18 Traditional versus Two-Phase Perspective on Turbulent … · 2013-03-18 · such as Erosion and Sediment Transport Measurement: Technological and Methodological Advances (Oslo,

Muste, Yu & Fujita: Traditional versus Two-Phase Perspective ...

BAW-Workshop: Boden- und Sohl-Stabilität – Betrachtungen an der Schnittstelle zwischen Geotechnik und Wasserbau1-1

18 Traditional versus Two-Phase Perspective onTurbulent Channel Flows with Suspended SedimentVergleich von traditioneller und auf Zweiphasenströmungbasierender Betrachtung turbulenter Gerinneströmungen mitSchwebstofffracht

M. Muste & K. YuIIHR-Hydroscience & Engineering, The University of Iowa, U.S.A.EngineeringIIHR-Wasser- & Ingenieurwissenschaften, Universität Iowa, U.S.A.

I. FujitaKobe University, JapanUniversität Kobe, Japan

ABSTRACT: The present paper provides new insights into sediment-laden flows using two-phase experimentalinvestigations facilitated by image velocimetry techniques. Two series of flume experiments with increasingconcentration of buoyant and neutrally-buoyant sediment fully suspended in a turbulent open channel flow arereported. The results illustrate that the suspended particles affect the underlying turbulent channel flowthroughout the depth irrespective of their inertia. Comparison of the results obtained for the two particle typesreveals the effect of the particle inertia on the horizontal and vertical velocity lag between water and particles inthe mixture, changes in flow turbulence, eddy viscosity, and sediment concentration. As expected, particleinertia mostly affects the vertical turbulence intensities and the increase in the sediment concentration bettersubstantiates the change trends. Particle turbulence intensities in the present experiments are larger than thoseof the fluid throughout the outer region revealing a significant momentum exchange between the phases.

KURZFASSUNG: Der vorliegende Beitrag stellt neue Erkenntnisse zur sedimentbelasteten Stömung vor, die ineiner zweiphasigen Modellierung experimentell mit unterstützender Hilfe der Bildverarbeitungstechnik ermitteltwurden. Über zwei Laborgerinneexperimente mit turbulenter Gerinneströmung wird berichtet, die sich mitteilweise und vollständig ausgebildeter Geschiebefracht beschäftigen. Die Resultate veranschaulichen denEinfluss von vollständig suspendierten Geschiebeteilchen auf die darunter befindliche turbulente Gerinne-strömung, den diese über die gesamte Wassertiefe unbeeinflusst von der Teilchenträgheit ausüben. DerVergleich der Ergebnisse, die mit zwei unterschiedlichen Teilchentypen erhalten wurden, zeigt keinenUnterschied hinsichtlich des Einflusses der Teilchenträgheit auf die horizontalen und vertikalen Geschwindig-keitsdefizite der schwebstoffbefrachteten Strömung, auf die Änderung von Strömungsturbulenz, Wirbelviskositätund Sedimentdichte. Wie zu erwarten war, hat die Teilchenträgheit auf die vertikale Turbulenzintensität und aufdas Anwachsen der Sedimentkonzentration Einfluss, was sich deutlich in den tendenziellen Veränderungenabbildet. In den vorliegenden Ergebnissen sind die Intensitäten der Teilchenturbulenzen größer als die derbenachbarten Strömungsregionen, was darauf hindeutet, dass ein signifikanter Impulsaustausch zwischenbeiden Phasen stattfindet.



1.1 IntroductionSuspended sediment is distributed over most of theflow depth and has larger downstream velocitiesthan sediment moving near the bed, therefore thetotal sediment load in rivers is often dominated bythe suspended load. Since the role of fine sedimenton the environment has only been recentlyunderstood, there is an immediate need for in-depthinvestigation of the spatially and temporally varyingprocesses that suspend, transport, and depositsediment. Suspended-sediment transport comprisesan especially complex two-phase flow. Even for itssimpler case in uniform open-channel flow,suspended sediment transport includes difficultiesattributable to sediment concentration and velocitygradients across the flow depth, non-homogeneouschannel turbulence, the irregularity of sedimentparticle shape, simultaneous presence of a range ofparticle sizes, and the multiple interactions betweenthe two flow phases.

Extensive research efforts in the last few decadeshave only partially elucidated the complexities ofsuspended-sediment transport. Lacking adequateformulation and quantification of the interactionbetween suspended particles and the carrier liquid, itis common practice to combine the availablesediment mechanics theory and empiricism to obtainpredictive formulations for suspended sedimenttransport. Raudkivi (1999) has recently remarkedthat the available theories are quite limited and moreresearch should be oriented toward understandingand formulation of the physical processes involved inthese flows. The understanding effort is timely,because there is an increased tendency to solvesuspended sediment transport problems usingnumerical models, despite that considerablequestions are raised on the quality of physicalrelationships on which these models are based.

The new generation of nonintrusive instruments nowfacilitates further understanding of channel flowscarrying suspended sediment. Increasingly powerfulsuch techniques allowed documentation of the nearwall coherent structures and their higher level of self-oganization leading persistent alternative low- andhigh-speed velocity streaks (e.g., Sumer & Oguz1978; Sumer & Deigaard 1981; Rashidi et al. 1990,Wei & Willmarth, 1990; Soulsby, 1994, Nino &Garcia, 1996). Among other insights, the newinvestigative tools undoubtedly revealed ameasurable velocity lag between the streamwisefluid and sediment velocities and a variation of itsmagnitude both with the depth and sedimentconcentration (Kaftori et al., 1995; Muste, 1995:Taniere et al., 1997; and Kiger & Pan, 2002).Additionally, studies have shown that the underlyingflow turbulence is attenuated or enhanced bysuspended particles in an intricate relationship withseveral sediment-flow parameters (e.g., Tsuji &Morikawa, 1982; Elghobashi & Abou-Arab, 1983;Rashidi et al., 1990; Gore & Crowe, 1991; Rogers &

Eaton, 1991; Yarin & Hetsroni, 1994). Despite theseinitial findings, there is a growing awareness withinthe scientific community that the sediment researcharea is stagnating and there is an imperious need fora better understanding of the fundamentals of theprocesses involved. Recent specialized meetings,such as Erosion and Sediment TransportMeasurement: Technological and MethodologicalAdvances (Oslo, Norway, 2002) and Sedimentationand Sediment Transport: at the Cross Roadsbetween Physics and Engineering (Monte Verita,Switzerland, 2002) are illustrative examples ofsearching efforts aimed at surpassing the status quo.The multitude of parameters involved and theirunknown interaction preclude at this time predictionof the changes produced by the sediment on thecarrier flow even in the simplest sediment laden-flows. Current efforts are directed toward criticalreview of the knowledge status, call for newapproaches, new strategies, and new methods fordeveloping an improved understanding of the cause-effect relationship in sediment-water interaction(Sherwood et al., 2003; Hanratty et al., 2003;Sundaresan et al., 2003).

Today’s principal scientific issue regarding sediment-laden flows is the understanding of why the phasesconfigure in a certain way (Hanratty et al., 2003) andsubsequent development and validation of modelsthat integrate the correct microphysics in appropriateaveraged equations. The formulation of these laterequations presents challenges since the structure ofthe phase distribution could affect the choice ofaveraging methods and closure relations. Thesolution to this problem involves the discovery of thesmall-scale interactions between the phases that arecontrolling the macroscopic behavior of themultiphase flows through complementary laboratoryand numerical experiments. It is obvious, however,that the description of this finer detail of the flowcannot be accomplished without using two-phaseinvestigative tools, models or experimentaltechniques capable of discriminating the plowphases.

The increased level of complexity for theinvestigation of suspended sediment transport usingthe two-phase flow approach might sound overstatedfor engineering hydraulics. However, improvementof modeling and predictive formulation of suspendedsediment transport cannot be sustained withoutfurther insights into the nature of particle–fluid andparticle–particle interactions and clarification of theenergy transfer between flow phases, among otherneeds. The findings reported in this paper attemptsto provide experimental evidence aimed at providingnew insights into the micro-mechanics of suspendedparticulate transport using two-phase experimentalinvestigations facilitated by image velocimetrytechniques.



1.2 EXPERIMENTS

1.2.1 Experimental ContextOpen channel turbulent flows are characterized bythe existence of persistent coherent structures,particularly in the near-wall region, that includeejections and sweeps and their higher state oforganization in low- and high-speed streaks. Particlein suspension in sediment-laden flows are movingunder the action of body forces and the coherent wallstructures. In turn, particles are acting on the flowthrough two mechanisms (Kaftori et al. 1998). Oneis due the presence of the particles at the wall as“moving roughness” and it is similar to effectproduced by stationary roughness. The second isthe result of the particle-fluid structure interactionthat takes place throughout the flow depth.Additional complexities occur if the concentration forthe suspended fraction exceeds 10-3 when particle-particle interactions become important.

Most of the available experiments on suspendedsediment transport with natural sand (specific gravityabout 2.65), from the classical work of Vanoni (1946)to recent two-phase experiments, Bennett et al.(1998), Muste & Patel (1997), Best et al. (1997),Kiger & Pan (2002), Righetti & Romano (2004) havereported the existence of long, persistent sedimentstreaks on the channel bed formed by particledeposited in the low-speed streaks associated withthe wall coherent structure. Even experiments withneutrally-buoyant particles, as those reported byRashidi et al. (1990) and Kaftori et al. (1995.a;1195.b, 1998) noted the streak presence. Sedimentstreaks materialize the low- and high-velocity streaksformed by the self-organized structures acting in thewall region. They are more prominent when particlesare heavier (even if the bulk sediment concentrationis in the 10-3 to 10-4 dilute concentration range) orwhen the bulk flow velocity in the channel low.Streak presence does not necessarily imply that thesediment is deposited on the channel bed, rather it ismoving along the streak direction acting like a“moving” roughness.

The writers carried out two sets of experimentsoriginated from clear water flows; one set withnatural sand (NS), the other with neutrally-buoyantsediment (NBS), formed of crushed nylon. The par-ticle size, shape factor, and sediment concentrationswere same for the two experiment sets. A majordifference between the writers’ experiments and theearlier experiments is the lack of sediment streaksfor the discussed experiments. The high Fr numbersfor the NS and NBS sets confirm that writers’ flowswere highly turbulent with all the sediment insuspension. Consequently, the primary interactioninvolved in the present experiments is the particle-fluid structure one, rather that the alternativeroughness-like mechanism. The insights from theprevious studies complement those of the presentstudy insofar that, for a range of particle and flow

characteristics, they show the combined outcome ofthe two effects on flow turbulence.

1.2.2 Experiment Setup and ProceduresThe experiments were focused on dilute dispersesediment in open-channel turbulent flow where thevolume fraction of particles is very small andinterparticle collisions limited. In such flows the two-way coupling, where the motion of the fluid has asignificant effect on the particle motion and viceversa, is dominant. Consequently, the experimentaldesign was driven by two key elements. First, theexperiments with sediment were conducted such thatno deposition of sediment on the bed was allowed.Without bedload transport, all the changes in theunderlying flow can be attributed to the presence ofsuspended sediment, thus facilitating understandingof underlying mechanisms of the suspensionprocesses and their subsequent formulation. Thesecond key element of the experimental design wasuse of a two-phase flow velocity instruments thatallowed separate and simultaneous non-intrusivemeasurements on solid and liquid phase. A com-bination of image velocimetry (IV) cross-correlationand particle tracking techniques has been designedand implemented to provide mean and turbulenceflow characteristics in a plane.

The experiments were conducted using a tilting re-circulating flume, 6.0 m long, 0.15 m wide at KobeUniversity, Kobe, Japan. The flume bed was madeof smooth finished stainless steel with glass wallsand bottom. Plastic honeycombs were set at theflume entrance to facilitate quick flow development,minimize air entrainment, and ensure flow uniformity.The volumes of the head and tail tanks were kept atminimum to avoid sediment deposition. The tankswere fitted with edge fillers to avoid sedimentaccumulation. Both tanks have been continuouslyinspected during the measurements for sediment re-tention. Flow depths were measured with a 0.01 mmresolution digital micrometer placed on an instru-mentation carriage. The flume was covered, theroom temperature kept approximately constant, andexperiment conducted in full darkness to preservethe flow quality and recording conditions.

Two series of tests were conducted starting withclear (distilled) water flows (CW). The experimentswere conducted at a single flow rate (maximumstreamwise velocity of approximatively 1 m/s), whichwas selected such that the turbulence intensitywould be sufficient for particle suspension main-tenance. The flow depth was kept small to obtain alarge channel aspect ratio (i.e., 7.5) that preventsformation of secondary flows in the channel.Sediment-laden flows were obtained by successivelyadding sediment to the original clear flows. Channelslope was kept at 0.0113 m/m for all tested flows.The flows were checked for flow uniformity followingeach sediment addition, but no measurable changein the free-surface slope was noticed using theavailable instrumentation. All reported measure-



ments were conducted on the flume centerline, in atest section located 5.3 m downstream the flume in-let. Preliminary velocity measurements in the stream-wise and spanwise direction in the test section areadocumented that a fully developed uniform free-surface flow was attained.

Two kinds of sediment particles were used in thetests; natural sand (NS) and neutrally-buoyantsediment (NBS) consisting of crushed Nylonparticles. The NS and NBS particles were carefullysieved within the 0.21~0.25 mm size range and werepractically of similar shape irregularity. The sedimentconcentration for the three consecutive NS and NBSflows were identical, in the 0.0005 – 0.0015 volu-metric concentrations range. Consequently, the onlydifference between the two sediment-laden flowswas the specific gravity of the sediment, i.e., 2.65 forthe natural sand and 1.02~1.03 for the crushedNylon. As mentioned before, no sediment depositionwas allowed to develop anywhere on the flume bedand in the flow circuit. No sediment streaks wereobserved on the channel bed during the conductedexperiments. Visible streaks occurred only for thehighest concentration with natural sand flow (NS3)when the velocity was lowered 20%. Tables 1 and 2present the summary of the main sediment charac-teristics and experimental conditions for the testedflows. Fall velocities displayed in the tables werecalculated using Dietrich’s (1982) formula with theparticle diameter with D50 = 0.23 mm and densities of2,650 kg/m3 and 1,025 kg/m3 for the natural sandand neutrally sediment particles, respectively.

The imaging system used for conduct of the velocitymeasurements comprised illumination, image cap-ture, and data acquisition components. Two pulsedYag-lasers, Model ULTRA (Big Sky Laser) wereused for illumination. These pulsed lasers have anominal e-2 beam diameter of 2.5 mm and emit 20mJ over 5 ns pulsewidth. The lasers were enclosedin a housing that combined and transformed the twobeams into a sheet. Lasers were pulsed at 15 Hz byan electronic timing box that triggered the lasers at0.2 msec time separation. Nylon 12 spheres of 0.02mm and 1.02~1.03 specific gravity were used aswater tracers. Distilled water was used for allexperiments to enhance the image quality. Waterwas recirculated more than two hours before eachexperiment to ensure that tracers were uniformlydispersed in the flow.

Images were captured with Kodak Megaplus, ES 1.0progressive scan camera. The timing box activatesthe doubled triggered exposure mode of the camerathat allows for two full-frame images to be acquiredwithin a time separation of 5 µs. The camera resolu-tion is 1008 by 1018 pixels with each pixel measu-ring 9 µm square. The digital images capturing wascontrolled by XCAP software. Image pairs wererecorded at 15 Hz and transmitted to a PC through aframe grabber board. About 6,000 image pairs wererecorded and stored for each flow case. 20 series of

300 image pairs (20s per realization) were sequen-tially collected over about 10 minutes for each casein order to randomly sample the flow field. The timebetween recordings was needed for transferring theimages to the computer.

Processing of the image pairs was made with acombination of Particle Image Velocimetry (PIV)Particle Tracking Velocimetry (PTV). PIV processingis based on pattern-matching algorithms applied toimages seeded with high water tracer concentrationsproviding regularly spaced velocity estimates. PTVtracks individual particle images and estimate theirdisplacement by analyzing image pairs to eventuallyassign velocities to each of the identified particle. Anovel algorithm for phase discrimination wasdeveloped for this application by Yu (2004). Phasediscrimination is based on the size criterion, similarto the approach employed earlier by Muste et al.(1998). The new processing software was conside-rably improved to minimize crosstalk, remove

Table 1. Experimental conditions for the first series of tests

Experiment CW1 NS1 NS2 NS3

Water Naturalsand

Naturalsand

Naturalsand

Depth (m) 0.021 0.021 0.021 0.021

Bed slope 0.0113 0.0113 0.0113 0.0113

Temperature (°C) 22~23 23 22 23~24

S.G. - 2.65 2.65 2.65

Size range(mm) - 0.21~0

.250.21~0.25

0.21~0.25

Fall velocity(m/s) - 0.024 0.024 0.024

Sed

imen

t

Vol.Conc.(×103) 0.00 0.46 0.92 1.62

Table 2. Experimental conditions for the second series oftests

Experiment CW2 NBS1 NBS2 NBS3

Water CrushedNylon

CrushedNylon

CrushedNylon

Depth (m) 0.021 0.021 0.021 0.021

Bed slope 0.0113 0.0113 0.0113 0.0113

Temperature (°C) 22~23 23 22 23~24

S.G. - 1.02~1.03 1.02~1.03 1.02~1.03

Size range(mm) - 0.21~0.25 0.21~0.2

5 0.21~0.25

Fallvelocity(m/s)

- 0.0006 0.0006 0.0006

Sed

imen

t

Vol.Conc.(×103)

0.00 0.46 0.92 1.62



reflections produced by sediment particles locatednear the bed, and improve water tracer detection inthe vicinity of sediment particle images.

The PIV-PTV processing was intertwined using anapproach similar to that developed by Cowen &Monismith (1997). The first processing step isconducted with PIV applied to small interrogationareas to estimate the flow displacement betweensuccessive images (Yu, 2004). The second proces-sing step uses those estimates in conjunction withPTV algorithms to estimate displacements of indivi-dual water tracers and sediment particles. The endresult is an irregular vector map with considerablyincreased number of vectors compared to PIVapplied to the same image pair. The accuracy of thedevelop PIV-PTV processing was tested using artifi-cial images and imposed displacements. The pro-cessed results showed differences less than 1%from the imposed displacements over the imagedarea. Flow properties and sediment distributionswere obtained by analyzing the entire series ofimages recorded for a given flow.

Velocity and particle number statistics were calcu-lated in a number of sampling bins stacked over theimage vertical. The length of the sampling bins wassame as the image length, while the heights werenon-uniform. The height of the sampling boxes wasgradually decreased near the bed (the smallestcomputational cell near the bed was y+ = 2.5) tomaximize the number of particles within eachsampling bin, minimize the effect of strong gradientsnear the bed, and to provide increased resolution ofthe measured quantities near the bed. An instan-taneous result was obtained as the average of all thewater tracers in a sampling bin at one instant in time.Time averages of various reported quantities wereobtained by further taking the mean over all realiza-tions in a recording series (ensemble). Excepting thecases where otherwise specified, all the statisticswere calculated using this procedure.

1.3 EXPERIMENTAL RESULTS1.3.1 Streamwise Velocity Distributions

for the Water-Sediment MixtureGiven that most of the available literature and currentanalytical formulations consider suspended sedimenttransport as a mixture of water and sediment, thestreamwise velocity profiles of the current measure-ments are presented first using the conventionalapproach (without flow phase discrimination) toreference the current to previous results. Table 3presents relevant flow parameters for the naturalsand (NS) and neutrally-buoyant (NBS) experiments.The friction velocity values reported in Table 3 areobtained from the momentum balance equation forthe channel flow using bulk flow measured quantities(u∗1) and based on the extrapolation of the measuredRe stress (u∗2) toward the bed (Muste and Patel,

1997). Given the larger measurement uncertaintiesfor the first method, the extrapolation of the Restresses approach was retained for determining thefriction velocity throughout the paper.

Using the above data reduction procedures, asystematic decrease up to 10% of the Karmancoefficient with sediment concentration is observedfor the NS flow cases, consistent with numerousprevious investigations (e.g., Vanoni, 1946; Einsteinand Chien, 1955). As expected, the depth-averagedstreamwise velocity of the mixture decreases withsediment concentration. For the NBS flow cases, nonotable changes are observed in the frictionvelocities computed with the momentum balance,while a slight decrease with concentration isobserved for the friction velocities determined withthe Re stress extrapolation method. A smallerreduction of Karman coefficient is also noted. Theresults for the NBS flow cases are in agreement withthe experiments with neutrally-buoyant particlesconducted by Elata & Ippen (1961), who observedno changes in resistance factor (for sedimentconcentrations up to 0.20%), clear decrease in kmwith sediment concentration, and increase of thevelocity in the outer layer.

Figure 1 contains average velocity profiles of themixture for all measured flow cases along with thereference log-law velocity distributions using Nezu &Nakagawa (1993) values for the constants in the law.

Table 3. Flow parameters of water-sediment mixture

NS experiments


Re 17,670 17,650 17,420 17,340

Fr 1.89 1.81 1.76 1.75

1*u 0.042 0.042 0.043 0.043u* (m/s)

2*u 0.042 0.042 0.043 0.043

mκ 0.402 0.396 0.389 0.367

Mean bulkvelocity(m/s)

mU 0.839 0.813 0.796 0.792

NBS experiments


Re 16,940 17,570 18,220 18,400

Fr 1.76 1.70 1.70 1.70

1*u 0.042 0.042 0.042 0.042u* (m/s)

2*u 0.042 0.041 0.040 0.040

κ 0.402 0.392 0.387 0.373

Mean bulkvelocity(m/s)

mU 0.798 0.772 0.773 0.772



The clear water flow cases show good agreementwith the reference curve. A progressive reduction ofthe velocity magnitude similar to that produced by arough wall is noted as the sediment concentrationincreases for the NS flow cases. An apparent in-crease of the normalized streamwise velocities canbe observed in Figure 1.b. for the NBS flows caseswith the increase of the sediment concentration, dueto the slight decrease of the friction velocity.

The common trends shown by the NS and NBSexperiments are the reduction of the mean bulk flowvelocity and a reduction of km with concentration.Among the factors commonly associated with thealteration of the velocity profiles can be changes inthe fluid viscosity and/or density (Coleman, 1986),the boundary roughness (Best et al., 1997), and mo-mentum exchange mechanism near the bed (Ume-yama and Gerritsen, 1992). The effective kinematicviscosity has been changed with less than 0.9% forboth NS and NBS experiments, hence it wasdeemed that this effect is negligible. The change indensity can be related to the Richardson number(Guo, 2001), but for the present flow conditions,similarly to previous studies (Wang & Qian, 1989;Einstein & Chien, 1955; and Bennett et al., 1998),there is not a clear trend between the reduction of kmand the Richardson number (Yu, 2004).

y+

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100 101 102 1030

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25NBS3Theoretical

b.)Figure 1. Streamwise velocity of water-sediment mixture:

a) NB experiments; b) NBS experiments



1.3.2 Velocity Distributions for theFlow PhasesStreamwise Velocity

This section presents the mean velocity profilesusing a two-phase flow investigative approach,where velocities of water tracers and sedimentparticles are separated and independently plotted toillustrate relevant flow physics. Table 4 summarizesselected water and sediment hydrodynamic charac-teristics for the NS and NBS flow cases. Subscripts“w” and “s” are for water and the sediment, re-spectively.

Comparison of Tables 3 and 4 illustrates that thefriction velocities determined from the distribution ofthe Reynolds stress for water (rather than themixture) are practically not changed with sedimentaddition. Despite that the friction velocities suchdetermined are not changed, it can be noted that thebulk flow velocity is gradually reduced whensediment is added to the successive flows for bothNS and NBS flow cases, as illustrated by Figures 1.aand 1.b, respectively. The Karman coefficient forwater velocity profiles in the sediment-laden flows forboth particle types is consistently smaller than that ofthe mixture and its decrease is proportional tosediment concentration. It can be noted that up tovolumetric concentrations of 10-3, the Karman co-efficient is practically unchanged. The observation isconsistent with previous results obtained by Muste &

Patel (1997) where the sediment concentration forsimilar experiments was of the order of 10-4.

Figure 2.a presents separately the streamwise velo-city profiles for water and sediment particles for theNS flow cases. Water velocity profiles are graduallydecreased compared with the reference clear waterflow, a trend that is more evident with the increase ofsediment concentration. It is apparent that particlevelocity profiles are “lagging” the water profilesthroughout the overlap and the outer regions. Table4 shows that the bulk flow velocities for sedimentparticles are up to 4~5 % slower than those for waterfor the most of the water depth. Measurementsshows that in the near-bottom region, for y+ < 10,sediment velocities are larger than water velocities.The changes in the outer flow are by now quitecommon (e.g, Muste & Patel, 1997; Kiger & Pan,2002). The changes near the wall were documentedonly recently by Kulick et al. (1994), Righetti &Romano (2004) using two-phase flow measurementswith Laser Doppler Velocimeters (LDV) and by Kiger& Pan (2002) with PIV-PTV.

Figure 2.b. contains plots of streamwise velocityprofiles separated according to the flow phase for theNBS cases. The major difference compared with theNS velocity profiles is a much decreased velocity lagbetween sediment and water, suggesting that the lagis mostly associated with particle inertia. Velocityprofiles in Figure 2.b. are similar to those obtainedwith LDV measurements by Kaftori et al. (1998) forflows laden with particles in the 100-900 µm sizerange and volumetric concentration of about 10-4.The experiments of Sumer & Deigaard (1981) andRashidi et al. (1990) conducted with neutrally par-ticles showed, however, that the velocity differenceincreases with the increase of the particle size.

The slight decrease in the water average streamwisevelocity profiles observed in Figure 2.a for the NSflow cases without a change in the friction velocitymight surprise because most of the previousobservations made on dilute sediment-laden flowswith volumetric concentrations in the 10-3 to 10-4

range showed an increase of the friction velocity withthe addition of sediment (Muste & Patel, 1997; Kiger& Pan, 2002; and Righetti & Romano, 2004). Thelater studies noted visible long sediment structures(streaks) along the bed. The same was observed byBest et al. (1997), Bennett et al. (1998), Graf &Cellino (2002) in their experiments conducted with acontinuous (moving or fixed) sediment layer on thebed. These later studies showed not only an increa-se of the friction velocity compared with the “referen-ce” clear water flow but a proportional increase withsediment concentration. Reminding that for thepresent experiments with practically same bulk flowconcentrations there was no sediment depositions orstreaks in the flume, the observed decrease of thevelocity profiles when the heavy sediment wasadded cannot be related to the bed “roughness”,rather suggests that the interaction between the par-

Table 4. Hydrodynamic characteristics for water andsediment

NS experiments


1*u 0.042 0.042 0.043 0.043u* (m/s)

2*u 0.042 0.042 0.042 0.042

wκ 0.402 0.402 0.380 0.374

wU 0.8390.813

(-3.1%)

0.796

(-5.1%)

0.793

(-5.5%)Mean bulkvelocity (m/s)

sU - 0.786 0.758 0.753

NBS experiments


1*u 0.042 0.042 0.042 0.042u* (m/s)

2*u 0.042 0.041 0.040 0.040

wκ 0.402 0.405 0.398 0.384

wU 0.7980.777

(-2.6%)

0.773

(-3.1%)

0.788

(-1.3%)Mean bulkvelocity (m/s)

sU - 0.769 0.769 0.777



ticle and turbulent coherent structures produces thischange. This conclusion is also supported by Lyn’s(1991) results, who found that for the lower concen-trations of sediment (“starved-bed” flows series) thefriction velocities were essentially unchanged, whilefor higher sediment concentrations, yet in the diluterange, increase of the friction velocity up to 20% anda correspondingslow down of the water the velocityprofile was found.

The velocity lag between water and particles requi-res some conceptual clarification. It is obvious thatthere could not be an actual slip between water andsediment particles in their instantaneous interactionbecause that would violate the no-slip condition ac-ting on the fluid boundaries (here played by sedimentparticles). Without local slip velocity, the outstandingexplanation for the average velocity lag in thestreamwise direction can be explained by the ten-dency of the sediment particles to reside in the flowstructures moving with lower velocities (Summer &Deigaard, 1981; Kaftori et al., 1995.b; Kiger & Pan,2002). The intriguing inverse lag near the bed stemsfrom the fact that sediment particles are not boundedby viscosity shear as fluid particle are, hence the no-slip condition at the channel bottom does not applyfor the sediment velocity profile.

U (m/s)

y/h

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U (m/s)

y/h

0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

0.2

0.4

0.6

0.8

1.0


b.)

Figure 2. Streamwise velocity for water and sedimentparticles: a) NS experiments: b) NBS experiments



Figure 3 plots the depth distribution of the lagbetween water and sediment particles for the NSflow cases. These plots confirm the previous resultsof Sumer & Deigaard (1981), Rashidi et al. (1990),Wang & Ni (1991), and Muste & Patel (1997)indicating that the lag is larger near the bottom.Figure 3 includes the velocity lag distribution ob-tained with Greimann et al. (1999) formulation

( ) ( )ηη 34.1exp166.0 2−= sG vu (1)

where uG is the Greimann’s velocity lag magnitude,η is the dimensionless height ( hy= ) and vs is thesediment settling velocity. The plots reveal thatsediment concentration increases the lag and itsdistribution over the depth and needs to beincorporated in the correlation.

Velocity-lag (m/s)

y/h

-0.10 -0.05 0.00 0.05 0.100.0

0.2

0.4

0.6

0.8

1.0

NS1RegressionGreimann

- 0.10

Velocity-lag (m/s)-0.10 -0.05 0.00 0.05 0.1


Velocity-lag (m/s)-0.10 -0.05 0.00 0.05 0.10


Figure 3. Distribution of the water-sediment velocity-lag forNS experiments

Vertical Velocity

A notable feature of the present results is thedistribution of the vertical velocity distributions.Figure 4.a shows vertical velocity distributions for theNS experiments obtained by calculating theconventional time average of the vertical velocitiesfor water and sediment using the availablemeasurement samples. As expected, the averagevertical velocity of water is very close to zero whilesediment particle vertical velocity distributionsdisplay a considerable upward shift of the meanvelocity. More insights into this apparently conflictingparticle hydrodynamics is illustrated in Figure 4.b,where the vertical velocity profiles for water andsediment particles are split according to theirdirection of movement on the vertical; i.e., upwardand downward. It can be noted that the upward anddownward vertical velocity profiles for water arequasi symmetric around the vertical axis, but notconstant in magnitude. Toward the bed (for

3.0<hy ) both velocity profiles increase inmagnitude and abruptly decrease near the bed. Forall flow cases, and more evident for the clear-watercase, the upward average velocity profiles exceed

the downward one. Results similar to those reportedin Figure 4.b for sediment were also found byBouvard & Petkovic (1985), Wei & Willmarth (1991),Kiger & Pan (2000), and Wang (2000).

V (m/s)

y/h

-0.10 -0.05 0.00 0.05 0.100.0

0.2

0.4

0.6

0.8

1.0CW1 Wat

V (m/s)

y/h

-0.10 -0.05 0.00 0.05 0.100.0

0.2

0.4

0.6

0.8

1.0NS1 WatNS1 Sed

V (m/s)

y/h

-0.10 -0.05 0.00 0.05 0.100.0

0.2

0.4

0.6

0.8

1.0NS2 WatNS2 Sed

( )

V (m/s)

y/h

-0.10 -0.05 0.00 0.05 0.100.0

0.2

0.4

0.6

0.8

1.0NS3 WatNS3 Sed

a.)



V (m/s)

y/h

-0.06 -0.04 -0.02 0 0.02 0.04 0.060.0

0.2

0.4

0.6

0.8

1.0

CW1 Wat-CW1 Wat+

V (m/s)

y/h

-0.06 -0.04 -0.02 0 0.02 0.04 0.060.0

0.2

0.4

0.6

0.8

1.0

NS1 Wat-NS1 Wat+NS1 Sed-NS1 Sed+

V (m/s)

y/h

-0.06 -0.04 -0.02 0 0.02 0.04 0.060.0

0.2

0.4

0.6

0.8

1.0


V (m/s)

y/h

-0.06 -0.04 -0.02 0 0.02 0.04 0.060.0

0.2

0.4

0.6

0.8

1.0


b.)

Figure 4. Vertical velocity profiles for water and sedimentfor the NS flow cases: a) average profiles; b) profiles split

according to the upward and downward movements.

An important observation related to the profiles inFigure 4.b is that there is a wide difference betweenthe number of measurements of upward and down-ward velocities in the particle samples throughout thedepth (a ratio of upward/downward particle numberup to 4). In contrast, the number of measurements inthe water samples is almost equal throughout thedepth. The high ratio of upward to downward par-ticles in the sample confirms one of the simplest sus-pension mechanism in sediment-laden flows pointedout among others by Wei & Willmarth (1991) andKiger & Pan (2002). Specifically, in a channel flowwith a mean sediment concentration gradient, theupward fluid motion will transport large amounts ofsediment upward compared with the downward fluidmotion because of the existence of the concentrationgradient. Such a suspension mechanism will elimi-nate the concentration gradient over time. The factthat sediment-laden flows preserve the sedimentconcentration distribution suggests that there shouldbe another process which maintains the concentra-tion gradient.

The vertical velocity distribution for water tracers andsediment particle for the neutrally-buoyant particles(NBS flow cases) are plotted in Figure 5.a showingthat there is practically no difference between thetwo phases indicating that the neutrally buoyantsediment follow closely the velocity of the underlyingflow structures. This conclusion is also supported bythe vertical velocity distributions split according to thedirection of movement plotted in Figure 5.b. Thelarger scattering of the sediment data for NBS3 testis related to the reduced number of particles that arealmost uniformly distributed over the flow depth. Theshape of the velocity distribution profiles is, however,similar to that of the NS experiments with a continuedecrease of the velocity magnitude in the outer flowregion and an abrupt decrease near the bed.

A direct implication of the vertical velocity distributionnon-symmetry for the heavy particles plotted inFigure 4 would be that the net vertical flux forsediment particles is not zero, as expected frommass conservation laws for a fully developedchannel flow. Wei & Willmarth (1991) showed thatdespite of this asymmetry, continuity is satisfied if itscalculation weighs the mean upward and downwardvelocities with the amount of time in the data recordthat the velocity is positive and negative,respectively, as will be illustrated later in the paper.The current velocity measurements were sampledwith a rate of 15 Hz which is much lower than thatused by Wei & Willmarth (1991) and does not allowappropriate reconstruction of the time dependentvelocity time series. To accommodate the low datasampling rate used in our velocity measurements,the algorithm proposed by McLaughlin & Tiedermann(1973) and extensively used in the LDV literature(e.g., Durst et al., 1981) is adopted instead.



V (m/s)

y/h

-0.10 -0.05 0.00 0.05 0.100.0

0.2

0.4

0.6

0.8

1.0

CW2 Wat

V (m/s)

y/h

-0.10 -0.05 0.00 0.05 0.100.0

0.2

0.4

0.6

0.8

1.0NBS1 WatNBS1 Sed

V (m/s)

y/h

-0.10 -0.05 0.00 0.05 0.100.0

0.2

0.4

0.6

0.8

1.0NBS2 WatNBS2 Sed

( )

V (m/s)

y/h

-0.10 -0.05 0.00 0.05 0.100.0

0.2

0.4

0.6

0.8

1.0

NBS3 WatNBS3 Sed

a.)

V (m/s)

y/h

-0.06 -0.04 -0.02 0 0.02 0.04 0.060.0

0.2

0.4

0.6

0.8

1.0

CW2 Wat-CW2 Wat+

V (m/s)

y/h

-0.06 -0.04 -0.02 0 0.02 0.04 0.060.0

0.2

0.4

0.6

0.8

1.0

NBS1 Wat-NBS1 Wat+NBS1 Sed-NBS1 Sed+

V (m/s)

y/h

-0.06 -0.04 -0.02 0 0.02 0.04 0.060.0

0.2

0.4

0.6

0.8

1.0


V (m/s)

y/h

-0.06 -0.04 -0.02 0 0.02 0.04 0.060.0

0.2

0.4

0.6

0.8

1.0


b.)Figure 5. Vertical velocity profiles for water and sedimentfor the NBS flow cases: a) average profiles; b) profiles split

according to the upward and downward movements.

The algorithm is formalized into the followingexpression:

∑∑==

=N

i i

N

i i

iMLT vNv

vN

V11

111 (2)

where the dimensionless net momentum flux islabeled as an “equivalent” velocity, VMLT, with

+− += NNN the total number of upward (N+)and downward (N-) data points in the sample.Equation (7) weighs the sample collected overtime with the number of particles moving upwardor downward. Equation (2) is plotted in Figure 6for all NS experiments showing that continuity forthe sediment fraction is fulfilled, despite theconsiderable asymmetry of the vertical velocityprofiles for particles shown in Figure 4.



Vp (m/s)

y/h

-0.1 -0.05 0 0.05 0.10.0

0.2

0.4

0.6

0.8

1.0CW1 Wat

Vp (m/s)

y/h

-0.1 -0.05 0 0.05 0.10.0

0.2

0.4

0.6

0.8

1.0NS1 WatNS1 Sed

Vp (m/s)

y/h

-0.1 -0.05 0 0.05 0.10.0

0.2

0.4

0.6

0.8

1.0NS2 WatNS2 Sed

Vp (m/s)

Vp (m/s)

y/h

-0.1 -0.05 0 0.05 0.10.0

0.2

0.4

0.6

0.8

1.0NS3 WatNS3 Sed

Figure 6. Distribution of vertical water and sedimentparticle fluxes per unit area corrected by McLaughlin &

Tiederman’s (1973) method

Similarly to the discussions on the horizontal velocitylag, it is reminded that there could be no velocitydifference between fluid and particles in an instan-taneous interaction. The velocity difference shown inthe time-averaged profiles for the NS flow cases isdirect representations of the effects of the particle-fluid structure interactions. Bennett et al. (1998, p.1262) hypothesize that during the upward movementof sediment in ejections and outward interactions therelative vertical velocities of the fluid and sediment isexpected to be positive and relatively high and todecrease in magnitude upwards (trends are clearlyillustrated by the profiles on the left in Figure 4.b).During the downward movement of sediment therelative velocity is expected to range from positive tonegative in the upper flow region and to increasenegative magnitude in the lower flow regions (trendsslightly confirmed by the left velocity profiles shownon the left in Figure 4.b).

When such relative velocities are averaged, therelative vertical velocities between water and sedi-ment tend are expected to tend to zero in the upperpart of the flow. Near the bed, large positive relativevelocities associated with the movement of sedimentin ejections are expected to be counteracted by largenegative relative velocities as descending grainssettle faster then the surrounding fluid. In betweenthese regions, large positive relative velocities asso-ciated with ascending grains are expected to exceedthe smaller negative relative velocities associatedwith the descending grains.

The mean relative velocity is never expected toattain the settling velocity in this area and the timeaveraged vertical velocities are always greater thanthe sediment particle settling velocities (the fall velo-city for sediment in this experiment is 0.024 m/s).This behavior is very well captured throughout thedepth by the time-averaged vertical velocity profilesshown in Figure 4.b as well as in the experimentsconducted by Bennet et al. (1998). It should be men-tioned that the time-averaged profiles underpredictthe actual relative velocities between the sedimentparticles and fluid in turbulent eddies.

The horizontal and vertical mean velocity differencesbetween fluid and particles reveal that particles insuspension tend to preferentially organize them-selves relative to the flow (leading rapidly to particlecluster formation). The preferential association of apositive shift for vertical velocities with a negativeshift of streamwise velocities for the particle profilesis supposedly the equivalent of the Reynolds stressturbulent correlations for the interaction between fluidstructures and particles. The magnitudes of thesedifferences are dictated by satisfying the net flux ofparticles in a flow situation where the mean con-centration particle is constant.



1.3.3 Turbulence Intensities for FlowPhasesTurbulence modification

Turbulence modification (modulation) defines chan-ges between the turbulence intensity of the equi-valent clear water flow (which is the sediment carrier)and the water in the sediment-laden flows. Theprocess is usually addressed in the two-phase flowcommunity through specific relationships betweencharacteristic time and length scales of the under-lying turbulent flows (using water characteristics inthe mixture) and the diameter, response time, relati-ve velocity between sediment and water, concentra-tion and specific gravity of the particles in suspen-sion. Given the dilute volumetric concentrations forthe flows investigated here (up to 10-3) it is deemedthat the particle-particle interaction is not significantand the importance of the particle-volume and massfractions is also limited. Consequently, the relevantcontrol parameters for the present discussion are:

lsD (ratio of the sediment size to a characteristic

turbulence flow scale), Stokes number, St =τp/τf(ratio of the particle response time to representativeflow time scale), particle Reynolds number,

νν Lsssp uDUUD =−=Re (where U is the

local mean streamwise velocity of water, sU is thelocal mean streamwise velocity of sediment,

UUu sL −≡ is the velocity-lag of sediment par-ticles), particle volume and mass fractions. Thephysical significance of these parameters is brieflydiscussed below.For lsD < 0.1 the particles are smaller than themost energetic eddies and will follow them for atleast part of its lifetime (Gore and Crowe, 1991).Fraction of the eddy energy will be transferred to theparticle and turbulence intensity is thus reduced. For

lsD > 0.1 to 1, particles tend to create turbulencein its wake near the scale of the most energeticeddy, thus increasing the turbulence intensity of thefluid. In this case energy is transformed from themean flow, which is moving the particles, to theturbulent kinetic energy of the fluid, thus overall thetotal energy will be decreased, as shown by thedecrease of the mean bulk velocity for all flow cases.Gore & Crowe (1991) consider this ratio as being themost important parameter for turbulence modulation.The second relevant parameter controlling theturbulence modulation in these experiments is the Stnumber related to the inertia of the particles insuspension. This particle to fluid characteristic ratioindicates that small particles (St << 1) will haveample time to respond to change in the flow velocityfollowing closely turbulent eddies, while largeparticles (St >> 1) move essentially independent ofthe fluid. In the first case damping of turbulent fluc-tuations will occur, while additional turbulence will beproduced in the latter case (Crowe et al., 1998). For

St ~ 1 particles tend to centrifugate toward the peri-pheries of the flow structures (eddies). The last con-trolling parameter discussed herein, the Reynoldsparticle number is based on the particle size, partic-le-fluid relative velocity, and fluid viscosity. Particleswith low Rep cause turbulence suppression by actingas an additional source of dissipation, while particleswith high Reynolds number enhance turbulence dueto wake shedding (Hetsroni, 1989). Threshold valuefor Rep according to Hetsroni (1989) is 400.

In the present analysis the most energetic turbulenteddies (eddies with the highest wavenumber) are as-sociated with the Taylor scales, λ, that characterizessmall eddies (microscales). This selection is basedon Hinze’s (1959) hypothesis that for a fully deve-loped turbulence state, the most energetic eddiesare not the largest eddies (integral scales) nor thesmallest (Kolmogorov scales) where dissipationoccurs. Taylor length scale sizes in between the lar-gest and smallest length scales, hence deemed tocontain the maximum kinetic energy. Taylor lengthscale is defined as (Tennekes and Lumley, 1972)

εν

λ215 rmsu′

= (3)

where ε is the turbulence dissipation rate per unitmass obtained as (Nezu & Nakagawa, 1993)

−

=

−

hy

hy

uh 3exp8.9

5.0

3*

ε (4)

The characteristic flow time scale is defined as(Elgobashi, 1994)

rmsf u′=

λτ (5)

The particle response time is established assumingStoke flow conditions (Kaftori et al., 1995)

w

ssp Dρρ

ντ 2

181

= (6)

where Ds is the particle diameter, ρs is the density ofthe sediment, ρw is the density of the water. UsingEquations (5) and (6), the relationship for Stokesnumber becomes

νε

ρνρ

ττ

1518

2

w

ss

f

p DSt == (7)

Turbulence Intensity Profiles

The plots of the turbulence intensities for mixture inthe NS and NBS experiments shown in Fig. 7 (wherefluid information is dominant) suggest that, overall,turbulence is affected by the presence of sediment inthe near-bed region for NS experiments and through-out the depth for NBS experiments. All flow casesshow an increase of streamwise and vertical turbu-lence intensities near the wall, for y+ ≤10.The stream-wise turbulence intensities for the NS experiments



are slightly attenuated for both NS and NBS experi-ments in the 10 ≤ y+ ≤30 region and practically not af-fected for y+ ≥ 30, as also found by Wang & Qian(1989). A slight increase of the streamwise turbulen-ce intensities can be observed for NBS experiments,similarly to the findings of Elata & Ippen (1961). Theincrease is proportional with the sediment concen-tration. The vertical turbulence intensities are slightlyincreased for the NS experiments and practicallyconstant for NBS experiments in the 10 ≤ y+ ≤ 30region. For y+ ≥ 30, the vertical turbulence intensitiesare slightly decreased for the NS experiments, whilevisible increased for the NBS experiments.

y+

Turb

ulen

ceIn

tens

ity

100 101 102 1030

1

2

3

4u'rms /u* (CW1)v'rms /u* (CW1)

y+

Turb

ulen

ceIn

tens

ity

100 101 102 1030

1

2

3

4u'rms /u* (CW1)v'rms /u* (CW1)u'rms /u* (NS1)v'rms /u* (NS1)

y+

Turb

ulen

ceIn

tens

ity

100 101 102 1030

1

2

3


y+

Turb

ulen

ceIn

tens

ity

100 101 102 1030

1

2

3


a.)

y+

Turb

ulen

ceIn

tens

ity

100 101 102 1030

1

2

3

4u'rms /u* (CW2)v'rms /u* (CW2)

y+

Turb

ulen

ceIn

tens

ity

100 101 102 1030

1

2

3

4u'rms /u* (CW2)v'rms /u* (CW2)u'rms /u* (NBS1)v'rms /u* (NBS1)

y+

Turb

ulen

ceIn

tens

ity

100 101 102 1030

1

2

3


y+

y+

Turb

ulen

ceIn

tens

ity

100 101 102 1030

1

2

3


b.)

Figure 7. Turbulence intensities for the mixture: a) NSexperiments; b) NBS experiments

Further insights in the turbulence modulation are pro-vided by separately plotting the turbulence intensitiesfor the two flow phases, as illustrated in Fig. 8. The-se plots reveal that for NS experiments (Fig. 8.a-c)the streamwise and vertical turbulence intensities forwater are smaller in the buffer region, 10 ≥ y+ ≤ 30,and are gradually larger in the inner region, y+ ≤ 10.In the logarithmic and outer region, y+ > 30, the verti-cal turbulence intensities decrease, obeying the dam-ping criterion with respect to St number. The stream-wise turbulence intensities in the same region showmuch less reduction. The streamwise velocity fluctu-ations trends for water are in very good agreementwith those of Kiger & Pan (2002) - closest flow NS1-and Righetti & Romano (2004) – closest flow NS2 –,while for the vertical velocity fluctuations with theresults of Righetti & Romano (2004). The results ofBest et al. (1998) show similar, but magnified trends,due to the fact that the channel bed was coveredwith a layer of particles identical with those insuspension. The particle streamwise turbulenceintensities are larger than those for water in the outerregion (y+ > 30) and smaller for y+ < 30 for all cases,excepting the NS1 flow case. Particle vertical turbu-lence intensities are larger than those for water for allconcentrations and throughout the depth.



Similar analysis for the NBS experiments (Figures8.d-f) shows that water streamwise turbulenceintensities are slightly smaller than those for clearwater in the 10 ≥ y+ ≤ 30 region (log layer) and aresignificantly larger close to the wall for y+ ≤ 10. In theouter region the water streamwise turbulence inten-sities are increased. The water vertical turbulenceintensities are larger than the clear water case for y+

≤ 10, practically constant for 10 ≥ y+ ≤ 30 andincreased considerably outside this region.Excepting the observed decrease of the streamwisevelocity in the region 10 ≥ y+ ≤ 30, all the othertrends are similar to those observed by Kaftori et al.(1998) in their study on the effect of particlepresence of underlying water flow in sediment-ladenflows. Rashidi et al. (1990) in experiments withneutrally-buoyant particles found that the largeparticles (1100 µm) indeed increase both streamwiseand vertical turbulence intensities for water in theouter layer (for y+ > 30), but have reverse effect forsmall particles (120 µm). The particle streamwiseand vertical turbulence intensities for all the NBScases are smaller than water in the y+ ≤ 30 regionand larger outside this area. In the near wall region(y+ < 10) both turbulence intensities for the particlesare larger than the water ones. These observationsare consistent with those made in LDV experimentsfor volumetric concentration of 10-4 by Kaftori et al.(1995.b).

Turbulence intensities for water in the mixture ex-ceeds those for the reference clear water flow in thevicinity of the wall (y+ < 10) for both heavy andneutrally-buoyant particles, as a consequence of theintense turbulence exchange between fluid andparticles in this regions. Comparison of the presentNS measurements with Righetti & Romano (2004)reveals that the region of significant turbulenceincrease near the wall is larger in their case,especially for the vertical component; the differenceis associated with their larger near bed sedimentconcentration. Particle turbulence intensities in thepresent experiments are larger than those of the fluidthroughout the outer region revealing a significantmomentum exchange between the phases. The in-tensification of the momentum exchange in the areaof the maximum bursting activity, i.e., 10 < y+ < 30, isreflected by the smaller streamwise particle turbu-lence intensities and the larger vertical turbulenceintensities compared with the carrier phase. This in-tensification is considered by Righetti & Romano(2004) responsible for the reduction of the turbulentenergy production in the buffer layer that might ex-plain the turbulent damping of the fluid in the outerlayer. Comparison of the present results with thoseobtained by Kiger & Pan (2002) and Righetti & Ro-mano (2004) indicates higher particle vertical turbu-lence intensities than for water in the mixture for the10 < y+ < 30 region. The difference can be associatedwith the increased number of particle in suspensionin this area compared to both later studies.

The overall trends described above and the compa-rison between the NS and NBS experiments shedlight on the effect of turbulence modulation in generaland the role played by inertia in the process. Compa-rison of the NS and NBS experiments reveals, as ex-pected, that inertia mostly affects the vertical tur-bulence intensities. Major differences due to inertiaare is the overall increase of water the turbulenceintensities in the outer region y+ > 30. This trend, ob-served by previous similar experimental results (Kaf-tori et al., 1995), are not predicted by the typical Stand lsD turbulence modulation control parameters,leading to the conclusion that particle-volume andmass fractions might be also involved in the chan-ges. Regarding the particle turbulence intensities thedifferences are more pronounced for the verticalturbulence intensities that are closer to those of thecarrier flow for the NBS experiments.

The NS-NBS comparison should be viewed from theperspective of large near-bed sediment concentra-tions for the NS experiments and quasi uniform dis-tribution of the sediment in the NS experiments. Thetrends summarized above are better substantiatedwith the increase in the sediment concentration, i.e.,in general, the differences that define the trends aremore visible with the increase of concentration. It isobserved that the differences are practically the sa-me for the streamwise velocity component through-out the depth and increased for the NBS comparedto the NS counterparts in the outer region for the ver-tical turbulence intensities. The differences betweenthe turbulence intensities of the flow phases in themixture are better substantiated for the vertical turbu-lence intensities than for the streamwise turbulenceintensities. For practically same underlying flow andparticle concentration, size and shape this differencecan be only associated with the difference in particledensities.

The present results demonstrate that modulation ofturbulence requires consideration of the complex in-terplay of the particle-fluid interaction with the globalflow characteristics. For the present results, wherethe lsD and Rep ratios were practically the same forthe NS and NBS experiments, the trends in turbulen-ce modulation would have been expected to stronglydepend on the Stokes number. While trends are inagreement with Stokes number predictions for NSexperiments, it does not explain the considerablewater turbulence enhancement in the outer layer forthe NBS experiments. Full understanding of turbu-lence modulation requires simultaneous considera-tion of the particle-fluid interaction microphysics (vor-tex shedding from particle wakes, particle inertia,particle-fluid structure interaction, and particleclustering) with flow the macro-level flow changesdue to bed roughness and the gradients of particleconcentration, flow velocities, and turbulence scales(in the absence of additional complexities induced bymultisize particle in the flow).



y+

v'rm

s/u

*

100 101 1020

1

2

(a) NS1

u'rm

s/u

*

0

1

2

3


λpd

St

>0.1 <0.1

>1.0 0.1<St<1.0 St<0.1

y+

v'rm

s/u

*

100 101 1020

1

2

(b) NS2

u'rm

s/u

*

0

1

2

3


λpd

St

>0.1 <0.1

>1.0 0.1<St<1.0 St<0.1

y+

v'rm

s/u

*

100 101 1020

1

2

(c) NS3

u'rm

s/u

*

0

1

2

3


λpd

St

>0.1 <0.1

>1.0 0.1<St<1.0 St<0.1

Figure 8. Turbulence intensities for the flow phases in NS

1.3.4 Reynolds stresses for water inthe mixtureReynolds stress typically quantifies the turbulentshear occurring for a fluid in a given turbulent flowregime and geometry. The physical signification forsediment particles, as reported in various studies,does not have a straightforward interpretation, henceit is not reported herein. For a turbulent, fully develo-oped open channel flow the

y+

v'rm

s/u

*

100 101 1020

1

2

(d) NBS1

u'rm

s/u

*

0

1

2

3


λpd

St

> 0.1 < 0.1

> 0.1 < 0.11

y+

v'rm

s/u

*

100 101 1020

1

2

(e) NBS2

u'rm

s/u

*0

1

2

3


λpd

tS

> 0.1 < 0.1

> 0.1 < 0.1

y+

v'rm

s/u

*

100 101 1020

1

2

(f) NBS3

u'rm

s/u

*

0

1

2

3


λpd

tS

> 0.1 < 0.1

> 0.1 < 0.1

and NBS experiments

Reynolds stress variation for the carrier fluid can beexpressed as a linear function of depth for most ofthe flow depth excepting very close to the bed whereviscous effects become dominant (White, 1991)

−=

′′−

hy

uvu 12*

(8)



Reynolds stress profiles for the NS and NBS experi-ments are plotted against Eq. (8) in Fig. 9.a and b,respectively. The stress distribution for all flow situa-tions reveals that the turbulent stresses follow wellthe linear distribution. Small changes in the magni-tude of the Reynolds stresses can be observed: aslight decrease for the NS experiments and theopposite for the NBS experiments. The stress peakincreases in magnitude and its location is shiftedtoward the channel with the increase of sedimentconcentration for the NS experiments. These trendsare not very clear in the plots of the stresses for theNBS cases due to the larger data scattering.No significant changes in the Reynolds stress distri-bution were reported by Best et al. (1998), Graf &Cellino (2002) for similar experiments with heavyparticles, while Righetti & Romano (2004) found re-duced stresses compared with the clear water flow.For flows with neutrally-buoyant particles Rashidi etal. (1990) found that fairly large particles increasesReynolds stresses (volumetric concentration of 10-4)while small particles reduced them. Kaftori et al.(1998) found no change near the wall and slightlyreduced Reynolds stresses in the outer layer in theirexperiments with particle in the range 100-275 µmand volumetric concentration of 10-4 (similar con-ditions to NS1 flow case) and increased Reynoldsstresses for larger particle (900 µm).

y/h

-u'v

'/u*2

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

CW1 Wat

y/h

-u'v

'/u*2

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

NS1 Wat

y/h

-u'v

'/u*2

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0NS2 Wat

y/h

-u'v

'/u*2

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

NS3 Wat

a.)

y/h

-u'v

'/u*2

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0CW2 Wat

y/h

-u'v

'/u*2

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0NBS1 Wat

y/h

-u'v

'/u*2

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

NBS2 Wat

y/h

-u'v

'/u*2

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0NBS3 Wat

b.)Figure 9. Reynolds stress distributions: a) NS ex-

periments, b) NBS experiments

While there is not a clear conclusion regarding thechanges in the Reynolds stress magnitude, thecommonality for the available studies is its linearvariation toward the bed in sediment-laden flows



justifying the use of the linear interpolation to the bedfor determining the friction velocity with Equation (8).

1.3.5 Eddy viscosity for water in themixtureThe turbulent momentum diffusion coefficient (eddyviscosity), mε , defined as

yUvu

m ∂∂′′

−=ε (9)

can be expressed using the log-law as (Nezu &Nakagawa, 1993)

( )ηηκε −= 1*hum (10)

The experimentally determined momentum diffusioncoefficients and Equation (10) using k determinedfrom experiments are plotted in Figure 10.

Turbulent diffusion coefficient

y/h

0.0 0.1 0.2 0.30.0

0.2

0.4

0.6

0.8

1.0

CW1Eq. (11)


y/h

0.0 0.1 0.2 0.30.0

0.2

0.4

0.6

0.8

1.0

NS1Eq. (11)


y/h

0.0 0.1 0.2 0.30.0

0.2

0.4

0.6

0.8

1.0

NS2Eq. (11)


y/h

0.0 0.1 0.2 0.30.0

0.2

0.4

0.6

0.8

1.0

NS3Eq. (11)

a.)


y/h

0.0 0.1 0.2 0.30.0

0.2

0.4

0.6

0.8

1.0

CW2Eq. (11)


y/h

0.0 0.1 0.2 0.30.0

0.2

0.4

0.6

0.8

1.0

NBS1Eq. (11)


y/h

0.0 0.1 0.2 0.30.0

0.2

0.4

0.6

0.8

1.0

NBS2Eq. (11)


y/h

0.0 0.1 0.2 0.30.0

0.2

0.4

0.6

0.8

1.0

NBS3Eq. (11)

b.)

Figure 10. Turbulent diffusion coefficient distributions: a) NS experiments: b) NBS experiments



The distributions show a “quasi” parabolic distribu-tion without a good matching of the theoretical distri-bution for the region y/h > 0.3. Differences betweenthe measured momentum diffusion coefficients andthe theoretical profile can be partially attributedchanges of the water velocity profiles for water in theflows with sediment. The plots suggest that themomentum diffusion coefficient is decreased for NSand more visible for the NBS experiments.Excepting the y/h < 0.3 region, the trends areobscured by the data scatter. It can be noted thatthe scattering decreases overall for the NBSexperiments compared to NS because for same bulksediment concentrations, in the NS experiments thesediment is mostly near the bed while the NBS iswell distributed over the entire flow depth, as will beshown later. Similar data quality and reduction forthe momentum diffusion coefficient profiles wereobtained in dilute sediment laden flows Best et al.(1997) and Graf & Cellino (2002) underlying thedifficulty of these types of measurements.

sdl

Ccc lsd −=′

∑=

=T

tlsdcT

C0

1

sdlwater

sedimentlsd m

mc

=

Channel Bottom

lsd (pixels)

l sd(p

ixel

s)

250 300

600

650

Dashed: Sediment particleSolid: Water tracers

2v2u

su

sv 3u

3v4u4v

5v5u

1u1v

yCvc

llonvN

v sdsd

N

nn

∂∂′′

=

×= ∑=

β

1

1'

Figure 11. Algorithm for calculation of the sedimentdiffusion coefficient

The addition of sediment seems to decrease themomentum diffusion coefficient for both heavy and

neutrally-buoyant particles, and implicitly reduces theeddy size in the outer flow region, for y/h > 0.3. Adecrease of momentum diffusion coefficient wouldimply an increase of β with the addition of sand.The questionable large values for β obtained apply-ing Rouse test to the measured concentration datacan be attributed to limitations of the Rouse equationin the y/h > 0.3 area. Specifically, in this regionparticle suspension might not be related to meanturbulence characteristics (Reynolds stress control),but with turbulent eddies with relatively greaterturbulence intensities and mixing length as arguedby Bennett et al. (1998) and Kiger & Pan (2002).

Sediment diffusivity coefficients could not be obtai-ned from the existing measurements due to thelimited number of recorded images and dilute sedi-ment concentrations. With enough such raw data, adirect measurement procedure as illustrated in Fig.11 could be employed to accurately determine thiscrucial parameter for suspended sediment transport.It should be additionally mentioned that this proce-dure also requires high water tracer concentrationsin the neighborhood of the particles.

1.3.6 Sediment Concentration ProfilesPTV does not measure directly concentration, butparticle number (fluxes), therefore a conversion isneeded to report sediment concentrations. Thevolumetric sediment concentration follows amethodology developed by Bennett et al. (1998) fortheir Phase-Doppler Velocimetry meaurements.Assuming that the distribution of sediment particlesin transverse direction is homogeneous, the areasediment particles occupy is proportional to theconcentration of sediment

imageanofAreaparticlessedimentofArea

∝vsC yx

nDi

∆∆

×=

2

4π

(11)

where n is the number of sediment particles, x∆and y∆ is the width and the height of sampling bin(cell), respectively. Knowing the average volumetricconcentration of sediment, it is possible to introducea coefficient, cA , to match the left- and the right-hand side of Equation (11). Using Equation (11) andthe coefficient cA , the time-averaged sedimentconcentration for cell can be calculated as

( )myxnDAyC

i

iicisi ×∆∆

×=

4

2π (12)

where in is the number of sediment particles of celli and m is the total number of image pairs.

For a steady uniform turbulent channel flow the localaverage concentration at elevation y in the flow, sCis given by Rouse equation (Vanoni, 1975)



*ku

v

sa

s

s

aha

yyh

CC β

−

⋅−

= (13)

where Csa is the mean sediment concentration at aconventional elevation α. The depth-averagedcoefficient β, defined as

∫−==

h

am

s dyyah

)(1 βεε

β (14)

relates sediment diffusion coefficient yyC

yvc

ss ∂∂

′′=

)()(ε

and momentum diffusion coefficient yyU

yvum ∂∂

′′=

)()(ε .

Normally the sediment reference concentration is ta-ken at a = h05.0 , where the top of the bed loadlayer is assumed. For the present cases where adistinct peak in sediment concentration was present,the maximum concentration value was taken as refe-rence. Rouse number, z , in Eq. (13) is given by

*uv

z s

κβ= (15)

β is generally assumed to be 1.0. Using fallvelocities determined with Dietrich’s (1982) formulas,k and u* for derived for each flow case the values ofz and subsequently β were obtained sing theconcentration measurements. The calculated Rousenumbers and β -values for the NS and NBSexperiments are shown in Table 5. The calculatedβ -values are much larger than 1.0 for NSexperiments and much smaller than 1 for the NBSexperiments. The β values obtained for the NSexperiments considerably contrast Graf & Cellino’s(2002) results obtained with direct measurements ofsediment diffusion coefficients and k =0.41.

Table 5. Rouse numbers and β -values for the tested flows

NS experiments

Experiment NS1 NS2 NS3

Fall velocity, vs(m/s) 0.024 0.024 0.024

Rouse number,z

0.8 1.04 0.94

β 2.65 1.75 2.04

NBS Experiments

Experiment NS1 NS2 NS3

Fall velocity, vs(m/s)

0.0006 0.0006 0.0006

Rouse number,z

0.07 0.07 0.19

β 0.52 0.55 0.22

Figures 12 show the profiles of sediment concentra-tion, and the Rouse equation plotted with the para-meters shown in Tables 5 for the NS and NBS ex-periments, respectively. Rouse equation fits well theNS data in the area 0.05< y/h <0.3, but departs fromthe data for the rest of the depth. Departure of themeasured sediment concentrations from Rouseequation very close to the bed, y/h < 0.05 can beassociated with the lack of particles on the bed in thepresent experiments, compared with the equilibriumsand bed (where the concentration profiles saturate)for which the equation was developed. Consequent-ly, the location of the maximum concentration is notat the bed as predicted by Rouse’s profile but atsome distance from the bed (as shown in Figure 11)

Concentration

y/h

10-4 10-3 10-20.0

0.2

0.4

0.6

0.8

1.0

NS1Rouse Eq.

Concentration

y/h

10-4 10-3 10-20.0

0.2

0.4

0.6

0.8

1.0

NS2Rouse Eq.

Concentration

y/h

10-4 10-3 10-20.0

0.2

0.4

0.6

0.8

1.0NS3Rouse Eq.

a.)



Concentration

y/h

10-4 10-3 10-20.0

0.2

0.4

0.6

0.8

1.0NBS1Rouse Eq.

Concentration

y/h

10-4 10-3 10-20.0

0.2

0.4

0.6

0.8

1.0

NBS2Rouse Eq.

Concentration

y/h

10-4 10-3 10-20.0

0.2

0.4

0.6

0.8

1.0

NBS3Rouse Eq.

b.)

Figure 11. Sediment concentrations: a) NS ex-periments; b) NBS experiments

1.4 IMPLICATIONS FORSEDIMENT TRANSPORT1.4.1 Traditional suspended sedimenttransport formulationThe investigation reported targeted essential aspectsof sediment transport, hence a summary of thegoverning equations related to this process arebriefly reviewed. The main quantities of practicalinterest in suspended-sediment transport in alluvialchannels are the average suspended concentrationof sediment Cs and the total unit sediment dischargeqs. Most of the existing analytical formulations used

for predicting suspended sediment transportconcentration and rates are based on the single-phase (mixture) approach (e.g. Wang & Adeff, 1986;Spasojevic & Holly, 1993; Gessler et al., 1999; andWu et al., 2000). These formulations are built theadvection-diffusion equation derived from massconservation in conjunction with a set ofassumptions

( ) ( ) ( ) ( ) ( )

∂∂

∂∂

+

∂

∂∂∂

+

∂∂

∂∂

=

∂∂

+∂∂

−∂∂

+∂∂

+∂∂

zC

zyC

yxC

x

wCz

vCy

vCy

uCx

Ct

smsz

smsy

smsx

smssmsmsmsm

ρερερε

ρρρρρ

(16)

where mρ = density of a mixture of water and sedi-

ment; szsysx εεε ,, = sediment diffusivity coeffi-cients in x-, y-, and z-direction, respectively. Themain assumptions associated with Eq. (16) are

(1) streamwise sediment particle velocity compo-nents is the same as fluid velocity

(2) sediment vertical velocity in turbulent flow isequal to the fall velocity of the sediment in stillwater

(3) turbulence effects of water and sediment, lum-ped into the diffusivity coefficients, are neglectedby considering that the turbulent momentumdiffusivity is equal to the sediment diffusivity.

For a steady uniform turbulent flow in a wide rectan-gular channel without any internal sources, integra-tion of Equation (16) over the flow depth and additio-nal assumptions on turbulence provides Cs via Rou-se equation (Equation 13). The unit suspended sedi-ment discharge qs is computed from the depth-inte-grated advective flux of sediment C U above the bedlayer y > a

∫ ⋅=h

ass UdyCq (18)

The corresponding total suspended sedimentdischarge in the stream is obtained from integrationof the unit suspended sediment discharge over theentire width of the channel. A general form for thedistribution of the mean velocity, U, in sediment-laden flows accounting for the sediment concentra-tion is given using a modified Coles’ law

+

Π

+++=hyCX

hyf

kBB

yuku

Usr

2ln1 *

* ν (19)

where, ks is the equivalent sand roughness, ν is thekinematic water velocity, B and Br are additiveconstants associated with smooth rough walls,respectively, Π is the Coles’ wake parameter, and



X(Cs) is a parameter related to the sediment concen-tration profile.

1.4.2 Limitations and perspectivesCurrently, all the parameters required by thetraditional suspended sediment transport formulationare determined from experimental observations thatare now regarded as classical flume experiments.Most of the available experimental evidence ishowever narrow, does not distinguish between flowphases, do not account for the role of theinstantaneous interaction between flow structure andsediment particles and is often conflicting. The lackof the agreement is partially a reflection of themultiple sources of bias errors (methods,instrumentation and analytical tools) that can beinvolved in the experimental investigation ofsediment-laden flows and (Muste, 2002).

A general limitation of the current analyticalapproach stems from the fact that Equation (16) hasnot yet appropriate experimental and/or numericalevidence to provide reliable information on theparameters controlling the microphysics of thesuspended sediment process and hence to formulateclosure relationships. Moreover, the results of thepresent study concurs with the previous findings(Squires & Eaton, 1990; Elgobashi, 1994; Kaftori etal, 1998; Rouson & Eaton, 2001) in revealing that thetraditional assumptions associated with theconventional theory of suspended sediment are notaccurate or quite questionable. The implications ofthe conceptual bias associated with the conventionaltheory are rarely evaluated. For example, Aziz(1996) demonstrates that the lack of consideration ofthe velocity lag might overestimate suspended-sediment load by up to 40%.

Use of Equations (13) and (19) encounters additionaldifficulties associated with the selection of propervalues for β, Csa, and of a velocity distribution lawvalid for sediment in suspension. The currentmethods of estimating β in Rouse equation arebased on the balance of downward settling of grainsand their upward diffusion in turbulent eddies(Vanoni, 1975). Many studies show that the β =1 isnot justified (e.g., Jobson & Sayre, 1970; Bennett etal., 1998) without a clear agreement on its trends.Perhaps the most serious concern with the Rouseequation (Equation 13) is that the sediment diffusivityis rarely calculated directly using quantitativeobservations of the motion of sediment in turbulenteddies. In one of those rare attempts, Graf & Cellino(2002) determined β totally independent from theRouse equation and found, in sharp contrast with thepresent results, that β <1 for suspension flow overmovable bed without bedforms and small sizesediment. This findings needs to be confirmed bymore experimental evidence, preferably obtainedwith techniques allowing separate flow-phase

measurements and fresh estimation approaches(see Figure 11).

Finally, there has been much controversy on theeffects of sediment on the mixture streamwisevelocity distributions used in Equation (19). Lyn’s(2000) analysis of these semi-empirical models forvelocity and concentration in flat-bed sediment-ladenflows showed that models developed over the last 25years are inadequate or at least incomplete. Theabove discussed limitations illustrates how tenuousis the database on which much of the computationalfluid dynamics edifices of suspended sedimenttransport are erected.

Use of models devoid of flow structure informationcannot reliably predict even first-order velocitystatistics. There is no doubt that near-wall structuresplay a crucial role in the sediment entrainment andsuspension mechanisms. Numerical studies con-firmed their existence (e.g., Rouson & Eaton, 2001)and suggest that they maintain their identity in bothsmooth and large scale roughness (Zedler & Street,2001). The strong three-dimensional, time-depen-dent nature of the bursting events and vortexstructures cannot be captured using the current time-averaging approach, which is strictly valid forstationary and homogeneous turbulence. The local,time-dependent characteristics of the processes callfor a combination of time, volume, and statistical (orensemble) averaging for accurately capture theglobal flow patterns. According to Greimann et al.(1999), recent applications have favored phase-weighted-ensemble-averaging, because it eliminatessome of the time and volume restrictions, inherent intime- and volume-averaging.

Given the intricate nature of the carrier flow and theadditional complexities brought by the presence ofthe particles, it is obvious that the one-phase flow(mixture) hypothesis of the current predictive for-mulations cannot actually capture the particle-fluid,particle-particle interactions, particle-boundary inter-actions (that includes bed roughness effect), and theeffect of the sediment on the underlying flow turbu-lence. Despite the close coupling between the turbu-lence characteristics of the flow phases, they aredistinct, and a feedback mechanism relates the twophases in the flow. Consequently a fresh experimen-tal approach using two-phase investigative tools isneeded. Fortunately the new generation of non-intrusive instruments currently available is capable ofseparately measure flow phases, revealing the linksbetween turbulence structures and sediment, and,importantly, the feedback of the sediment on theunderlying flow.

An increased number integrated data-driven mode-ling using at hand experimental techniques and thebest available numerical approaches are devised tofurther understanding and formulation of suspendedsediment transport processes. Progress in computersimulation methods and kinetic-theory analyses areleading to new opportunities to obtain the equations



of motion for multiphase flows which are stronglyinfluenced by or dominated by the disperse phase(e.g., Boivin et al., 2000, Zedler & Street, 2001).Innovative solutions specific to sediment area areemerging by modeling the fluid-particle mixture as apseudo-fluid with modified properties which incor-porates results of measurements obtained with two-phase flow investigative instruments (Cao et al.,2003; Cheng, 2004).

1.5 CONCLUDING REMARKSIn this study PIV-PTV measurements were acquiredfor a series of two experiments with three dilute sedi-ment concentrations and two types of sediment toinvestigate the overall effects of sediment presenceon the mean and turbulence flow characteristics.The experiments were conducted with all the sedi-ment in suspension without visible streaks formed onthe flume bed, hence the changes in the flow can beattributed to the interaction between sediment in sus-pension and flow turbulent structure. The principalconclusions drawn from this work are the following:

- Bulk flow velocity in sediment-laden flows reduces with concentration disregard of their inertial characteristics indicatingextraction of energy from the mean flow due to particle presence.

- Karman constant is gradually reduced with the addition of sediment for both neutrally-buoyant and heavy particles indicating disruption of turbulence flow mechanism in the inner region.

- Mean streamwise velocities for the heavy particles lag those of the carrier flow in the outer region with up to 5% for the range of conditions of the present study due to the combined effect of the mean gradient transport and the preferential organization of the particles within the lower velocity region of the turbulent structures.

- Mean streamwise particle velocities are larger than water very close to the wall because they are not bound by viscosity shear as in the case of water.

- Mean vertical velocities for heavy particle are higher than water velocities.

- The neutrally buoyant sediment does not display any observable difference compared to the water mean velocity profiles.

- Frequency distributions of vertical turbulence intensities have positive skewness revealing a net upward momentum flux throughout the depth.

- Turbulence intensities for the carrier water flow are slightly reduced for the heavy sediment and increased for the neutrally-

buoyant sediment in the region y+ > 30. For y+ < 10 turbulence intensities are increased for both sediment types.

- Particle turbulence intensities are larger than those of the carrier water flow for both types of sediment for y+ > 30.

- The linear Reynolds stress variation is preserved in sediment-laden flows. The peak of the Reynolds stress profiles moves closer to the wall for heavy sediment and the Reynolds stresses are slightly diminished.

- Eddy viscosity for water in sediment-laden flows is the same as for water in the region y/d < 0.3 and smaller outside this range for both types of sediment.

- Rouse equation is valid for y/h < 0.3. Because of the lack of sediment in the immediate vicinity of the wall, the Rouse equation does not predict well sediment concentration for y/h < 0.05.

The experimental results of this study illustrate thatparticle presence in a turbulent channel flow affectsthe flow throughout the depth irrespective of theirinertia. The experimental evidence also proves thatuse of the traditional formulations, assumptions, andmodels for suspended sediment transport could bepart of the differences, incompleteness, andinconsistency with respect to insights into sedimenteffects on water flow of existing in the suspendedsediment literature. Until computational resourcesprovide full numerical simulations of flow aspects,further understanding sediment transport could beprovided by systematic, highly resolved two-phasemeasurements targeting a sound description of themicromechanics of the suspended sedimenttransport. The gathered experimental evidence canassist numerical modeling in two ways. First, theexperimental evidence provides databases readilyusable for development and validation of complextwo-phase models. Second, while new physics isgradually incorporated in the two-phase models, thesame experimental evidence can be used to improvethe semi-empirical correlations currently used by thehydraulic engineering community mixture-basedmodels. The results presented in this paper serveboth goals, with special emphasis on theirimplications on the suspended sediment transportgoverning equations assumption traditionally used inhydraulic engineering.

AcknowledgementsThe measurements presented in the paper wereconducted at Kobe University (Japan) while the firstauthor was supported by a Japanese Society for thePromotion of Science Fellowship. This support isgratefully acknowledged.



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1.7 List of symbolsa reference point for Rouse equationC depth averaged sediment concentration

aC sediment concentration at depth a

50D median diameter of sediment particle

sD sediment particle diameter

pd particle diameter+pd particle diameter ( )ν*ud p≡

Fr Froude numberk skewnessN total number of particles

+N number of upward-moving particles

−N number of downward-moving particles

sq total unit sediment discharge

U depth averaged streamwise velocity of water

mU depth averaged streamwise velocity of water-sediment mixture

sU depth averaged streamwise velocity of sediment

Gu sediment velocity lag (Greimann, et al., 1999)

*u shear velocity

1*u shear velocity obtained from the momentum

balance ( )gRS≡

2*u shear velocity obtained from the measured Reynolds stress profile

tu root mean square of fluctuation component of streamwise velocity

( )uu ′′≡

MLTV equivalent vertical velocity by McLaughlin and Tiederman

υ′ root mean square of fluctuation component of vertical velocity

( )υυ ′′≡

sυ fall velocity of sediment particlev kinematic viscosity of waterh flow depthy distance from the channel bottom+y dimensionless distance from the channel

bottom ( )ν*yu≡Re Reynolds number

pRe particle Reynolds number

mε turbulent momentum diffusion coefficient

St Stokes number

Tλ Taylor microscaleξ the rate of turbulent energy dissipationκ Karman constant

mκ measured Karman constant of water-sediment mixture

pτ pτ particle response time

fτ representative flow time scale

Kτ Kolmogorov time scale ( )ξν≡

el length scale of the energy containing eddies

η dimensionless height ( )hy≡

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