Transfer of nonsorbing solutes to a streambed with bed forms: Laboratory experiments

Transcription

1 WATER RESOURCES RESEARCH, VOL. 33, NO. 1, PAGES , JANUARY 1997 Transfer of nonsorbing solutes to a streambed with bed forms: Laboratory experiments Alexander H. Elliott and Norman H. Brooks W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena Abstract. Experiments were performed to determine the mechanisms and rates of solute exchange between a flowing stream and porou streambed. Mass balance, flow visualisation, and depth profiles of concentration were used to investigate the exchange of an inert tracer in a laboratory flume. The measured mass transfer was compared to the exchange predicted by models of exchange related to bed forms, which are presented in a companion paper. For the initial stages with stationary bed forms or slowly moving bed forms the net exchange was predicted satisfactorily and was dominated by bed form-induced interstitial flows (pumping). In the initial stages with rapidly moving bed forms the exchange was dominated by scour/deposition as bed forms propagated (turnover). At later times the models of bed form-related exchange significantly underpredicted the measured exchange. The additional exchange, and the exchange to a flat bed, may be related to bed inhomogeneity or irregular variations in pressure at the bed surface which are not related to bed forms. Such effects are likely to be more pronounced in the field situation. 1. Introduction solute transport. They did not, however, evaluate the net mass exchange. The purpose of these experiments was to examine in detail Richardson and Parr [1988] examined the release of tracers the exchange of solute between a flowing stream and a porous from a flat bed. The exchange was modeled as a vertical difstreambed. In the past, the bed-stream exchange has usually fusion process. They proposed an empirical relation between been described using a calibrated exchange model. We made the effective normalized diffusion coefficient and the properties detailed observations and model-experiment comparisons, of the bed and flow over the bed. The actual mechanism of with the goal of understanding the exchange processes in such exchange was not determined. depth that we could predic the mass exchange solely from Nagaoka and Ohgaki [1990] measured concentrations and physical parameters of the system (such as mean flow velocity). velocities very near the surface of a flat bed with 1.9- or 4.1- cm-diameter bails. It was demonstrated that small-scale turbu- Further, our studies of the exchange of an inert conservative tracer have served as a precursor to further studies of the lent eddies result in exchange to the a depth of one ball, but exchange of reactive or sorptive tracers and particles [e.g., that below this and to a depth of a few bails the exchange is influenced more by large-scaleddies of the flow. Similar ex- Rutherford, 1994; EyIers, 1994]. This is clearly relevanto the periments were performed by Shimizu et al. [1990]. transport and fate of contaminants river systems. Several investigators, including Bencala [1984], McBride Several investigators have performed laboratory studies of [1986], Cerling eta!. [1990], Harvey and Benca!a [1993], and bed-stream exchange. Yousef and Gloyna [1970] studied the Castro and Hornberger [1991] have examined bed-stream exexch ge of sorptive radionuclides in a long flume with living changes of solutes in the field. The exchange is described as a biota. The buildup of tracer in the bed and the concentration vertical advection-diffusion process with calibrated exchange in the water column were measured. They modeled the ex- parameters or as lumped-parameter or linear time series change as a type of compartment exchange with calibrated model with calibrated parameters. Rutherford et al. [1993, 1995] exchange coefficients and capacities. reported measurements of benthic oxygen uptake and has re- Savant et al. [1987] observed the flow patterns inside a bed lated this uptake to bed-stream exchange mechanisms and covered with stationary triangularipples. They demonstrated deoxygenation rates within the bed. that pressure variations over the bed surface cause interstitial In this study the net mass exchange was measured, the penflow through the bed surface and within the bed. Such ex- etration of the tracer (a dye) was observed visually, and depth change has been termed "pumping" [Elliott and Brooks, this profiles concentration within the bed were taken. The mass issue]. Such flows have also been observed in rivers by Grimm exchange was compared with the predictions of the models and Fisher [1984]. Savant et ai. [1987] argued that such flows developed by Elliott and Brooks [this issue]. The models conare more importanthan molecular diffusion in bed-stream centrated on the effects of bed forms and the associated processes of pumping (discussed above) and turnover (trapping and release of solute as bed forms propagate). Now at Department of Natural Resources Engineering, Lincoln University, Canterbury, New Zealand. Copyright 1997 by the American Geophysical Union. 2. Apparatus and Procedure Paper number 96WR In this study new experimental apparatus and techniques /97/96WR $ were developed. The water in a 5-m tilting flume (Figure 1) 137

2 138 ELLIOTT AND BROOKS: TRANSFER OF NONSORBING SOLUTES, EXPERIMENTS 50 cm ::i'i.... t speed controller. The discharge was measured with a standard orifice meter in the return pipe Inlet and outlet. The inlet (upstream) section of the flume consisted of a curved block and sealed box about 70 cm long (see item 7 in Figure 1). The top of the box was 1 to 2 cm below the mean bed level. For the experiments with a bed covered by regular triangular bed forms, blocks of Lucite the same size and shape as the bed forms in the rest of the flume were placed on top of the box in the inlet section. In the experiments with natural bed forms the box was allowed to be covered with natural bed forms. In the inlet section turbulence generated in the pipes and diverging section dies away and the flow can adjust to conditions approximating those in the rest of the flume (although we did not investigate this rigorously for this setup). The impermeable boundary just below or at the Figure 1. Schematic diagram of the flume: 1, 5-m-long, 15- bed-water interface in the inlet section minimizes bed-stream cm-wide flume with Lucite walls and sand bed with ripples; 2, exchange in that section. At the downstream end an imperviconverging section; 3, stainlessteel centrifugal pump; 4, 4-cm- ous vertical plate retained the sand bed and prevented pore diameter pipe; 5, orifice meter; 6, diverging section; 7, inlet water from discharging except through the bed surface or section; 8, subsurface flow discharge box; 9, peristaltic pump to through the subsurface recirculation system. recirculate subsurface flow; 10, impermeablend plate Recirculation of subsurface flow. In the later experiments (after run 10) the subsurface flow was recirculated. There is a horizontal flow in the bed which is induced by the flowed over a sand bed and was continually recirculated. Dye hydraulic gradient down the flume. Without subsurface recirwas added to the water at the start of the experiment and culation, unwanted mass exchange occurs because fluid is within a few minutes was mixed vertically and horizontally drawn down into the bed at the upstream end of the flume to within the water column. The net loss of solute from the flow- provide the horizontal flow, and the subsurface flow then is ing water into an initially clean bed was determined by mea- discharged up out of the bed at the downstream end. This suring the slow decrease of solute concentration in the recir- cause significant mass exchange for large time. With subsurculating water. The concentration changes were measured for face recirculation, the horizontal flow at the upstream end is up to 14 days. The experimental apparatus and techniques, provided by the subsurface flow drawn from the downstream summarized below, are described in detail by Elliott [1990]. end of the bed. In the later experiments a slim box was installed in each end 2.1. Flume of the flume (see Figure 1). The boxes were closed except one Flow circuit. The tilting, recirculating (closed- vertical face of each box was covered by stainlessteel mesh circuit) flume (Figure 1), typical of those used for sediment and polypropylene cloth and one face of each box had a small transport studies, is a 5-m-long rectangular channel with a inlet/outlet. The subsurface flow passed through the mesh and width of cm and a depth of 50 cm. The whole apparatus, was recirculated from the discharge (downstream) end of the comprising the channel, end transition boxes, variable speed flume to the inlet end by a peristaltic pump. The speed of the pump, and return pipe, rests. on a tiltable frame. pump was set so that the flow rate approximated the longitu- By using a recirculating flume (with recirculation time of less dinal subsurface flow rate through about 3/4 of the crossecthan 1 min), the contaminant concentration in the water col- tion of the bed. The pore water velocity through this section umn is kept essentially uniform throughout the system at any was predicted on the basis of the water surface slope in the given time. Essentially the same body of water is passed over flume and the bed permeability. Incidentally, this flow rate the bed many times. Apart from slow evaporation and possible could also be used to predicthe additional mass flux if undervolatilization of the tracer, the flume as a whole (bed, channel, flow recycling were neglected. While not ideal, underflow repipes, and water column) constitutes a closed system. In the cycling was a considerable improvement over impermeable closed-circuit flume, small fluxes of contaminant to/from the end conditions. bed will, with time, result in measurable solute concentration Sampling ports. Vertical arrays of sampling ports changes in the water above the bed; in an open system, con- were installed at several locations in the sides of the flume for centration changes might take place only over a long reach. the purpose of sampling interstitial fluid. A 100-/xL Hamilton The flume was equipped with a movable instrument carriage syringe with a fine needle was used for sampling. Samples were with a detachable point gauge running on rails along the top of taken through silica-rubber sepia in the flume walls. Samples the flume on each side. The flume walls and bottom were made were taken either near the wall by inserting the needle only just of Lucite to permit flow visualization and easy installation of through the septum or more toward the center line by inserting sampling ports. as far as possible (5 cm). The channel depth of 50 cm allowed for a deep bed (typically The spacing of the ports was chosen to be as small as pos- 20 cm deep). The flowing water depth above the bed was less sible without causing interference between samples taken than 7 cm to keep the width-to-depth ratio (15.25/7) greater through adjacent ports. A volume of 100/xL of interstitial fluid than 2. The water and sediment were recirculated by a centrif- was withdrawn for each sample and diluted into 5 ml of ugal pump which was constructed of stainlessteel to avoid deionized water. Assuming a bed porosity of 0.3, the sample corrosion of the pump and contamination of the water. The volume corresponds to a sphere of radius a little over 4 min. pump was driven by an AC motor with a continuously variable Hence a port spacing of 10 mm seems reasonable.

3 ELLIOTT AND BROOKS: TRANSFER OF NONSORB][NG SOLUTES, EXPERIMENTS Sand Properties and Preparation Sand properties. A medium sand ("Ottawa 30," dg = 470 tam and s o = 1.30) and a fine sand ("Oklahoma 90," d a = 130 /am and sg = 1.33) were used. The bulk porosity was for the medium sand and for the fine (weeks for Lissamine). The sand/dye mixtures were left in the dark with periodic shaking; the control was dye solution kept in the dark without weeks to check for contamination by the flume materials or sand. The hydrauli conductivity, measured in a falling-head sorption losses to the wall. Water was added to the flume to correct for evaporativ enrichment. No contamination or loss permeameter, was 0.11 cm/s for the medium sand and cm/s for the fine sand. was found. A similar experiment was carried out over 2 days Sand preparation. Before the first run the sand with Amino G Acid and showed no loss apart from those was washed in a solution of sodium oxalate in deionized water expected from photochemical decay. In summary, these batch tests indicated that Lissamine be- (0.1 g/l) to remove clays, dust, and organicoatings. After each experiment the sand was removed from the flume and haves as an excellent conservative tracer in the experimental rinsed thoroughly with deionized water in a fluidization appa- conditions. Amino G Acid is not quite as good, owing to ratus before the next experiment. Water was drained from the photochemical decay, but it was adequate for the shorter washing system between each rinse. No chemicals were added experiments. to the water. This procedure removed all measurable traces of 2.4. Bed Form Geometry the dye from the sand and associated pore water. Various bed configurations were used in the experiments Tracers: Description, Visualization, Measurement, Initial experiments were with a flat bed. It was soon realized and Stability that small bumps in the bed surface induce bed-stream ex Description. Two fluorescent dye tracers were selected for their stability and nonadsorbence to the sands or the change, so subsequent experiments all had a bed covered with bed forms. In some experiments bed forms with a triangular flume apparatus. Deionized water was used in the experiments profile were formed with a bed form cutter (described by Elliott to avoid chlorine-induce decay of the dye. One of the dyes, [1990]), and the bed forms were stationary. In other experi- "Amino G Acid" (7-amino, 1,3 naphthalene disulphonic acid), ments natural bed forms were formed under conditions of was found to decay slowly owing to the laboratory lighting. Therefore this dye could not be used in the longer experisediment transport and the exchange experiment was performed at a lower velocity so that the bed forms were stationments. The other dye, "Lissamine FF" (Brilliant Sulphafiavine) ary. In further experiments moving bed forms (ripples rather was found to be stable under laboratory conditions for many than dunes) were used. All experiments were run under uniweeks. sand. A solution of Lissamine was circulated in the flume for 2 form steady flow Visualization. The penetration of the dye front The bed form surface elevation was measured using a maninto the bed could be observed through the Lucite walls of the ually operated point gauge with automatic data recording. flume using a portable ultraviolet lamp. At various times dur- Measurements were taken roughly every centimeter down the ing each experimenthe dye front position (the boundary be- center line of the flume and sometimes down the flume near tween areas of dyed and undyed interstitial water, as deter- the wall. Approximately points were taken per wavemined by eye) was recorded on the flume walls. These records form. were later photographed and transferred to drawings. In the The least-squares linear trend of the data was removed from earlier experiments the front positions were not recorded be- the profiles before extracting the statistical measures of the cause an appropriate lamp was not available. In some experi- bed form, including the r.m.s. value of the signal (c r) and mean ments the streamlines of the flow were determined by follow- distance between alternate crossings of the mean bed level (X, ing a small amount of dye injected into the bed near the wall. wavelength). These values are given in the next section and Concentration measurements. Depth profiles of were used as the key measurements of bed form geometry. dye concentration in the pore water were measured from 100 The propagation of the bed forms was determined by fol- /xl of water withdrawn through the sampling ports. The dye lowing the movement of the crests of randomly selected bed concentrations were measured on a Shimadzu RF-540 fluo- forms. The propagation velocities of individual bed forms were rospectrophotometer. The accuracy of the concentration mea- highly variable. The mean propagation velocity was taken to be surements was approximately +_0.5% of the initial value in the the arithmetic mean of the measurements of propagation vewater column at the start of an experiment. All the solution locity of the crests. The coefficient of variation of crest speeds examples from an experiment were analyzed at the same time varied from 0.27 to 0.69, and typically 30 crests were measured. to reduce errors due to variations in the intensity of the fluo- In some experiments with moving bed forms the depth of rimeter lamp. scour was determined by excavating several narrow lateral Stability and losses. Amino G Acid solutions left troughs, filling the troughs with stained sand, then measuring under ambient laboratory lighting decayed photochemically at the depth to which stained sand had been scoured and replaced the rate of 0.5% per day relative to solutions left in the dark by unstained sand. (which did not decay). The mass exchangexperiments using Amino G Acid lasted less than 2 days, after which time the 2.5. Experimental Protocol concentration in the flume had changed by typically 25% owing The experimental protocol for each experiment was as folto bed exchange. Thus decay during the experiment did not lows: introduce serious errors into the computation of mass transfer. 1. The flume was rinsed with deionized water before load- Amino G Acid was not used in the later experiments, which ran ing prewashed sand. Deionized water was added to the flume, over a period of many days. and air in the sand was removed by vigorous manual swirling of In simple batch experiments neither of the dye showed any the sand and water while the flume was running. The bed was sorption to the cleaned sands over a period of several days compacted by manual thumping on the side of the flume.

4 140 ELLIOTT AND BROOKS: TRANSFER OF NONSORBING SOLUTES, EXPERIMENTS 2. The bed was then leveled to the mean bed level (for experiments where bed forms were to form naturally) or the crest level (for those experiments where the bed forms were to be formed artificially) using a horizontal bar attached to the instrument carriage. The water was drained entirely from the level flume, leaving the bed saturated. 3. Then a measured volume of water was added to bring the water to the desired water depth. This water depth was taken to be the mean water depth, d, except in the case of triangular bed forms, in which case a correction of half the bed form height was made to account for the sand removed when cutting the bed forms. 13. Water was added to the flume once or twice a day to balance the evaporation of water from the flume. Thus evap. orative enrichment of the dye was prevented. The flume was stopped and sufficient water to bring the water back to the original level was added. Typically, 750 ml was added per day. 14. In earlier experiments, when the subsurface flow was not recirculated, the experiment was terminated when the end effects became significant, as judged visually (usually after a day or two). The later experiments lasted up to 2 weeks. 15. The bed form profiles were then measured with the flow stopped. The flow was restarted, and a rough check of the mean flow velocity in the channel was made by observing the 4. The bed forms were then formed. In the flat-bed run the time for a cloud of dye to travel the length of the flume. Pore bed was simply left in its leveled state. For those experiments water tracking also was done at this stage so that the injected with stationary triangular bed forms the flume was drained and dye would not interfere with the mass exchange measurements. some interstitial water was removed using the subsurface-flow 16. A few experiments were repeated to demonstrate that recirculation apparatus. The bed forms were then cut. In those experiments with naturally formed bed forms the flow was the results are repeatable to a reasonable degree under the same conditions [Elliott, 1990]. started up at the desired velocity (discharge) and the system was left to run until the bed forms had developed fully and, 3. Experimental Parameters and Data Analysis after adjusting the slope of the flume, the flow was steady and The experimental parameters are shown in Table 1. U is the uniform. In some cases the adjustment procedure took days mean flow velocity; S is the measured hydraulic gradient; U b is because the changes in the bed forms and elevations were slow the bed form propagation speed; d is the mean depth of the and subtle. water column above the bed; O'wan is the r.m.s. bed surface 5. In those experiments in which scour depth was mea- elevation at the flume wall; H is the bed form height (for sured, the flume was drained to install a narrow lateral trough natural bed forms H is taken to be twice the r.m.s. bed surface filled with stained sand, then refilled with water to the prede- elevation averaged at the flume wall and center line); X is the termined level. bed form wavelength (the mean distance between alternate 6. The slope of the water surface (S) was then determined, crossings of the mean bed elevation); and do is the mean depth where S is the slope of the water surface relative to a still water of the sand bed. The other parameters are derived parameters. surface. The parameter V/A, is the effective mixing depth of the water 7. The flow was then started again and the subsurface column, where V is the volume of water in the flume system recirculation was started. This concluded the preparation for excluding interstitial water and A, is the plan area of the bed; the experiment. h m is the amplitude of head variation (total variation 2h,,,), 8. A measured quantity of a 10 g/l stock solution of dye based on the measurements by Fehlman [1985] of the dynamic was added to the flume. To help achieve a uniform concentra- head distribution along the surface of triangular bed forms and tion in the water column, the dye was poured in over the time is calculated according to (1), which is discussed further by it takes for water to circulate around the system, typically 30 s. Elliott and Brooks [this issue]; Um is the predicted maximum The quantity of dye was calculated to give a dye concentration pore water seepage velocity (Um= kkhm, where k = 2 r/x of 5 mg/l in the water column. and K is the bed hydrauliconductivity); u * long = S/khm is the 9. Water from the water column was sampled at various normalized underflow velocity; Ot/t* = O/(kttm) is the nortimes by dipping a test tube into the flowing water. The vertical malization factor for time (t* = kumt, where t* is the normixing in the water column was so rapid that it did not matter 'malized time); and U, is the normalized bed form propagation which heighthe water was taken from. The initial samples (for velocity (S; = OUb/u, ). the first 30 min) were taken at a few positions along the flume to determine when the dye had mixed longitudinally. The sampling in the first hour or so was made about every 10 min (more U 2 ( 0- ] H/d _< 0.34 frequently in the first half hour). After several days the sampling was much less frequent, perhaps once a day. The test h, = ( tubes were covered with plastic film and stored beside the 0.34] H/d H/d _> 0.34 flume. All samples were analyzed at the same time at the end The values of some of the parameters in Table 1 are differof the experiment. ent from those used by Elliott [1990]. In the work of Elliott 10. At certain times the front positions of the dye penetra- [1990] the values of hm (and of parameters dependent on h, ) tion into the sand were observed and marked on the flume were corrected on the basis of the ratio of the measured form walls. in the initial stages of the experimenthe flow in the drag to the form drag predicted by Fehlman [1985]. In the present flume was stopped while this was being done. analysis, no such correction was made, because there were large 11. To establish depth profiles of concentration in the pore errors associated with the measurements of form drag. water, pore water samples at several depths were taken at The measured concentration changes were used to detervarious times and at various positions along the flume. The mine M, the net mass transferred per unit bed area divided by samples for depth profiles were not taken in all the runs. C, the concentration in the water column: 12. The maximum scour depth at the trough positions was recorded on the flume walls whenever a change in depth of removal of dyed sand was noticed. 3/2 (1) V( Co - C)/Ab = c (2)

5 , ELLIOTT AND BROOKS: TRANSFER OF NONSORBING SOLUTES, EXPERIMENTS 141 Table la. Measured Experimental Parameters Bed Form Bed Form U, S, U, d, H, o',¾ n, X, d,, Run Speed Type cm/s 10-4 m/m cm/min cm cm cm cm cm Sand flat bed M flat bed M 7 intermediate natural M 8 stationary natural M 9 stationary triangular M I0 stationary triangular M 12 stationary triangular ' M I4 stationary triangular ' M 15 stationary triangular " M 16 stationary triangular M 17 stationary natural F 18 slow natural M 19 rapid natural F 20 intermediate natural M Symbols are defined the text and in the section notation. F, fine sand; M, medium sand. Description of the bed form speed refers to the speed of the bed forms in relation to the predicted maximum pore water velocity. All runs except runs 7, 9, 11, and 13 used Lissamine dye. Run 8 bed forms were formed under flow conditions of run 7; run 16 bed forms formed underun 18 conditions; run 17 bed forms formed underun 19 conditions. Runs 2, 5, and 6 were repeat runs of run 20; run 4 was a repeat of run 3' and runs 11 and 13 were repeat runs of run 14. where Co is the initial concentration. M/0 is the effective depth of penetration of the solute, where 0 is the porosity of the bed. That is, if M were known, then the concentration in the overlying water could be determined as if the solute were mixed to a depth M/0 in the bed, and the concentration in the bed and in the overlying water were equal. The models proposed by Elliott and Brooks [this issue] were used to predict m, the mass transfer per unit bed area divided by the initial concentration, by means of the following convolution integral [Elliott and Brooks, this issue, equation (8)]: f '=0 ' _ C(t- r) m = Ct R(r) Co where (the residence time distribution) and//(the flow into the surface) are determined from the detailed modeling of the exchange processes. From the definitions of m and M the following simple relation can be determined: so that (3) C0 M=m - (4) M = R(r)C(t - ') d ' (5) Equation (5) takes into account the reduction in concentration as the experiment proceeds. Rather than calculate a separate convolution integral for each experiment, a simplified approximation to the convolution was used [Elliott, 1990]: M 0 R(r) dr (6) This approximation applies for typical experimental conditions as verified by performing the full convolution numerically, with an error of less than 10%. Thus the mass exchange at time t is close to that which would be calculated if a concentration C(t) were maintained in the overlying water right from the start of the experiment. This can be interpreted to mean that the concentration in contaminated parts of the bed is approximately the same as the concentration in the overlying water. This is borne out by the measuredepth profiles of concentration within the bed (see, for example, Figure 8). Note that Table lb. Derived Experimental Parameters V'/A,, h m, Run H/d A/H cm cm "' "' ! Um, Ot/t*, 10-3 cm/s u 'ong min U, - u* '" '" '" '" '" '" '" '" !! long Symbols are defined in the text and in the notation section.

6 142 ELLIOTT AND BROOKS: TRANSFER OF NONSORBING SOLUTES, EXPERIMENTS FLOW ' 75 min 150 min RUN min 650 min I 5 cm Figure 2. Dye fronts and partial streamlines the bed for one bed form in run 9 (stationary triangular bed forms). Fronts at 75, 150, 320, and 650 min are shown. Each arrow was recorded 10 min after the previous arrow (or after the start of the record), each cross was recorded 30 min after the previousymbol, and each circle was recorded 90 min after the previou symbol. this might not be a good approximation if the concentration 4. Observations by Flow Visualization were to drop further or more rapidly than it did in the experiments. Figure 2 shows the dye fronts and streamlines in the sand The depth of penetration was normalized by the bed form bed for a run with stationary triangular bed forms (run 9). The wavenumber as follows: figure illustrates clearly that the pumping process has a strong influence for stationary bed forms. The pattern is similar to 2,rkM (2,r)2M 40M that predicted by the model of Elliott and Brooks [this issue]. 0 0x 0x (7) Fluid enters the upstream face of the bed form where the pressure is high (because the flow in the stream impinges on The coefficient 2 r follows from the analytical modeling of the upstream face). The fluid mostly leaves the bed on the the exchange. Note that when M* = 40, the depth of solute downstream face and trough of the bed form where the prespenetration (M/0 ) is approximately equal to the wavelength of the bed forms (X). sure is low (owing to the separation of flow over the bed form The initial concentration (C0) used to calculate M was in crest). The interstitial velocity is greater near the bed surface. some cases adjusted so that the first data point fits the model The dye front moves progressively deeper as dye is transported predictions. This was done to compensate for difficulties in further along streamlines which go into the bed surface. measuring or calculating the initial concentration. Only con- Figure 3a shows the dye fronts for a whole bed of stationary centrations relative to the ideal we!l-mixed initial concentra- triangular bed forms (run!4). Initially, the dye fronts are quite tion (mixed longitudinally and vertically in the water above the regular, as expected for regular triangular bed forms. The bed) are required to derive M (see(2)). However, in some frontshow the scalloped pattern which is typical of pumping cases it was difficult to measure the initial concentration be- with stationary bed forms. Later, irregular features which are cause some mass exchange with the bed (up to an estimated larger than the bed forms and are not related to the shape of 4% drop in concentration) occurred before the dye became the bed surface appear. These anomalous large-scale features well mixed in the water column. There are also inaccuracies increase the average depth of penetration over that expected associated with calculating the initial concentration on the for regular fronts. The anomalies may be due to flows created basis of the mass of dye used and the volume of water in the by large-scale pressure variations. Such variations may be influme. Therefore where necessary the adjustment procedure duced by inlet disturbances or slight bulges in the flume wall was used and the first mass exchange data point is not a (contractions and expansions in the channel width). Anothe measured value. In four runs where particular care was taken postulated reason for the front anomalies is longitudinal variin measuring the dose of dye added and in measuring concen- ations in permeability which would result in fluid being drawn trations, the correction was less than 2% and showed no sys- into the bed in areas with higher permeability (to supply the tematic bias [Elliott, 1990]. higher underflow to those areas).

7 ELLIOTT AND BROOKS: TRANSFER OF NONSORBING SOLUTES, EXPERIMENTS 143 (a) Stationary Triangular Bedforms, Run 14 (b) Stationary Natural Bedforms, Run 17. _, (c) Slowly- Moving Bedforms, Run 18 J' 50 cm (d) Rapidly- Moving Bedforms, Run 19 V, Figure 3. Dye fronts for representative runs. The downstream half of the flume is shown in each case. There is a gap about half way across each diagram where there was a vertical support strut on the flume. (a) Stationary triangular bed forms (run 14) at 1, 2, 4.3, 9, 24, 51, and 100 hours (dashed line), 7 days (doubledashed line) and 11 days (triple-dashed line); (b) stationary natural bed forms, fine sand (run 17) at 5, 23, 49, and 101 hours (dashed line, 4 days), 167 hours (double-dashed line, 7 days), 240 hours (triple-dashed line, 10 days) and 336 hours (quadruple-dashed line: 11 days); (c) slowly moving bed forms (run 18, U, - U ' n( u= 0.35) at 0.5 hours (heavy full line), 5 hours (dashed line), 22 hours (double-dashed line), and 81 rs (triple-dashed line); and (d) rapidly moving bed forms (run 19, U, - Ul*o,g = 30) at 0.25, 0.75, 2, 9, 20, and 45 hours (dot-dashed line) and 114 hours (dashed line). The front patterns for a run with natural stationary bed flow are moving. Despite the unsteady nature of the flow the forms are shown in Figure 3b (run 17). The variable front front patterns any one time show the scalloped patterns patterns reflect the variability of the bed form surface. Initially typical of pumping. The excursions of fluid are large because the fronts reflect the smaller bed forms because the interstitial the bed forms move only slowly in relation to the interstitial velocity is larger for short wavelengths [see Elliott and Brooks, velocity. Therefore the fronts move up and down, albeit in a rather confused fashion. this issue, equation (13)]. As time progresses, the smaller features of the front patterns merge into larger and deeper fea- The fronts for rapidly moving bed forms (U, >> 1) are tures which reflecthe larger bed forms which can induce flow shown in Figure 3d (run 19). The fronts do not show the deeper in the bed. scal16ped pattern typical of pumping because the interstitial The fronts for a run with slowly moving bed forms (U << 1) fluid cannot move far before the bed shape changes and the are shown in Figure 3c (run 18). The interstitial fluid moves up flow is reversed. In the initial stages the depth of penetration and down because the bed forms which cause the interstitial was limited to the depth of scour. The depth of scour is fairly

8 144 ELLIOTY AND BROOKS: TRANSFER OF NONSORBING SOLUTES, EXPERIMENTS a) Stationary bed, natural bedforms, Run17 b) Slowly-moving bedforms, Run 18 I I ' I... """' ' 5 ½ _1o --IN- 4.2 days 15 --El- 7 days -X- 11 days --O- 19 days I I I I C) Rapidly-moving bedforms, Run 19 I I-. -O- 175 min. 300 min _,. --IN-- 14 hr. ' --X- 22 hr... I I I --X,- 81 hr, d) Flat bed, Run /t- 15 min - -O- 45 min --EF- 240 min - -IN- 9 hr -X- 20 hr -X hr I,,, I I Relative concentration, C/C o 5 hr, Loc. 1--, - 24 hr, Loc. 1 -E]- 24 hr, L.oc. 2--Oi I I Relative concentration, C/C o Figure 4. Depth profiles. (a) Stationary bed forms and fine sand (run 17); (b) slowly moving bed forms (run 18, U - u long = 0.35; profiles at wall); (c) rapidly moving bed forms (run 19, U, - u ong = 30; profiles at wall); (d) flat stationary bed (run 3). Location 1 is 0.5 m from the inlet box, and location 2 is 2.0 m from the inlet box. constant along the flume so the front patterns do not show occur at the bed surface (even though the concentration in the much variability in space. In the later stages the depth of dye overlying water drops as the dye in the water column is depenetration was greater than the scour depth. The fronts pleted, this drop is slow enough in the experiments that the showed some large-scale spatial variability which may indicate steepest gradient would still be at the surface if a diffusion-type large scale steady pressure variations or variations in bed per- process were driving the exchange). meability. The depth profiles with slow bed forms (U << 1) are A strong UV lamp was not available at the time the flat-bed shown in Figure 4b (run 18). The sharp front moves up and runs were performed. However, it was noticed in the last flat- down with time. This is consistent with the observed front bed experiment (with a weak UV lamp) that there were local patterns. Depth profiles with rapid bed forms (U, >>!) are areas of deeper dye penetration, some of which were related to shown in Figure 4c (run 19). The dye moved progressively bed imperfections. deeper with time, as the front patternshow. Figure 4d shows the depth profiles for run 3 with a flat stationary bed. The front 5. Depth Profiles of Solute Concentration was sharp which indicates that even with a flat bed the penetration was the result of advective rather than diffusive transin Pore Water port. Depth profiles of solute concentration in pore water at various times at one flume crossection for a run with stationary bed forms are shown in Figure 4a (run 17). The depth of 6. Mass Exchange penetration clearly increases with time. Below the bed surface 6.1. Stationary Bed Forms is a region with fairly uniform concentration, and below this For the runs with stationary bed forms the mass exchange region the concentration drops fairly rapidly to zero. In fact, in (effective depth of dye penetration, M/ 9) versus the square this run, which was with the fine sand and low seepage veloc- root of time is shown in Figure 5. The spread of the data is ities, the change in concentration is less abrupt than in other considerably reduced by normalizing the data (Figure 6). Esruns where diffusion played less of a role. Nevertheless, even in sentially, the mass exchange is normalized by a fraction of the this run the penetration is dominated by advective transfer bed form wavelength (M* -- 2,n'kM/e ), while time is normal- (steep fronts) rather than diffusion. If diffusion were driving ized by the time it takes for pore fluid to move 1/2 r of a the exchange, then the maximum concentration gradient would wavelength when moving at the predicted maximum pore ve-

9 ELLIOTT AND BROOKS: TRANSFER OF NONSORBING SOLUTES, EXPERIMENTS 145 1ocity, Um (that is, t* = ku,,t). Figure 6 also shows the predicted exchange for pumping driven by a sinusoidal-head variation with underflow [see Elliott and Brooks, this issue]. For t*/o < 50 the mass exchange increases approximately in proportion to (t*/o) z/2, which would be predicted by a diffusion model. For a vertical diffusion process ¾= 2 (8) / x 0.07s / N Run where D is an effective diffusion coefficient in the pore fluid. I.- F' [] Run The slope of the initial part of the curves in Figure 5 can 1 o/_. Run _70 I? o Run Run therefore be used to determine the apparent diffusion coeffi- 0 i I I I cient. Run 17, which had the smallest slope, gives an apparent diffusion coefficient of 1.0 x I0-4 cm2/s, which is greater than ( t */O) 2 the molecular diffusion coefficient of 4. I x 10-6 cm2/s expected for Lissamine [Elliott,.1990]. The pumping model is Figure 6. Normalized net mass exchange (M*) for runs with preferred over the diffusion model, however, because this bet- stationary bed forms. The model curves are for the sinusoidalter reflects the underlying advective process (as demonstrated head model with underflow. by the flow visualisation and depth profile data) and is still straightforward to apply. For the initial stages (t*/o < 100), when the depth of dye (perhaps associated with smaller bed forms or shorter wavelength Fourier components of the nonsinusoidal pressure dispenetration is less than approximately 0.5 of a bed form wavetribution) which would affecthe rate of mass exchangenterlength (M* less than about 20), the experimental data (in ing the bed but not the net experimentally observed mass Figure 6) are grouped fairly closely and the models are within exchange. Such an effect would not be detected in the labora- 40% of the experiments. This demonstrates that the model for tory experiments. Further, there could be rapid exchange into the net exchange due to pumping is appropriate for approxithe top of the bed to a depth of a few grains [e.g., Shimizu et al., mately t*/o < 100. The satisfactory model-experiment comparison for the net 1990], which would not be detected in the experiments. The data spread in Figure 6 increases with time. The pumpmass exchange for small time does not necessarily demonstrate that the rate of mass entering the bed is predicted well by the ing model does predicthat the mass exchange will vary due to model. By the time the first few concentration measurements the effect of underflow (u l*ong)' However, the experimental data did not show a consistentrend to decreasing M* with were made, some tracer was already leaving the bed, which will increasing u* long' This may be due to errors in determining affecthe net mass transfer. This is evidenced by the net mass exchange increasing proportion to t /2, not t (see Figure 5). long or may be because other processes also affect the exchange. The models for pumping predict that in this t /2 regime, for a At later times (t*/0 > 100) the measured mass exchange is given amplitude of driving head the net mass exchange is considerably larger than predicted by the model. One potential independent of the wavelength of the pressure variation [see Elliott and Brooks, this issue, equation (24)], yet the rate of explanation for this is that dye was lost from the system, so that the mass balance overestimates the mass transferred to the mass entering the bed does depend on the wavelength. Therebed. This is not the case, however. Control experiments were fore it could be argued that there might be short-wavelength run to check that dye was not absorbed by the flume apparatus components of spatial pressure variations at the bed surface or sand and that there was not significant photochemical or chemical decay of the tracer. Further, the exchange depth determined by mass balance has been compared to the average depth of penetration from oo 2o the record of dye fronts. The exchange measured by mass balance was up to 25% greater than the exchange indicated by the front positions. Comparisons between the recorded front positions and the depth profiles solute concentration indicate that the recorded front positions were too shallow in some cases once the front had become dispersed. This accounts for, X q- Run8 Run 9 - some of the discrepancy between the measured mass exchange Run 10 and the exchange indicated by the front positions. Even so, the Run 12 Run 14 - maximum' error of 25% for the mass exchange is small in relation to the model-experiment discrepancy of up to 100% O Run 16 A Run for large time. Therefor errors in measuring the mass ex- I I,I, change do not [xplain the large model-versus-experiment dis crepancies for large time. t / (min The model studies [Elliott and Brooks, this issue] indicate that molecular diffusion and lateral pore-scale dispersion can Figure 5. Dimensional net mass exchange (M/O) for runs increase the mass transfer. For the experimental conditions with stationary bed forms following a step change in concentration in the overlying water. See Table 1 for the flow and bed this accounts for up to a 40% increase mass transfer at t*/o = Therefore molecular diffusion and pore-scale disper- conditions for each run. I 1' ' I ' I I 50 - Model, U'ion = Model, U'long=O Model, U*long=O , :8: 11 oo..,*,./ '[ ++ X Run8 o r-. t [... + Run 9 O.OB9

10 146 ELLIOTt AND BROOKS: TRANSFER OF NONSORBING SOLUTES, EXPERIMENTS I I I I I ' ' [ ' ' '"'l ' [ '"b'][ t'l' ' ' '*'' scour depth (y) is the depth to which stained sand was removed, while the predictions were based on a theory for turn. over by random bed forms [see Elliott and Brooks, this issue, section 4.2]. The measured scour depth increases approxi. mately in accordance with the model, although the measured 0o oø r rn - depth is less than predicted. The discrepancy may result from errors in determination of the bed form propagation velocity, o wavelength, or r.m.s. elevation. Note that the depth of solute penetration (M/O) due to pure turnover (without pumping) D,, Turnover Model - will be approximately equal to the depth of scour (y). [] O Run 18 Scour O Run 19 Scour The measured mass exchange and predicted exchange for [] Run 20 Scour the runs with moving bed forms is shown in Figure 8. The model predictions are based on simulations with triangular bed, t, l,,i I, t ' ']lie! I,I I I lo loo looo forms, using aspect ratios based on the measured H and )t N [Elliott and Brooks, this issue]. For a run with slowly moving Figure 7. Depth of bed form scour ( ) for moving bed forms bed forms (Figure 8a, U, - u* long = 0.35, run 18) the mass (runs 18, 19, and 20) compared with the depth of solute pen- exchange was much larger than the scour depth, indicating that etration calculated according to the "pure turnover" model (no turnover is negligible for this value of U, - u * long- The mass pumping) with random bed forms. N is the number of bed forms that have passed. exchange with slowly moving bed forms was slightly smaller than the exchange for stationary bed forms formed under the same flow conditions (run 16; see Figure 8a). In the stationarybed case, U, - u* ong = -0.12, so the two experiments are not sion may account for some but not all of the model-experiment directly comparable. Nevertheless, the unsteady flow in the bed discrepancy for the stationary-bed runs for large time. The records of the penetration fronts show areas of penetration which do not seem to be related to the features of the bed. These features clearly are related to increased mass transfer. The modeling studies [Elliott, 1990] indicate that large- (as evidenced by the front patterns and depth profiles) did not give markedly different exchange compared with the stationary bed. The model (combined pumping and turnover with triangular bed forms) considerably underestimates the mass transfer for scale variations in pressure at the bed surface or large-scale slowly moving bed forms. Part of this can be attributed to using horizontal variations in bed permeability can cause large-scale uniform triangular instead of random bed forms in the model. variations in pore velocity, which in turn results in increased Models of combined turnover and pumping indicate thathe mass transfer. The modeling studies of such variations indicate that the permeability would have to vary by a factor of 2, or the randomness could be expected to increase the exchange by approximate 70% for U* b /g* long = Further, the model pressure would have to vary by half the variation induced by is sensitive to the value of U} - u * long [Elliott and Brooks, this bed forms (large-scale variations of typically 0.1 times the velocity head), to account for half the model-experiment discrepancy in the stationary-bed runs. Each of these seems plausible, although we do not have direct experimental evidence of either. The experiments were performed in a laboratory flume with a we!l-packed bed and fairly uniform sand. It appears that even with such controlled conditions, variations in permeability or issue, Table 1], so that errors in predicting h, or measuring U can lead to large changes in the predicted net mass exchange. This is particularly relevant given the high variability of bed form crest velocities for this run (coefficient of variation = 0.69; 28 bed forms measured). Other reasons for the discrepancies may be dispersion or large-scale variations in pore velocity, as for stationary bed forms. Further, our model of the pattern of porewater movements under random moving bed pressure affect the mass exchange. In the natural environment forms may not be adequate. even more variability can be expected, and it can be expected For bed forms moving at a speed comparable to the maxithat such variations will exert a strong influence on the mass mum interstitial velocity (Figure 8b, U, - u* on = 1.1, run 7) exchange, especially once the exchange by bed form-induced the mass exchange was considerably larger than the predicted pumping diminishes (as time becomes large). The model studies [Elliott, 1990] indicate that random bed forms will give more exchange than regular bed forms owing to the influence of the larger-than-average bed forms. This may also explain some of the model-experiment discrepancy for the scour depth, which indicates that turnover still has only a small influence on the exchange. The measured mass transfer significantly exceeds the predicted exchange for large time, although the comparison. good for small time (t*/o < 4). Including the random component of the bed forms does improve signifrandom bed form runs. For example, for typical experimental icantly the comparison for large time [Elliott, 1990]. conditions the predicted exchange is up to 30% extra for ran- The experiment with U, - u* long = 10 and X/H = 27 dom bed forms at t*/0 = 300. (Figure 8c, run 20) gave exchange much in excess of the scour In summary, several mechanisms not included in the basic depth, whereas the model predicted exchange less than the pumping model can all increase the mass exchange signifi- scour depth. A similar model prediction holds for the model cantly for large times, and one or a combination of these with random bed forms [Elliott and Brooks, this issue, section mechanisms may account for the model-experiment discrepan- 5.3]. It can be concluded tha the model gives a poor prediction cies for large time. of the mass exchange for (H/X)(U,- U ong ) = The exchange for rapidly moving bed forms, with U, Moving Bed Forms ]o,g = 30 and (H/X)(U,- U ong ) = 2.5, is shown in Figure The observed depth of bed form scour by moving bed forms 8d (run 19). In the initial stages of the experiment the exchange is compared to the predictedepth in Figure 7. The observed was limited to the depth of scour. This is indicated Figure 8.d

11 ELLIOTT AND BROOKS: TRANSFER OF NONSORBING SOLUTES, EXPERIMENTS 147 a) Slowly-Moving Bedforms, Run 18, U, - u, m = 0.35 b) Moving Bedforms, Run 7, U; - u,,g = 1.1 Run Measured exchange + Predicted exchange Measured scour o oø 30 - O Run16 exchange (stationary) o 20 o o., co ø Run 7 2- Measured exchange Predicted exchange ) 0 - '... Scour model 8-6- ) c) Moving Bedforms, Run 20, U - u o. = 10 Run 20 Measured exchange... Predicted exchange X Measured scour 0 -,... I I I d) Rapidly-Moving Bedforms, Run 19, U;, - u m = 30 Run 19 Measured exchange Predicted exchange Measured scour W - 14 ) - ß ß x x x>o< x x x - _ X _ X X X X X X xx X o,, xx t ' t...! ' '1 "' i L... o o lo ( t* lo) m (t* lo) 1/2 Figure 8. Normalized measured net mass exchange, scour depth, and model predictions for selected runs with moving bed forms. The quantity U - u 1*on is the bed propagation velocity minus the pore water underflow velocity, all divided by the predicted mayamum interstitial pore water velocity due to pumping. The model predictions of net mass exchange (solid lines) are based on the model of combined pumping and turnover processes using regular triangular bed forms. The model of scour depth (pure turnover) is based on random bed forms. In run!9 the mass exchange is negative at the start of the experiment because the concentration was greater than the theoretical well-mixed concentration, Co. x and was observed visually for the first 9 hours (t*/o < 4), at holds for large time within _+50%. This may indicate some which time approximately 90 bed forms had passed, and the similarity in underlying processes. Note that the modelaverage depth of solute penetration was approximately 1.5 experiment discrepancy associated with the extra exchange times the bed form height. At later times the model predicts processeseems more noticeable in run 20 because the scour mass exchange smaller than the scour depth whereas the mea- depth and predicted depth of exchange are so small. From the sured mass exchange was larger than the scour depth. A similar slope of the nondimensional curve for each run where there is prediction holds for the model with random bed forms [Elliott, sufficient data for large time, and using the relations M* = 1990] (except that the predicted exchange is closer to the scour 2,rkM/0 and t * = k-kh, ' t and (1) for h,,,, we find depth), so the models provide a poor prediction of the total dm/o Ku2U exchange. At later times the experiments indicate that mass exchange is influenced by interstitial flow because the dye dtu2,b(290), penetrates deeper than the depth of bed form scour. Our where the coefficient fit is %. This equation indicates model of the pattern of pore water movements under random that the underlying mass exchange processes for large time moving bed forms may not be adequate. However, as in the could be common to all the runs and independent of the bed other experiments, steady large-scale variations in the pore form wavelength (2rr/k) and the bed form-related driving water velocity may be the cause of such interstitial flow. head (h,,). This is consistent with large-scale irregularities in The normalized mass exchange curves for both moving and pore water velocity driving exchange for large time. stationary bed forms show some similarity for large time. In all runs where there is sufficient data for large time, dm* d(t*/o) /2 (9) 6.3. Fiat-Bed Runs 2 (10) The exchange for the flat-bed runs is shown in Figure 9. The mass increases approximately in proportion to t /2 which is

12 148 ELLIOTT AND BROOKS: TRANSFER OF NONSORBING SOLUTES, EXPERIMENTS 8-- O Run I 1 I I O I large time with moving and stationary bed forms. This O Run ;3... cient/3 for (10) is 0.11 for run 1, and for runs 3 and 4, 6 - ß Run 4... fit to Run 1... fit to Run 3 M/0 (cm) fit to Run o.t-,. :"'... o ' t /2(rnin /2) The exchange processes with a flat bed could be the same as the process which caused model/experiment discrepancies for is supported to some degree by a quantitative analysis. The coeffi- which is comparable to the coefficient for the runs with bed forms ( %). We tentatively conclude, then, that once the rate of net mass exchange due to bed forms decreases, the rate of increase of net mass exchange becomes equal to that which would be found for a flat bed with the same average stream velocity and bed permeability. Such exchange might result from large-scale variations in pore water velocity which are unrelated to bed forms Discussion of the Relative Importance of Various Exchange Processes Figure 9. Mass exchange for runs with a flat bed (runs 1, 3, Through flow visualization and measurements of mass exand 4). The lines are least squares fits. change, these experiments have highlighted the processes of also a feature of a diffusion process. The effective diffusion pumping and turnover due to bed forms. The experiments have coefficient can be determined from the slope of the curves and also suggested that for large time, other processesuch as (8). Run 1 gave an effective diffusion coefficient of 5.4 x 10-4 large-scale variations in head at the bed surface or variations of cm2/s while run 3 and run 4 (a repeat of run 3) gave a coeffi- hydraulic conductivity within the bed can affect the net mass cient of 1.5 x 10-4 cm2/s. exchange. In natural rivers such variations can be expected to The fact that the net exchange can be modeled with a dif- affec the exchange more than in the laboratory. Moreover, in fusion coefficient does not mean that the actual exchange pro- natural streams other processes such as groundwater recharge/ cesses are diffusive. Actually, the depth profiles (Figure 4d) discharge, large-scale variations in bed topography (such as show sharp changes in concentration which are indicative of pool/riffle sequences and bends), bank storage, thermal conadvective transport rather than a true diffusive process. The vection, and preferential flow paths in the bed could affecthe effective diffusion coefficients are larger than the estimated bed-stream mass transfer. molecular diffusion coefficient of 4.1 x 10-6 cm2/s for Lissa- It is beyond the scope of the present study to compare these mine in water and larger than the pore-scale diffusion coeffi- processes, but we do have some suggestions relating to this cient based on the underflow pore velocity of KS/O [Elliott, question. When comparing the processes, one needs to con- 1990]. Therefore these processes do not explain the exchange. sider whether it is the rate of mass entering the surface or, It can also be shown that the exchange is not due to end effects alternatively, the net mass exchange (mass in minus mass out), due to the impermeablend walls [Elliott, 1990]. which is of most interest. For example, if the solute decays Irregularities in the spatial distribution of temporally aver- rapidly within the bed, then the rate of mass transfer into the aged pressure at the bed surface may account for the exchange. bed will be of most interest, because little solute will leave the From (24) of Elliott and Brooks [this issue] and (8), for a bed. Further, the rate of mass transfer into the bed may be of sinusoidal-head variation the effective diffusion coefficient in more interesthan the net mass exchange for studies of biothe initial stages is approximately logical activity within the bed. In other cases, such as when assessing the role of the bed in a contamination/recovery cycle D = - -- gh m ( for a conservative tracer (either sorbing nonsorbing) the net mass transfer may be of more interest. Therefore for run 1 the variation in pressure (2h,,,) would From the experiments it appears that the bed forms have a need to be only 0.13 mm or about 0.1 times the velocity head. dominant influence on the net mass exchange for small time. For run 3 the required variation is even smaller. Such varia- From model studies and from the experiments it is clear that tions seem reasonable. They may be the same types of varia- following a step change in concentration in the overlying water, tions that lead to larger-than-expected exchange for the runs the rate of net mass exchange (net flux) related to bed forms with bed forms. Very precise measurements of the pressure decreases over time to the point where it becomesmall in distribution at the bed surface would be required to determine relation to the initial rate. This is because after some time most whether such pressure irregularities exist and are the cause of of the solute which enters the bed reemerges from the bed. the mass exchange. This reduction in the rate of net mass transfer provides the Richardson and Parr [1988] have measured the mass ex- opportunity for other processes to take effect. These other change from a flat bed over periods of up to 30 min. They processes may have a small flux into the bed, but the solute developed empirical equations for the mass exchange as a may stay within the bed for a large time, so that the net mass function of bed properties and streamflow. Their equations transfer gradually increases. These slower processes seem to be predict a diffusion coefficient of 1.5 x 10 -s cm2/s for run 1 and associated with larger-scale features. The large scale gives a 1.8 x 10 -s cm2/s for runs 3 and 4. These predicted values are an small flux because the associated pressure gradients and interorder of magnitude less than our measured values. One explana- stitial flow may be small, but the large scale also ensures that tion for this is that the pressure irregularities in Richardson and the solute is retained the bed for a long time. The extreme Parr's experiments may have been smaller than in our experi- example of this is net regional groundwater recharge, which ments. The comparison indicates the danger of applying Richard- may be slow but is associated with a very large spatial scale. son and Parr's equations to another setup or to the field situation. Ideally, the net exchange due to the other processes could be

13 ELLIOTT AND BROOKS: TRANSFER OF NONSORBING SOLUTES, EXPERIMENTS 149 estimated and compared with the exchange which would be 7.1. Stationary Bed Forms expected as a result of bed forms, but we do not in general have For stationary bed forms the dye penetration patterns, depth enough understanding of those other processes. As a rough profiles and streamlines show that the mass exchange is influindication, the modeling studies [Elliott and Brooks, this issue] enced strongly by steady interstitial flows, which in turn are indicate that rate of mass transfer due to bed forms becomes driven by pressure variations over bed forms (pumping). small once the depth of penetration approaches approximately In the initial stage (dimensionless time t*/o < 100), when 0.5 of the bed form wavelength for stationary or slowly moving the average depth of penetration is less than approximately 0.5 bed forms or once the depth of exchange approaches approx- of the bed form wavelength, the net mass exchange for stationimately 1.5 times the bed form height for pure turnover (which ary bed forms compares well with the model predictions of theoretically applies for rapidly moving bed forms). In the pumping based on an idealized sinusoidal head variation aplaboratory experiments other processes appeared to have a plied to the bed (<40% discrepancy; see Figure 6). Therefore significant effect at later times (as the dye move deeper). In pumping dominates the net exchange in the initial stage, and natural streams those processes are likely to be more intense the sinusoidal-head model, which is fairly simple, can be apand further processes not observed in the laboratory will op- plied with some confidence for the initial stage of exchange. erate, so it can be expected that other processes may affect the In the later stage (t*/o > 100), when the average depth of net mass exchange more and earlier. penetration exceeds 0.5 of the bed form wavelength, the sinu- In some cases the rate of mass entering the surface (flux into soidal-head pumping model consistently underpredicts the net the surface) will be of more interest than the net mass ex- mass exchange. Pore-scale dispersion and molecular diffusion change. It is tempting to conclude from the results of the can account for some but not all of the extra mass exchange. laboratory experiments for small time that the bed forms have Some underprediction is expected for the natural bed forms, a dominant influence on the rate of mass entering the bed. The because modeling predicts that irregular (natural) bed forms bed form-related exchange is certainly dominant in relation to have more exchange than regular bed forms. Large-scale irthe large-scale processes (at least in the laboratory), but there regularities in the pressure distribution above the bed, or irmay be rapid exchange processes near the surface which were regularities in the bed permeability, may also contribute signot detected in the experiments. For example, there could be nificantly to increased exchange (as discussed further below). rapid exchange to a depth of a few grain diameters due to 7.2. Moving Bed Forms turbulent pressure fluctuations, as demonstrated for gravel- For bed forms which moved slowly in relation to the intertype beds by Shimizu et ai. [1990] and Nagaoka and Ohgaki stitial velocity, the mass exchange was influenced strongly by [I990]. Such exchange might support vigorous biological activpumping, while turnover (entrapment and release of pore waity in the uppermost part of the bed (to a depth of a few grain ter associated with scour and deposition as bed forms propadiameters). Such exchange would not give much net mass exgate) had little effect. The model (for combined pumping and change for a conservative nonsorbing tracer, because the tracer turnover with uniform triangular bed forms) underpredicted would leave the bed soon after it enters, and the depth of the exchange (see Figure 8a). The discrepancy can be reduced penetration is small. The experiments in this study would not if pore water dispersion and randomness of the bed forms is detect such exchange, because such exchange would probably included in the model. Further, inaccuracies in determining occur before the tracer became well mixed into the water sensitive parameters for the model (driving head or the bed column, and the associated change in concentration in the form propagation velocity) could result in significant changes water column would be too small to detect (at least for the in the model predictions. However, the model may not adesands used in these experiments). Similarly, Rutherford et al. quately represent patterns of pore water movement under ran- [1993] have suggested (on the basis of field observations) that dom moving bed forms, and processes not included in the there could be rapid exchange into a fluidized layer of sand model (for example, large-scale variations in the pore water near the surface of a mobile bed. velocity) may affect the exchange substantially for large time. In principle, estimates of the rate of mass entering the bed as For bed forms moving at a speed comparable to the maxia result of processes related to bed forms could be compared mum interstitial velocity, turnover did not affect the exchange with estimates of the rates for other processes (if known) to greatly. The model for combined pumping and turnover gave a determine the dominant process. The work of Harvey and good prediction for t*/o < 4, but the exchange was under- Bencala [1993] gives some insight into how the rate might be predicted at later times (see Figure 8b). estimated for exchange resulting from large-scale streambed In the initial stages of the experiment with rapidly moving topography, and the analysis would be straightforward if the bed forms (U, = 30; Figure 8d), when the average depth of net groundwaterecharge rate were known. penetration was less than 1.5 times the mean bed form height, the exchange was dominated by turnover and the depth of dye penetration was close to the depth of bed form scour. This 7. Summary and Conclusions scour was predicted adequately by the scour model (pure turn- Experimental techniques were developed to study the ex- over model with random bed forms; see Figure 7). Even with change of a nonreactive tracer between a porous bed and a such rapidly moving bed forms, interstitial flow eventually stream. Mass balance was used to determine the net exchange caused the depth of penetration to increase beyond the scour in a 5-m-long recirculating flume, while flow visualization (with depth. The model for bed form-related exchange based on the a fluorescent dye) and depth profiles of interstitial concentra- combined processes of pumping and turnover predicted a tions were used to study the actual exchange processes. The depth 'of penetration less than the scour depth, whereas the experimental results were compared to model predictions, measured exchange for large time was much greater than the which focus on the exchange processes of pumping and turn- scour depth. Therefore the model of bed form-related exover [Elliott and Brooks, this issue]. change does not provide a good prediction of the measured

14 150 ELLIOTT AND BROOKS' TRANSFER OF NONSORBING SOLUTES, EXPERIMENTS total exchange for large time. The discrepancy may be due to inadequate modeling of the patterns of pore water movement dr, bed depth, m. d a geometric mean grain diameter, m. induced by moving bed forms. However, the exchange for large H bed form height, m. time with moving bed forms was similar to the exchange for a flat bed and was also similar to the exchange for large times for stationary bed forms, which suggests that the modelhm amplitude of the dynamic head fluctuations at the bed surface (total variation = 2hm), m. K hydraulic conductivity of the bed, m/s. experiment discrepancy more likely due to processes com- k wavenumber, usually bed form wavenumber (2rr/X), --1 mon to all the runs. For example, steady large-scale pressure m. irregularities which are not related to the bed forms could be responsible for the model-experiment discrepancy. m mass transfer per unit bed area, divided by Co, m. M mass transfer per unit bed area, divided by C (M/O 7.3. Flat Bed is the effective depth of solute penetration), m. M* normalized value of M, equal to 2,rkM/0. For the experiments with a flat bed the net mass exchange increased with t 1/2 (see Figure 9). Pore water movement induced by steady pressure irregularities at the bed surface is the N number of bed forms which have passed. F::/ mass flux into the surface, divided by C and averaged over the bed surface, m/s. most likely cause of the observed exchange. Effective diffusion coefficients were determined, but these should not be applied R flux-weighted mean value of R, the residence time function. to natural situation since the irregularities will be of a different scale and magnitude. No predictive model is proposed for s g geometric standar deviation of grain diameters, m. S hydraulic gradient. the flat-bed case. t time, s The Role of Large-Scale Irregularities The extra exchange for large time with stationary or moving bed forms and the exchange for flat beds is consistent with the large-scale irregularities observed in the dye penetration patterns. The relatively small flux associated with these irregularities has a significant effect on the cumulative net exchange only once the rate of increase of net exchange due to bed forms diminishes. Longitudinal variations in bed permeability or irt* normalized time, equal to kumt = k2khr. U mean flow velocity in the channel, m/s. Ut, bed form propagation speed, m/s. U, normalized bed form propagation velocity, equal to OUb/Um V' volume of water in flume excluding interstitial fluid, m 3. U on underflow velocity (longitudinal porewater velocity due to hydraulic gradient), equal to KS, m/s. regularities in the pressure distribution at the bed surface u on normalized underflow velocity, equal to u ong/um. could cause the observed irregularities in dye fronts and the Um pore water Darcy velocity scale, equal to kkh,, m/s. extra mass exchange. The model studies indicate that for the stationary bed forms, a reasonable degree of variability in permeability (a factor of 2) or irregularity in pressure (0.1 of the velocity head), both of which are plausible, can account for half of the extra mass exchange. Further, the exchange for y depth of bed form scour, m. 0 porosity of the bed material. X bed form wavelength, m. cr r.m.s. bed elevation, m. cry, at r.m.s. bed elevation at the flume wall, m. large time with bed forms is similar to that for a flat bed, which suggests that the processes responsible for the exchange are r time lag, s. similar and are not related to the bed forms. Analysis of the rate of increase of the net mass exchange for large time in runs Acknowledgments. This study was supported under USGS grant G1488, the Andrew W. Mellon Foundation, and a Walter with bed forms also suggests a commonality of process, and the L. and Reta Mae Moore Fellowship. The authors thank James J. form of the increase suggests that the exchange processes need Morgan and Robert C. Y. Koh for their advice on this project. The not be related to bed forms. Thus the experimental observa- authors also thank the Water Resources Research reviewers of the tions are consistent with exchange processes resulting from original manuscript for their detailed and helpful comments. large-scale irregularities. In natural streamsuch variations and irregularities can be References expected and will influence the mass exchange, especially once Bencala, K. E., Interactions of solutes and streambed sediment, 2, A the rate of exchange due to pumping or turnover diminishes. dynamic analysis of coupled hydrologic and chemical processes that As a rough indication from the laboratory experiments, pro- determine solute transport, Water Resour. Res., 20(12), , cesses not related to bed forms start to dominate the net mass exchange for a nonsorbing conservative solute once the depth Castro, N.M., and G. M. Hornberger, Surface-subsurface water interof penetration approaches approximately 0.5 of the bed form actions in an alluviated mountain stream channel, Water Resour. Res., 27(7), 16!3-1621, wavelength for stationary or slowly moving bed forms or once Cerling, T. E., S. J. Morrison, R. W. Sobocinski, and I. L. Larsen, the depth of exchange approaches approximately 1.5 times the Sediment-water interaction a small stream: Adsorption of 37Cs bed form height for rapidly moving bed forms. General sug- by bed load sediments, Water Resour. Res., 26(6), , gestions for an approach to comparing rates and scales of Elliott, A. H., Transfer of solutes into and out of streambeds, Rep. KH-R-52, Keck Lab. of Hydraulics and Water Resour., Calif. Inst. of various exchange process were also presented. Technol., Caltech, Pasadena, Elliott, A. H., and N.H. Brooks, Transfer of nonsorbing solutes to a Notation streambed with bed forms: Theory, Water Resour. Res., this issue. Eylers, H., Transport of adsorbing metal ions between stream water A, plan area of the bed, m 2. and sediment bed in a laboratory flume, Rep. KH-R-56, Keck Lab. of Hydraulics and Water Resour., Calif. Inst. of Technol., Pasadena, C solute concentration in the overlying water, mg/l, C{. initial concentration, mg/l. Fehlman, H. M., Resistance components and velocity distributions of

15 ELLIOTT AND BROOKS: TRANSFER OF NONSORBING SOLUTES, EXPERIMENTS 151 open channel flows over bedforms, M.S. thesis, Colo. State Univ., W. Chiu, Modelling benthic oxygen uptake by pumping, J. Environ. Fort Collins, Eng. N. Y., 121(1), 84-95, Grimm, N. B., and S. G. Fisher, Exchange between interstitial and Savant, A. S., D. O. Reible, and L. J. Thibodeaux, Convective transport surface water: Implications for stream metabolism and nutrient cy- within stable river sediments, Water Resour. Res., 23(9), , cling, Hydrobiologia, 111, , Harvey, J. W., and K. E. Bencala, The effect of streambed topography Shimizu, Y., T. Tsujimoto, and H. Nakagawa, Experiment and macroon surface-subsurface water exchange in mountain catchments, Wa- scopic modelling of flow in highly permeable porous medium under ter Resour. Res., 29(1), 89-98, free-surface flow, J. Hydrosci. Hydraul. Eng., 8(1), 69-78, McBride, G. B., A procedure for prediction of the flux of solutes across Yousef, Y. A., and E. F. Gloyna, Radioactivity transport in water, the sediment/water interface in rivers, paper presented at Interna- Summary Rep. EHE-70-05, Tech. Rep. 20, U.S.A. Energy Comm., tional Conference on Water Quality Modelling in the Inland Natural contract AT-(11-1)-490, Univ. of Tex. at Austin, Environment, Br. Hydromech. Res. Assoc., Bournemouth, Engl., N.H. Brooks, Keck Laboratory of Hydraulics and Water Resources Nagaoka, H., and A. J. Ohgaki, Mass transfer mechanism in a porous , California Institute of Technology, Pasadena, CA riverbed, Water Res., 24(4), , ( brooksn@cco.caltech.edu). Richardson, C. P., and A.D. Parr, Modified Fickian model for solute A. H. Elliott, Department of Natural Resources Engineering, P.O. uptake by runoff, J. Environ. Eng. N.Y., 114(4), , Box 84, Lincoln University, Canterbury, New Zealand. ( Rutherford, J. C., River Mixing, John Wiley, New York, elliotta@lincoln.ac.nz) Rutherford, J. C., G. J. Latimer, and R. K. Smith, Bedform mobility and benthic oxygen uptake, Water Res., 27(10), , Rutherford, J. C., J. D. Boyle, A. H. Elliott, T. V. J. Hatherell, and T. (Received June 26, 1996; accepted September 9, 1996.)