical light sheet data shown in Figure 3. This suggests the assumption made in deriving equation(19) is valid and the velocity fluctuations from the horizontal light sheet 3 mm above the bed can be used toestimate the bed shear velocity. Table 1 shows that there is close agreement between the bed shear velocitycalculated from the PIV data and those calculated independently from the sediment motion calibration. 4.2. Trace Experiments Examples of calibrated temporal concentration profiles from the Cyclops 7 fluorometer within the mainbody， the water column， and the fiber optic fluorimeters located within the sediment bed are provided inFigure 4. The increase in concentration within the water column is evident， showing that not every experi-ment was run until full equilibrium conditions were developed. The effect of spatial difference in instrumentposition below the sediment-water interface is clearly visible， with the instruments closer to the interface 口 Figure 4. Examples of raw data. showing more rapid reductionsin concentration， and hence mix-ing， than those further away.Comparing Figures 4a and 4billustrates the increase in ex-change from the initial high con-centration within the bed tothe water column resulting fromincreased particle diameter， forthe same bed shear velocity. InFigure 4a， for mean particle diam-eter of 0.00035 m， with a bedshear velocity of 0.015 m/s， ittakes over an order of magni-tude longer for the concentration0.083 m below the sediment-water interface to reach equilib-rium compared with Figure 4c，for mean particle diameter of0.00185 m， with a bed shearvelocity of 0.0120 m/s. The results in Figure 4c show thatthe exchange of solute tracerfrom the pore water starts tooccurir -0.015 m belowthesediment-water interface within60 s of the test starting， whereasthere is no significant reduction ofconcentration at -0.117 m until11 h into the test. The noise onthe dye traces， Figure 4b， in theprofiles at -0.151 m is caused byslight temperature fluctuations， asan increase in temperature willcause a decrease in fluorescence[Smart and Laidlaw， 19771.Although the temperature wasrecorded in the upper part of thewater column during the experi-ments， no temperature correctionhas been applied as the noiseis recorded only on the lowerfluorometers and did not affectthe analysis..1Thetemperaturethroughout the tests was21±1℃. 5. Analysis To assess and refine the analysis techniques applied to the new experimental data， a one-dimensionalimplicit finite difference solution to Fick's second law of diffusion [Crank and Nicolson， 1947] was employed.Firstly， the model was used to investigate the proportion of the temporal concentration profile that shouldbe included when calculating the initial slope used in the OConnor and Harvey [2008] method for water col-umn data. The model was then employed to check the robustness of the Nagaoka and Ohgaki [1990] Profile Boundary，y(m) From Analysis Upper Lower Specified No Noise With Noise -0.025 -0.050 20.00 18.90 18.80 -0.050 -0.075 6.00 5.36 5.33 -0.075 -0.100 2.00 1.85 1.85 -0.100 -0.125 0.60 0.60 0.599 -0.125 -0.150 0.20 0.20 0.197 method for analyzing in-bed data and to identify the best goodness of fit parameter for optimizing the in-bed mixing coefficient. The proportion of the temporal profile that should be included when calculating the initial slope is notstated by OConnor and Harvey [2008]. A sensitivity analysis was conducted using three different model sim-ulations： a constant mixing coefficient； a distribution with seven discrete coefficients and an exponentialspatially varying coefficient. Different percentages of the equilibrium，fully-mixed concentrations were usedto define the end of， or last value to be included in， the initial slope. The coefficients obtained from takingdifferent percentages of the equilibrium concentration were compared with the coefficients specified in themodel simulations. The R2values of the linear best fit lines used to obtain the gradient of the initial slopewere also studied. This analysis indicated that using a value of 15% of the equilibrium concentration todefine the end of the initial slope is the most consistent and accurate method. Further details are providedin Chandler [2012]. The sensitivity analysis was extended to three different experimental profiles. The high-est R? values of the linear best fit to the experimental data correspond to between 20 and 30% of the equi-librium concentration. This analysis， combined with the analysis of one-dimensional diffusion modelsimulations， concluded that a value of 25% of the equilibrium concentration should be used to define theinitial slope in the analysis of the experimental data. The Nagaoka and Ohgaki [1990] methodology， for analysis of the in-bed data， has been evaluated using aseven discrete mixing coefficient zone model simulation. Temporal concentration profiles taken from spatialpoints that correspond to the change in mixing coefficient between the different zones were analyzed[Chandler， 2012]. Table 3 gives the output from the Nagaoka and Ohgaki [1990] analysis for the model datawith and without random noise added. The noise was added to check the robustness of the method. Thecoefficient of determination， R?， [Young et al.， 1980] was used as the goodness of fit parameter between themeasured and predicted profiles for the results presented in Table 3. This study showed that the applicationof the technique was not sensitive to noise and generally produced values to within 10% lower than thespecified values. These analysis techniques were applied to the complete data set comprising temporal concentrations distri-butions recorded simultaneously in both the water column and at various depths within the sediment bed，as shown in Figure 1. Typical distributions are shown in Figure 4. The temporal concentration distributionrecorded within the water column was analyzed using the data from the start of the experiment until a con-centration of 25% of the equilibrium concentration was reached. Predicted in-bed temporal distributionswere fitted to the recorded data. Overall， for the 14 test cases considered， a total of 25 interface mixingcoefficients were obtained from the in-flow data and 78 in-bed mixing coefficients were evaluated. Theseresults are summarized in Table 4. 6.Discussion The main focus for this study is to identify appropriate empirical scaling relationships for both the interfacemixing coefficient and the spatial variation of the in-bed mixing coefficients. The unique data collectedfrom the erosimeter have been compared to proposed scaling relationships and a new multiple linearregression analysis performed， employing the experimental variables of mean particle diameter and bedshear stress. Table 4. Evaluated Mixing Coefficients Conditions Interface Mixing In-Bed Mixing Coefficients，D(10’m’/s) Test Coefficient， Number dg(m) ux(m/s) K(10-10m²) D(10-’m²/s) -0.032m -0.066 m -0.100 m -0.134m 1 0.005 0.0407 112.27 19.220 48.511 14.596 1.160 0.0406 97.02 18.879 136.481 40.828 34.911 0.0403 115.89 16.546 78.124 14.175 5.237 2 0.0298 106.91 12.944 37.926 7.183 1.728 0.0304 102.49 14.462 86.667 5.876 1.717 3 0.0198 103.12 6.190 32.099 9.037 一 0.0200 102.34 7.801 120.389 13.172 1.212 0.121 4 0.0152 102.51 3.796 19.090 5.304 0.439 0.029 0.0154 107.74 7.193 27.877 4.855 0.698 0.067 5 0.0101 109.05 4.133 16.228 4.327 0.142 0.026 0.0100 108.77 3.264 12.762 3.257 0.361 0.027 6 0.00185 0.0298 20.68 4.897 0.594 0.202 0.0299 20.31 4.861 9.845 3.976 0.461 0.043 7 0.0197 21.13 2.061 3.435 1.058 0.119 0.031 0.0197 20.56 1.865 3.854 1.213 0.102 0.023 8 0.0153 20.18 0.879 - 1.341 0.077 0.016 0.0153 19.59 0.879 1.797 0.508 0.062 0.013 9 0.0099 20.35 0.292 - 0.101 0.012 0.0098 20.26 0.328 0.957 0.173 0.019 10 0.000625 0.0152 3.15 0.124 0.210 0.057 0.008 0.0153 3.18 0.096 0.187 0.052 0.010 11 0.0101 3.20 0.029 0.096 0.028 - 0.0099 3.21 0.042 0.127 0.028 - 12 0.00035 0.0152 1.69 0.025 0.102 0.019 - 13 0.0100 1.07 0.011 0.074 0.012 - 14 0.00015 0.0098 0.46 0.001 0.000 - - 6.1. Interface Mixing Coefficient Interface mixing coefficients range over four orders of magnitude， from around 1.0 × 10-10 m²/s for0.00015 m diameter particles exposed to a 0.01 m/s bed shear velocity， to 2.0 × 10-6m²/s for the largestdiameter particles tested， 0.005 m under a bed shear velocity of around 0.04 m/s.All values are provided inTable 4. Good repeatability between tests is evident. There are small variations in the permeability， due toslight differences in the packing of the glass spheres and the propeller speed， from which the bed shearvelocity is inferred. To ease comparison with previous work， interface mixing coefficients have been nondi-mensionalized using the molecular diffusion coefficient in sediment pore water， D1m. From flume data collected by Richardson and Parr [1988]， a linear relationship was proposed to the squareof the permeability Peclet number， arguing that the exchange processes were dominated by shear inducedflow， and produced a gradient of 6.59 × 10. Assuming the same relationship， the new erosimeter data，which includes particles of greater diameter， gives a best fit linear relationship gradient of 6.31 × 10°(R²=0.897)， shown in Figure 5a. As with the original data set， it is the extreme values which are limiting.Excluding the small diameter low shear stress and the large diameter high shear stress tests， produces a gra-dient of 1.12×10-5， though does not improve the goodness of fit (R?=0.874). Packman and Salehin [2003] suggested that the interface mixing coefficient was proportional to the squareof both the stream Reynolds number and the particle diameter. Investigating this relationship for theerosimeter data is not possible as there is no stream velocity or flow depth. Instead， replacing the streamReynolds number with the shear Reynolds number， Re and the flow depth with the roughness heightallows a similar approach to be adopted. The best fit relationship using these parameters is linear， Figure 5b，having a gradient of 1.11x10+(R²=0.966). The repeatability of the erosimeter tests is better than previous experimental studies collated by O'Connorand Harvey [2008]. The new interface mixing coefficients lie within the scatter of the previous experimentaldata however they are consistently lower than the proposed scaling relationship of gradient of 5.0 ×10 “.This is most pronounced at the extremes， where combinations of either large diameter sediment and highbed shear velocity or small diameter and low bed shear velocities have been used. The coefficients， nondi-mensionalized using molecular diffusion， plotted against RePe/5 in Figure 4c， exhibit a trend similar to that Figure 5. Comparison of water column derived exchange coefficients. shown by O℃onnor and Harvey [2008]. The gradient of the best fit linear relationship between the parame-ters is 8.89×10-5(R²=0.876). Taking the new interface mixing coefficients obtained from the erosimeter experiments， from a range ofparticle diameters and bed shear velocities， with the permeability Peclet number， Pek between 1000 and77，000 and the shear Reynolds number， Re，between 5 and 600， a multiple linear regression analysis wasperformed to determine the best fit values assuming a relationship of the form De/D'm=(dg)(u*)". Theresulting relationship with R²=0.957， is shown in Figure 5d. Expanding the relationship proposed by O'Connor and Harvey [2008]leads to values of 2.2 for both parameters B and y， whereas the new relationship， derived directly fromerosimeter data， suggests that the effect of bed shear velocity is less， with mean particle diameter having agreater influence. This is further supported by the relationship shown in Figure 5b， where values of 2.0 and1.0 for the powers of dg and u* respectively provide a good fit to the data. Overall this suggests that for flatbeds comprising uniform particle diameter， the interface mixing coefficient is affected to a greater extentby the particle diameter than bed shear velocity. 6.2.In-Bed Studies The in-bed mixing coefficients are plotted in Figure 6 at the midpoint between the two profiles used toobtain the coefficient. There is good correlation between repeat tests and there is a clear variation of themixing coefficient with depth below the interface. The effect of different mean sediment diameters andbed shear velocities is evident. There is more variation in the high permeability， high bed shear velocityexperiments， on the right hand side of Figure 6，which is probably due to the higher coefficients and the slight variability in setup duringthese initial experiments. Thereis an almost constant exponentialreduction of the mixing coeffi-cient with depth， which appearsto be independent of the experi-mental parameters of mean sedi-ment diameter， dg and bed shearvelocity， U*， covering four ordersof magnitude. Figure 6. In-bed mixing coefficients. A multiple linear regression anal-ysis was performed to determinethe best fit values for the con-stants assuming a relationship tothe experimental parameter ofthe form D=a(dg)(u*)"ey. Theresulting relationship is and is shown in Figure 7 for each of the mean particle diameters studied across the range of bed shearvelocities， together with the evaluated in-bed mixing coefficients. These show good agreement， with themajority of the data points falling within the range of bed shear velocities. Equation (29) can be used in con-junction with a 1-D diffusion model to predict the temporal and spatial concentrations within the Figure 7. Predicted vertical variation of in-bed mixing coefficients. erosimeter. This assumes that the source of the mixing is from turbulence generated at the sediment-waterinterface and that the turbulent fluctuations dissipate with distance below the interface. These processesare analogous to Fickian diffusion. As these tests have not been conducted for stratified， mixed grain or nat-ural， angular sediments， there are limitations to the applicability of these results to natural aquatic systems.However， as a first approximation a relationship has been derived with the empirical permeability parame-ter， K， which produces the same vertical spatial variation and dependence on bed shear velocity， giving Clearly if the permeability of the bed sediment varies spatially it will influence these estimations， reducedpermeability likely reducing the depth of influence. Comparing the relationships produced from multiple linear regressions for the interface exchange coeffi-cient and the in-bed mixing coefficient， (28) and (29)， it is interesting to note that variation with mean parti-cle diameter is very similar， the main difference being provided by the greater effect of the bed shearvelocity on the spatial variation. Also there is between a half and one order of magnitude differencebetween the magnitude of the interface mixing coefficient and the in-bed mixing coefficients closest to theinterface. The interface mixing coefficient， calculated from the water column data， is a function of theexchange throughout the top portion of the bed and not therefore strictly the coefficient at the specificlevel of the interface. This is true of all the coefficients calculated using the initial slope method [OConnorand Harvey， 2008]， as a change in concentration is required to obtain the initial slope. This change in con-centration means that a certain depth of interstitial fluid must mix with the water column. It is thereforeunsurprising that the water column data give a lower coefficient than in-bed measurements near thesediment-water interface. The aims of this study were to investigate the applicability of the erosimeter in studying hyporheicexchange and to obtain the vertical variation in mixing coefficient within flat sediment beds without sedi-ment motion. A unique data set has been generated from which the vertical variation in mixing coefficientwithin a sediment bed exposed to turbulence driven hyporheic exchange has been evaluated. The original EROSIMESS-system (erosimeter) was redesigned to improve its use within a laboratory environ-ment and to incorporate an in situ permeability test and fiber-optic measurement system within the bedsediment. The flow field within the erosimeter was evaluated using particle image velocimetry (PIV)， whichvalidated the calibration between the propeller speed and bed shear velocity and demonstrated the uni-formity of the flow field at the sediment water interface. Fiber-optic fluorometers， developed for this study，have enabled concentration profiles to be measured within the bed sediment， permitting the vertical varia-tion of in-bed mixing coefficients with depth below the sediment-water interface to be quantified. Comparing the water column data derived interface mixing coefficients with different scaling relationshipsexhibits similar trends to previous studies， confirming that the erosimeter is a viable option for studyinghyporheic exchange in the laboratory.Multiple linear regressions shows that the interface mixing coefficientis most accurately described by a function of the mean particle diameter， to the power 2.1 and the bedshear velocity to the power 1.55 within the range of the permeability Peclet number， Pek between 1000and 77，000 and the shear Reynolds number， Rex， between 5 and 600. The vertical variation of in-bed mixing fits well to a constant exponential function over the full range ofparameter combinations tested. A relationship to predict the spatial variation within a sediment bed hasbeen developed and relies on the bed shear velocity and either the particle diameter or the permeability.Quantifying the variation in mixing coefficient below the sediment-water interface will allow chemical con-centrations within sediment beds to be modeled more accurately. The relationship enables predictions ofthe depth to which concentrations of pollutants will penetrate into the bed sediment， allowing the activelayer (the region where exchange will occur faster than molecular diffusion) to be obtained. This is animportant aspect for consideration in determining the ecological impact of in the exchange of dissolvedoxygen，nutrient and anthropogenic inputs. AcknowledgementsThe authors gratefully acknowledgethe Engineering and Physical SciencesResearch Council (CASE/CNA/07/75)and Unilever Safety and EnvironmentalAssurance Centre (SEAC) for theirfinancial support for l.Chandler. AlsoJ. VlasKamp and N. Reynolds for theirhelp with the PIV study and the use oftheir equipment and special thanks toI. Baylis for dedicated technicalsupport. Copies of the data can beobtained from the correspondingauthor Professor lan Guymer(i.guymer@warwick.ac.uk). Notation A Surface area of sediment bed，L. b.c Equation constant Solute concentration，ML-3. Mixing coefficient，LT-1. Effective interface mixing coefficient，LT-1 C G Initial solute concentration within sediment pore water， ML.D Molecular diffusion coefficient in sediment pore water， L²T-1. Average mixing coefficient of region between sensors，LT-1. Average mixing coefficient of region below sensors， L2T-1. Geometric mean particle diameter，L. Particle size for which 90% of sediment is coarser，L. Particle size for which 90% of sediment is finer， L. e Base of natural logarithm. Acceleration due to gravity， MLT/K KkL flow depth， L. Hydraulic gradient. Permeability，L. Hydraulic conductivity， LT. Roughness height， L. Distance between sensors， L. Mw Mass accumulation in water， ML N Number of vector fields. Pek Permeability Peclet number Discharge，L'T-1. Temperature correction factor. Coefficient of determination. Stream Reynolds number. Re Shear Reynolds number. time， T. t average main stream velocity， LT. u/ Instantaneous velocity fluctuation in x-direction，LT-1 U Ensemble average velocity in x-direction， LT. u* Bed shear velocity，LT'. V/ Instantaneous velocity fluctuation in y-direction，LT W Instantaneous velocity fluctuation in z-direction，LT. Horizontal coordinate， L. y Vertical coordinate or distance between manometer gland points， L. z Lateral horizontal coordinate，L. A Bed-form height， L. a， B， y， 8 Equation constants. A Porosity. Dummy variable. Bed-form wavelength， L. u .Dynamic viscosity， ML-T-1 Kinematic viscosity， L2T-1. Pw Fluid density， ML-3. Stress or bed shear stress，ML-1T-2. References Bear， J.(1972)， Dynamics of Fluids in Porous Media， Am. Elsevier， N. Y. 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(2000)， Comparison of models for transient storage of solutes in small streams， Water Resour. Res.， 36， 455-468.Worman， A.， A. 1. Packman， H. Johansson， and K. Jonsson (2002)， Effect of flow-induced exchange in hyporheic zones on longitudinal trans-port of solutes in streams and rivers， Water Resour. Res.， 38(1)，1001， doi：10.1029/2001WR000769. Young， P.， A. Jakeman， and R. McMurtrie (1980)， An instrumental variable method for model order identification，Automatica， 16， 281-294 CHANDLER ET AL.POROUS BED MIXING River ecosystems are influenced by contaminants in the water column, in the pore water andadsorbed to sediment particles. When exchange across the sediment-water interface (hyporheic exchange) is included in modeling, the mixing coefficient is often assumed to be constant with depth below the interface. Novel fiber-optic fluorometers have been developed and combined with a modified EROSIMESS system to quantify the vertical variation in mixing coefficient with depth below the sediment-water interface. The study considered a range of particle diameters and bed shear velocities, with the permeability Peclet number, PeK between 1000 and 77,000 and the shear Reynolds number, Re; between 5 and 600. Different parameterization of both an interface exchange coefficient and a spatially variable in-edimentmixing coefficient are explored. The variation of in-sediment mixing is described by an exponential function applicable over the full range of parameter combinations tested. The empirical relationship enables estimates of the depth to which concentrations of pollutants will penetrate into the bed sediment, allowing the region where exchange will occur faster than molecular diffusion to be determined.