Laboratory Measurements on Turbulent PressureFluctuations in and above Gravel BedsMartin Detert1; Volker Weitbrecht2; and Gerhard H. Jirka, F.ASCE3Abstract:Thestatisticsofpressureuctuationsaboveandwithinthreetypesofporousgranularbedssuchasingravelbedstreams,rivers, and man-made canals are investigated by data gained via laboratory ume experiments. The ow conditions examined include adiversity of hydrodynamic loads that increase up to the point where single grains are moving from time to time, without causing severemodicationtothebedtextureandtherelatedpositionsofthepressuresensors.Analysisisperformedbymeansofhistogramsandspectral techniques and vertical intensity proles. Two simplied equations are found that describe the vertical decrease for the standarddeviation of the measured uctuations indicating drag and lift, respectively, nondimensionalized by the mean bed shear stress. The formeructuation is described by a crude linear t, whereas the latter clearly shows that the lift intensity decreases exponentially in the porousbed with a decay distance of one to two times the equivalent grain roughness. Within the subsurface layer the standard deviation reachesa nonzero constant, mainly dominated by long-wave pressure elds that are convected in the outer ow. These ndings can be used infuture sediment transport models that use force balance approaches to determine incipient motion conditions.DOI: 10.1061/ASCEHY.1943-7900.0000251CE Database subject headings: Open channel ow; Gravel; Turbulence; Power spectral density; Laboratory tests; River beds.Author keywords: Open-channel ow; Gravel bed; Turbulence; Pressure uctuation; Spectral density; Interstitial.IntroductionThedynamicsofowovergravelbedsisdeterminedbythein-tricateinteractionbetweenturbulentvelocityeldsandpressureeldse.g., Hoand et al. 2005; Detert et al., Synoptic velocityand pressure elds at the water-sediment interface of stream-beds, J. Fluid Mech., unpublished, 2010. In order to understandthe detailed mechanisms of bed instability leading to the erosionofindividualparticles, itisnecessarytodeterminethetemporalsequence of synoptic velocityandpressure signals since bothquantities are jointly responsible for the hydrodynamic forces onthe particles.However, most of the past studies concerning gravel beds un-derlyingopen-channel owfocusedonvelocitymeasurementsalone, such as velocities at a point e.g., Aberle and Nikora 2006orvelocityeldse.g., Royetal. 2004;Hurtheretal. 2007. Incontrast, veryfewstudieswithdetailedturbulent pressuremea-surements have been reported to datee.g., Hoand 2005; Smartand Habersack 2007. This limitation is due to the technical dif-cultiesthathaveexistedsofarthatpreventedthedevelopmentofsufcientlysmall-scalehighresolutionpressuremeasurementdevices in the laboratory.Understanding the genesis of the instantaneous local pressureneeds a knowledge of the entire turbulent uid domain. By takingthe divergence of the Navier-Stokes momentumconservationequations, thePoissonequationfor theuctuatingpressure pwithin an incompressible ow is obtained in Reynolds decompo-sition, e.g., Chang et al. 1999 12p = 2uixjujxi+2xi xjuiuj uiuj 1where=fluid density; i , j =1; 2; 3 following the Einstein nota-tion; the spatial coordinates are xi; and the velocity vectors are ui.Thersttermontheright-handsideiscalledtherapidrespec-tively, linear or mean-shear source term because it responds im-mediately to a change in the mean velocity gradient. The secondtermis calledtheslowor nonlinear or turbulence-turbulencesourceterm.Itfollowsthatboththevelocitygradientsanduc-tuation gradients in the entire ow domain inuencepat a cer-tainmoment, but the impact of single sources decreases withdistance. Undisturbed, direct pressuremeasurementswithintur-bulent ows are impossible, as an ideal probe had to be innitesi-mally small in order not to inuence the ow. Pointmeasurements usingaverysmall-scalemeasurement setupre-cently conducted by Tsuji et al. 2007 are promising in minimiz-ing this disturbance. Nonintrusive ultrasonic-based pressure eldmeasurementshavebeenreportedby, e.g., HansandWindorfer2003 and Yu et al. 2005. However, truly complete informationabout pressureuctuationsor entirepressureeldsseemsonlyrealizable by numerical simulations.Kim1989analyzedthepressureuctuationsinaturbulentchannel owwithsmoothwallsobtainedfromdirect numerical1Postdoctoral Hydraulic Engineer and Researcher, Laboratory of Hy-draulics, HydrologyandGlaciology, ETHZurich, Gloriastrasse37-39,CH-8092Zurich, Switzerland; formerly, Institutefor Hydromechanics,Univ. of Karlsruhe, D-76128 Karlsruhe, Germany corresponding author.E-mail: mdetert@ethz.ch2Research Engineer, Laboratory of Hydraulics, Hydrology and Glaci-ology, ETHZurich, Gloriastrasse37-39, CH-8092Zurich, Switzerland;formerly, Institute for Hydromechanics, Univ. of Karlsruhe, D-76128Karlsruhe, Germany. E-mail: wv@ethz.ch3Emeritus Professor, Institute for Hydromechanics, Univ. ofKarlsruhe, D-76128 Karlsruhe, Germany.Note. This manuscript was submitted on April 16, 2009; approved onApril 2, 2010; publishedonlineonApril 15, 2010. Discussionperiodopenuntil March1, 2011; separatediscussionsmust besubmittedforindividualpapers. Thispaperispartofthe Journal of Hydraulic Engi-neering, Vol.136,No.10,October1,2010.ASCE,ISSN0733-9429/2010/10-779789/$25.00.JOURNAL OF HYDRAULIC ENGINEERING ASCE / OCTOBER 2010 / 779J. Hydraul. Eng. 2010.136:779-789.Downloaded from ascelibrary.org by INDIAN INST OF TECHNOLOGY - ROORKEE on 08/14/14. Copyright ASCE. For personal use only; all rights reserved.simulationDNS. AsshowninFig. 1, pincreasestowardthewall and reaches its maximum slightly above it. A detailed analy-sis revealed that the slow source term is substantially larger thantherapidterm, except veryclosetothewall, yt/ 0.15notshown in Fig. 1, where=channel half-width, here equal to theboundary-layer thickness. Analysis of pressure elds of ow overand within a permeable bed was given by Breugem et al. 2006.They studied the inuence of wall permeability on turbulent owson top and through a porous medium of cubes also by DNS. Thevertical proleofpinthefreestreamroughlyagreeswiththatgiven by Kim1989 but is supplemented by an exponential de-crease inside the permeable wall see Fig. 1. The peak value justabove the permeable wall is revealed to increase with Re=ud/ , where u=shear velocity; d=characteristic obstaclelengthscale;and=kinematicviscosity,andwiththeroughnessgeometry function, =Vf / Vo, where Vf=volume of uid withinthetotal volumeVo. Thisdependencyisattributedtoturbulenttransport across the wall interface and the reduction in mean shearduetoaweakeningof thewall-blockingandthewall-inducedviscouseffects,respectively. Todate,anexperimentalvalidationoftheresultsfortheturbulenceintensityprolesfromBreugemet al.2006 has not been available.Whereas the measurement of pressure within a turbulent owisextremelydifcultasanappropriatenoncontactmeasurementdevicedoesnot exist, turbulencewall pressuresTWP canbemeasured as the measuring technique can be incorporated into thewall.TWP havemainlybeenstudiedineldsofacoustic, aero-nautic, or naval applications, with a large number of works in the1970s and 1980s. A review is given by Eckelmann 1988. Blake1970 measured boundary-layer TWP with pinhole microphoneson both smooth and rough boundaries. He showed that the shapeofthepressurespectraisthesameforbothwalltypes,buttheydiffer in their scaling. The former scales by a viscous length / uandthelatterscalesbytheaveragegeometricroughnessheight.At the wall the magnitude of p was found to be almost equal forsmooth and rough walls. Emmerling 1973 used an opticalmethod to investigate the instantaneous structure of wall-pressureelds. Zones of high-amplitudepappeared in irregular time in-tervalsandweretheoreticallyassociatedwithburstingphenom-ena.Maximalpressurepeaksofuptopmax=6pwereobserved.Thesevaluesareof thesamemagnitudeastheonesfoundbySchewe1983, as he observed maximal pressure peaks of up topmax=7p. Thesendingsimplythatthe TWP canbecomeverylarge and therefore should dominate mass and momentum transferin the case of a permeable wall and could possibly inuence bedstability. Characteristicwall-pressurestructureswerefoundwithhigh amplitudes, whose sources are located in the buffer layer ofthe boundary layer. The mean characteristic wavelength was iden-tied to be 145/ u, indicating correlation with bursting phenom-ena. Fromthe measuredprobabilitydensityhe calculatedthatthesestructuresplayanimportantroleinthewallregionoftheboundarylayer. A scalinglawforpwasgivenbyFarabeeandCasarella 1991. Basedondatafromeight studies whichap-peared within 19701990 and data from their own measurements,theydevelopedarelationforpdependingonlnReandtheboundaryshear o=u2. Klewicki et al. 2008 conrmedthisrelationshipbymeasurement dataobtainedinthesalt playaofUtahs west desert, however, with a slight change in the multipli-cative constants.The aforementionedexplanations refer tothe pressure inauid or at a wall. However, the hydrodynamic forces acting on asinglegrainalsoexpressibleasforceperarea, i.e., pressureare hardly comparable to the pointwise local pressure as the owisindirectinteractionwiththeobstacle. Thetermsdragandliftare used for the streamwise and vertical components, respectively,of the hydrodynamic force. Many experimental investigationswereundertakentoreveal thecharacteristicsandtopredict thedragandliftforces.TherecentcontributionsbyHoand2005and coworkers using single piezoresistive pressure sensors as wellas by Schmeeckle et al. 2007 using force transducer techniquescomprise up-to-date knowledge andadvancedmeasuringtech-niques.Vollmer et al. 2002 presented quasi-low-pass ltered labora-torydatathatindicateanexponentialdecayofpressureuctua-tionswithinporousgranularbeds. Smart andHabersack2007gainedsophisticatedelddataofnear-bedandsubbedpressureuctuations that showa near Gaussianfrequencydistribution,wherethenear-bedp3o. However, uptonownoin-depthmeasurement campaignwithunambiguousboundaryconditions,highly resolved in time and space, has been performed to describetheverticalstatistical propertiesofuctuatingpressureinandabove different porous beds. To bridge this lack of knowledge isthemaincontributionofthepresent paper, wherethemeasuredverticalintensityofhydrodynamicloadsatandinporousgravelbeds will be described statistically. This information will help tounderstand the intensity and occurrence of physical processeswithin gravel beds, especially to improve the analytical predictionof the initial point of sediment entrainment.Experimental SetupLaboratory FacilitiesThe experiments were carried out in a rectangular laboratoryumeat theInstitutefor Hydromechanics IfH, UniversityofKarlsruhe, withaneffectivelengthof17.0mandawidthofB=0.9 m. The water depth ranged from h=0.13 to 0.22 m. A right-handed coordinate system is implied, where x is orientated in thestreamwiseowdirection,yintheupwardvertical,andzinthetransverse direction. x=0 holds at the middle of the measurementarea, y=0 denotes a nominal wall level, where an extrapolated logt of u y would reach zero, and z=0 is located in the centerlineFig. 1. Intensities of pressureuctuations. DNSresults for p/ otaken from Kim 1989 smooth walls, Re=u/ =179 and Breu-gem et al. 2006 rough permeable wall, Re=176, =0.60. Here,y=0refers to the smooth wall and the roughness tops, respectively.780 / JOURNAL OF HYDRAULIC ENGINEERING ASCE / OCTOBER 2010J. Hydraul. Eng. 2010.136:779-789.Downloaded from ascelibrary.org by INDIAN INST OF TECHNOLOGY - ROORKEE on 08/14/14. Copyright ASCE. For personal use only; all rights reserved.of the ume. The inlet was located at x=10.5 m relative to themeasurement area to guarantee a fully developed boundary layer.Theoutlet at x=+6.5 mwascontrolledbyavertical thinplateweir. Hence, inuencesofbothinletandoutletwerenegligible.The bottom of the ume had a slight slope of 0.05%. The waterdepth h was measured at three points at x=9.33; 0.00;+4.42 mbyultrasonicprobes.Theyweremountedonexternalcylindrical water tanks that were in hydraulic interconnectionwith the porous bed via exible tubes 25 mm in diameter. Duetothisarrangement, uctuationsandsmall-scaleoscillationsofthe actual water level were low pass ltered.Bed MaterialThree different bed materials were inserted: uniformgravel,gravel from the river Rhine, and spheres. The river Rhine gravelwastakenfromagravel bankabout 10kmdownstreamoftheIffezheim barrage low water conditions, 02.08.2006. At this po-sitionanarmoringlayer withathickness of onetotwostonediameters was found. The underlying material revealed to be bi-modal, withcentersat d10=0.4 mmfor15%oftheweight andd60=14.7 mmfor 85%of theweight. Table1summarizestheproperties of the bed parameters. The grain sizes di were obtainedbysieveanalysis. Theroughnessgeometryfunctionandthestone densityswere determinedbyanexternal experimentalsetup. The permeability coefcient kfwas obtained from Hazens1892 equation for the uniform gravel and the Rhine gravel andfrom Kozemy-Carmans equation Carman 1956 for the spheres.Measurement SetupFig. 2 illustrates the measurement setup. It consisted of an arrayof up to 16 miniaturized piezoresistive pressure sensors MPPSslocatedwithinandslightlyabovethegravellayer. Typically,thedataacquisitionwascarriedoutfor205s. Additionalresultsre-garding the velocity regime using a two dimensional 2D particleimage velocimetry PIV system and an acoustic Doppler currentprolerADCPcanbefoundinDetert2008andDetertetal.Synopticvelocityandpressureeldsatthewater-sedimentin-terface of streambeds, J. Fluid Mech., unpublished, 2010.MPPSsFig. 3 shows the MPPS geometry and components. The principleoftheMPPSisbasedonthepiezoresistiveeffect.Incontrasttothe piezoelectric effect, this effect only causes a change in resis-tance, but it does not produce electrical charges. The core of theMPPSis a micromechanical silicon wafer with implanted pi-ezoresistors on its bending panel. For the MPPS used in this studythe differential pressure is measured with reference to atmo-sphericpressure. Thecomponentsfor theMPPSwereobtainedfromAktiv Sensor GmbH, Berlin. The sensor elements ATD0.040-G00-BG-K1408 and AUblank PGA-V0-D18Awere as-sembledattheIfHtoadaptthemtotheirapplicationwithintheexperimental ume. Depending on the conguration, the sensorsmeasure both the surrounding static pressure and the surroundingdynamicpressure. Thus, theoutput signal reectstheeffectiveforce per pinhole area in the direction of the pressure tube.To miniaturize the pressure transducer the amplifying blanketshad to be arranged in an external box. Unfortunately, the length ofthe exible cables to the external amplifying board could not beshorter than2.5mdue tothe boundaries of the experimentalsetup. Thus, slight antenna-noise effects had to be accepted. Flex-ible PVC tubes were used to provide atmospheric pressure in thepickup, alsowithalengthof2.5m. ThepickupsoftheMPPSwere encapsulated with slowly hardening epoxy resin and sealedupwithclear varnishtomakethemwater resistant. Thenalmeandiameterofonesensorheadwas15mm.Theready-builtsensorswerepoint calibratedby AktivSensorGmbHto19VTable 1. Parameter of the Bed Materials Uniform Gravel, Gravel from the River Rhine Armoring Layer, and Spheres; the Weighted Mean of the WholeGrain-Size Distribution Is Represented by dMeyer-Peter and Mller 1949; for #uni dd50 and for #rhi dd70Run number Bedd15, d, d85mmkfm/ss103kg/ m3 Packing#uni Uniform gravel 7.7, 10.2, 13.2 0.390.02 0.7 2.46 Loose#rhi Rhine, armored 13.8, 26.1, 38.8 0.330.02 1.5 2.51 Loose#sph Spheres 25.4 0.26 1.6 1.36 DensestFig. 2. Sketch of the experimental setup, dimensions in meters, not to scale: a view in the streamwise direction, with 16 MPPS and both 2D PIVarrangements of setups Aand B;b side view, where the positions of the one dimensional ADCP probe can also be seenJOURNAL OF HYDRAULIC ENGINEERING ASCE / OCTOBER 2010 / 781J. Hydraul. Eng. 2010.136:779-789.Downloaded from ascelibrary.org by INDIAN INST OF TECHNOLOGY - ROORKEE on 08/14/14. Copyright ASCE. For personal use only; all rights reserved.accordingto04kPawithatoleranceinaccuracyoflessthan1.0%full scale. Temperatureerrors arecompensatedelectroni-cally, leading to a remaining nonlinearity of typically 0.1% fullscale. The response time guaranteedbythe manufacturer was10 ms, limitedbythesignal conditioningbytheamplifyingblankets. Toavoidaliasingeffectsduetohighfrequencynoise2 kHz, the recording was made at f 2, 125.7 Hz, additionallysupportedbyafourth-order Butterworthlow-pass lter withacutofffrequencyof500HzDataTranslationSAK52-150-501-10. A 16-bit AD card Data Translation 321 allowed a theoreti-cal resolutioncorrespondingto0.15Pa. Withintheume, thesensors were locally xed on a grid to keep them in an accuratelydenedposition. Testsunder umeconditionsshowedthat theMPPS were even able to react within 2 ms. In one measurementarrangement somesensors werealignedwithinthelaser sheet.Thelaser doublepulseswereclearlyidentiableinthesignal.This unforeseen effect was used to validate the synchronization ofthe PIV and the MPPS signal.The MPPS are used in horizontal Fig. 4a and vertical Fig.4barrangementstodistinguishbetweendragandlift uctua-tions. Apositivepressuredeviationinthestreamwisedirectionover pressure refers to a drag-force-like event, D=p Fig.4a. A negative pressure deviation in the vertical direction lowpressurereferstoalift-force-likeevent, L=pFig. 4b. Inthefollowing, thepressureuctuationsmeasuredintheverticaldirectionaredenotedbythestresstermLandinthehorizontaldirection by the stress term D, respectively. However, it has to benoticed that the sensor in the drag conguration Fig. 4a inu-ences the pressure signal because it is protruding with half of itsdiameter intothe oweld. It is assumedthat the differencebetween the conguration in Figs. 4a and b is only of quantita-tive matter and that the overall characteristics are very much com-parable.Flow ConditionsTable2givestheowconditionsthatwereprovidedduringthemeasurements. Qis the ow rate, and the bulk velocity is deter-minedbyU=Q/ Bh.Thelocationofthemaximumvelocityindistancetothebed, h, isthroughout smallerthanh, indicatingthepresenceof slight secondarycurrents. This phenomenonisunavoidableinumeexperiments withanaspect ratioof B/ h=4.2Song and Graf 1994. However, a closer inspection of thevelocity elds showed that the ow behaves like a 2D ow in thenear-bedcenterlineregionfor details, seeDetert 2008, Chap.4.2.1. The bulk Reynolds number is dened by Reh=Uh/ , withthe kinematic viscosity of water =106m2/ s at 20C. The shearvelocity u, the equivalent grain roughness ks, and the zero-planedisplacementyytweredeterminedfromlogtsof u yfromindependent PIVandADCPmeasurements, withtolerances of3% for u.ResultsThe following three subsections concentrate on the uniform owconditions of experiment number #uni6as these measurementsgave representative results for all experimental runs of #sphi,#unii, and#rhi9whilethefourthsubsectiongives turbulenceintensity proles for the different experimental runs.Time SeriesFig. 5shows synchronous time series of pressure uctuationsptmeasuredwiththeexperimentalconditionsof#uni6overt=3.0 s. The pinholes of the four pressure pickups were posi-tionedat y=+10; +5; 7; 22 mm. The MPPSat y=+5 mmFig. 4. Arrangements of the MPPS: a MPPS as a drag indicator; bMPPS as a lift indicatorFig. 3. Sketch of the head of an MPPS, units in millimetersTable 2. Experimental Flow Conditions; the Integers1,3,6,9 at the End of the Run Number Approximately Refer to the Ratios of Qi, Ui, or Reh,i; at#uni9 the Provided Flow Led to Very Slight Sediment Transport, Where Isolated Single Grains Were Observed to Be Moving OccasionallyRunnumberQm3/ shmmUm/shmmum/sRehRehksmmyytmm#uni3 56.6 200 314 165 30 62.8 4.95 26.52 2.62#uni6 120.0 200 667 175 63 133.4 11.03 26.52 2.62#uni9 180.0 211 948 155 95 200.0 14.73 26.52 2.62#rhi9 180.0 215 930 155 86 200.0 13.33 15.53 6.62#sph1 18.6 129 160 125 13 20.6 1.88 20.51.5 5.50.5#sph3 56.6 199 316 170 30 62.9 5.10 20.51.5 5.50.5782 / JOURNAL OF HYDRAULIC ENGINEERING ASCE / OCTOBER 2010J. Hydraul. Eng. 2010.136:779-789.Downloaded from ascelibrary.org by INDIAN INST OF TECHNOLOGY - ROORKEE on 08/14/14. Copyright ASCE. For personal use only; all rights reserved.wasfacingupward, asshowninFig. 4b; thusit indicatestheuctuatinglift. Theother threesensorswerearrangedwiththepinhole facingupstream, as depictedinFig. 4a. Thus, thesesensors indicate the uctuating drag. For the measurements givenin Fig. 5, the sensors indicating D were vertically aligned in thecenterline of the ume, whereas the L sensor was positioned at alateral distance of 80 mm relative to the others.ThesignalsgiveninFig. 5clearlyshowthedampingoftheamplitude with increasing depth into gravel. As expected thedeepest sensor at y=22 mm gives the smallest pressure uctua-tions. However, the uctuations recorded by the second sensor aty=7 mmi.e., onegraindiameter belowtheroughnesstopscan hardly be distinguished from the deepest sensor. More intensesmall-scale uctuations can be seen only synchronous to positivepeaks of the most exposed sensor at t =45.5; 45.8; 46.6; 47.4 s.Due to its lateral distance from the other sensors, the signal of theL sensor slightly above the roughness crest shows no correlationwiththeother sensors. However, therecordeductuations areclearly more turbulent in comparison with the sensors within thegravel bed. The signal of the most exposed sensor gives the mostextremepressureuctuations. Maximal positivepressurepeaksreach up to p/ o+40, whereas the negative pressure peaks areless extreme, around p/ o20. This indicates that positivepeaksofDaremoreextremethanthenegativepeaks, i.e., thesignal is skewed. Acloser examinationof this phenomenonisgiven in the next section.HistogramsTocharacterizetheprobabilitydistributionofextremevaluesofthe pressure uctuations, histograms of the measured signals arepresented in the following. They are compared with a probabilitydensityfunctionPDF derivedbyHoandandBattjes2006.ThisPDFiscapableofdescribinginstantaneousdragforcesonbed roughness elements. It is distantly related to the2distribu-tion, whichwasproposedbyPapanicolaouet al. 2002forthePDF of drag forces. However, the 2distribution includes a sum-mation from 0 to innity, whereas Hoands formulation is easierto use in practice.Hoands formulation is derived by assuming a characteristic,normallydistributednear-bedvelocityub,thatisproportionaltothe drag force by FD=ubub. This single characteristic ub is seento be the only source for drag forces. The PDF is derived asPFD =122FDexp 12FD/ sgnFD22where the noncentrality parameter = ub/ub3givesthereciprocaloftherelativenear-bedturbulenceintensityruled by ub. Fits to the mean and standard deviation are given byfit= 2+ 1 exp 1.63 4andfit= 42+ 2 + exp 0.552 5ThePDFisnegativelyskewed, i.e., eventsof FD0aremoreextreme. HoandandBattjes2006testedEq. 2againsttheirown measurements. As a proxy to the streamwise drag force FD,theyusedthestreamwisepressuredifferential Dmeasuredat acubicmodelstonewithanedgelengthof30mm. Theshapeofthe PDF was predicted almost perfectly for lower drag intensitiesintherangeof 2D. However, slight differencesfor extremedragvalues were observed, where the trendof D was betterdescribed by an adaptation of . In his Ph.D. report, Hoand alsotested pressure measurements indicating lift uctuations, L,against anadoptedversionof Eq. 2. However, themeasureddistributionsofLdidnot followthetheoretical curve. Instead,theyrevealedtobealmostGaussianshapedbetween2L,andbeyond that the atness of the distribution is higher than given bya normal distribution.InFigs. 68, Eq. 2hasbeenusedtodeterminethepresentPDFs from the pressure measurements at the experimental condi-tionsof#uni6forbotharrangementstorecordDandL. Thegures are given in two different ways: on the left they are plottedwith linear scales in order to evaluate the shape of the distributionaround the mean; on the right they are plotted with semilogarith-mic scales to better represent the shape of the tails. Three differ-ent bed exposures are analyzed, y=7 mm in Fig. 6, y=0 in Fig. 7,and y20 mmin Fig. 8. Figs. 6 and 7 include plots ofHoands PDFEq.2, adopted for both D and L.A denite near-bed cannot be found for D and L sinceub and ub are subjected to a larger scatter. Thus the results withEq. 2wereobtainedwith=2.7; 5.4 tocoverareasonablerangegainedbythevelocitymeasurements Detert 2008. TheguresalsoincludeplotsofthestandardGaussianorstandard-normal densitydistribution. Fig. 6revealsthat HoandsPDFEq. 2 provides a good approach to both histograms of D andL at y=7 mm. In tendency, =2.7 gives an acceptable approxi-mation to the measured shape. However, negative deviations canbe seen around the mode value and the negative tails for1.8D; L. In the semilogarithmic plot it can be seen that thepositivetail of D isdescribedwell byvaluesof =2.75.4,whereas the maxima of its negative tails are better approximatedfor5.4. ForLasimilartendencyisrevealed.Thepositivetail of L isdescribedwell byvaluesof 2.7, whereasthemaximaofitsnegativetailareapproximatedfor5.4. NotethatEq.2equalstheGaussiandistributionifitisappliedwith=. These ndings lead to the following conclusions concern-ingthepropertiesof pressureuctuationsmeasuredslightlyontopof thegravel bed. 1AsbothPDFsof D andL canbeapproximated by Eq. 2, here both the local drag and the local liftmust be mainly inuenced by the near-bed velocities. In the senseof Hoand 2005, the underlying process is called a quasi-steadymechanism, as it is mainlyduetolarge-scalevelocityuctua-Fig. 5. Simultaneoustimeseriesof pressureuctuations pt for#uni6. Linewidths fromthicktothincorrespondtoy=+10; +5;7; 22 mm, indicating the uctuating part of the drag and lift asD; L; D; D. Here, thesensors indicatingdraguctuations arevertically aligned; the sensor indicating lift uctuations is at z=+80 mm relative to the other sensorslight gray line.JOURNAL OF HYDRAULIC ENGINEERING ASCE / OCTOBER 2010 / 783J. Hydraul. Eng. 2010.136:779-789.Downloaded from ascelibrary.org by INDIAN INST OF TECHNOLOGY - ROORKEE on 08/14/14. Copyright ASCE. For personal use only; all rights reserved.tions.However,hismeasurementsdidnotshowthatthisdepen-dencyalsoholds for L, althoughheexpectedthis for higherprotrusions Hoand 2005, p. 105. Note that Hoand had aslightlydifferent setupwithcrushedstonesandarelativelargecubical housing of 30 mm for his pressure sensors. 2 The posi-tivetailsof 3D; L arebetter describedbyhigher relativenear-bedturbulenceintensities, 1/ , thanthenegativetails. Inother words, at higher near-bedturbulenceintensities, thedragand the lift uctuation is more likely to be positive than negative.Similar ndings hold for the measured PDFs at the gravel tops,as shown in Fig. 7. Again, =2.7 givesat least intendencyanacceptableapproximationtothemeasuredshape,wherethepositivetailsofDandLarepredictedalmost per-fectlybythisvalue.Thenegativetailsobtainabettermatchingforlowerturbulenceintensities, whereDcanbeapproximatedby=5.4 and Lby=. Thus, the trend goes to lower near-bed turbulence intensities. Nevertheless, the quasi-steady mecha-nism is still dominant. As shown in Fig. 8, all PDFs of D and Lloose their skewness deeper inthe gravel at y20 mm. ThePDFs are well predicted by a simple Gaussian distribution, or inthe sense of Hoands PDF Eq. 2 =holds, i.e., ubub. Thus, turbulence due to near-bed velocity uctuationsplaysnofurther role. FollowingHoand2005, e.g., Fig. 6.1,TWP uctuations can be seen as the responsible mechanism now.TWP areduetoconvectingpressureeldsandnotduetonear-bed velocity elds. Consequently, a symmetrical i.e., a non-skewed PDF can be expected.The PDFs measured at y=+7; 0; 20 mm revealed that theinterfacial layer say, 0y/ ks1representsasharpboundary.Abovethisregion, dragandliftuctuationsaremorerelatedtothenear-bedvelocity, andbelowtheyaremorerelatedtoTWP.Thedeterminedhistograms showthat thehydrodynamicloadsactingonthebedmaterial canbedescribedbyHoandsPDFEq.2. Based on this information the probability of grain par-ticles tobe unstable couldbe estimatednumericallyinfuturestochasticsediment transport modelsthat useforcebalanceap-proaches to determine conditions of incipient motion.Spectral AnalysisInthefollowingthespectral distributionof thesignalsisana-lyzed. Fig. 9 shows typical representative power spectra Spp of themeasured signals at different vertical positions. They refer to thesamepressuresignalsthatwerealreadypresentedastimeseriesinFig. 5. Additionally, Fig. 9includes asupplementarysignalrecorded at y=38 mm, deeper within the gravel layer. The one-sidedspectraareestimatedbyWelchsaveragedmodiedperi-odogrammethodof spectral estimation. Segment lengths of n=21761.7swith50%overlapwereused,withHammingwin-dows of the same length. The results were smoothed by a movingaverage window of 50 elements, with the shape preserved.Withanoverall viewof Fig. 9thedampingof thepressureuctuations within the gravel layer becomes obvious as the spec-traof thesignalsof themoreshelteredsensorsthroughout arebelow the more exposed ones. Furthermore, the lower frequencies2 Hz also contain the larger part of the turbulent energy. Onlythe spectrumof the signal measuredbythe uppermost sensorclearly follows the expected Kolmogorov-scaling tendency withinthe inertial subrange. At frequencies off 10 Hz, its curve dec-lination conforms with the classical 7/3 power law for pressuree.g.,Moninand Yaglom1975. Thisscalingalsoroughlyholdsfor thespectraat y=22; 38 mm withinthegravel. How-Fig. 6. PDFsofmeasuredinstantaneouspressureuctuationsslightlyabovethegravel crest at y=+7 mm#uni6: aDtenindependentsignals;b L14 independent signals compared with Eq.2 and a Gaussian distribution normalized by its respective standard deviationi784 / JOURNAL OF HYDRAULIC ENGINEERING ASCE / OCTOBER 2010J. Hydraul. Eng. 2010.136:779-789.Downloaded from ascelibrary.org by INDIAN INST OF TECHNOLOGY - ROORKEE on 08/14/14. Copyright ASCE. For personal use only; all rights reserved.ever, sincetheturbulent uctuationsaredampedwithinthepo-rous layer, the resulting curves are shifted toward lower values ofSppand f, respectively. As all spectradeeper inthebedwerefound nearly to resemble these two spectra not shown here, it isconcludedthatlittleadditionaldampingtakesplacedeeperthan12ks. The variance p2, i.e., the area under the curves, staysalmost constant.Incontrast tothisKolmogorovconformity, thesignalsmea-sured in the roughness layer at y=+5; 7 mm reveal a differ-entspectralbehaviorfortheturbulentenergycascade.Here,thecurves show a decrease slower than f7/3. At f 30 Hz, the curveof the MPPS aty=+5 mm even crosses the spectrum of the up-permost sensor. This behavior can possibly be explained with anenergy transfer from the horizontal to the vertical uctuations. Asthe freestream ow in the streamwise direction is hindered due tosingle grains in the roughness layer, it transforms to a more threedimensional3Dowwithintheintersticesbetweenthegrains.Therefore, kinetic energy from the streamwise ow is shifted to-wardthe vertical andtransversal directions. Withinthe gravellayer, theclassical 7/3power cascadethat indicatesisotropicbehavior is enhanced by a transformation of small-scale turbulentkinetic energy. However, it has to be noted that the validity of a7/3lawfor pressureisnot generallyaccepted. AlthoughLeeand Sung 2002 and Hoand 2005, p. 106 solely found a 7/3powerlawfortheirTWPspectraasmeasuredunderfreeshearowbehindabackward-facingstep, GotohandRogallo1999proposed a second range asf5/3. Lately, Tsuji et al.2007 evenFig. 7.PDFsofmeasuredinstantaneouspressureuctuationsatthegraveltopsaty=0#uni6:aDtwoindependentsignals;bL14independent signalsFig. 8. PDFs of measured instantaneous pressure uctuations within the gravel bed at y20 mm #uni6, nine independent signals left: linear;right: semilogarithmic scaleJOURNAL OF HYDRAULIC ENGINEERING ASCE / OCTOBER 2010 / 785J. Hydraul. Eng. 2010.136:779-789.Downloaded from ascelibrary.org by INDIAN INST OF TECHNOLOGY - ROORKEE on 08/14/14. Copyright ASCE. For personal use only; all rights reserved.foundcharacteristicisotropyat exponents of 5/ 3, but theynever observed a7/3 power law in their pressure spectra at all.Inthe present measurements large-scale oscillations with f1 Hz are observed that are not damped within the porousgravel layer. It is hypothesized that these pressure uctuations aredominated by a long-wave oscillating water level. By neglectingsurfacetension, therst-order wavetheorygives theresultingstandard deviation of the bed pressure due to surface wavesp =ga2 coshkh6whereadenotesthewaveamplitude, andthewavenumber isgiven by k=2/ withbeing the wavelength. Within the tran-sitionfromdeeptoshallowwaterbetween0.05h/ 0.5,thecorresponding wave frequency becomesf = 1g/k tanhkh 7Fig. 9 includes a plot of Eqs.6 and7, where=0.254.0 mandaconstant small amplitudeof a=0.6 mmisassumed. Theplot matches the spectra at f 1 Hz reasonablywell. Conse-quently, the long-wave oscillations of the outer ow are hypoth-esized to dominate p within the gravel layer. However, it cannotbeanswereddenitelywhethertheyareduetolong-waveoscil-lations of the water level or if they are due to macropressure eldsresultingfromcoherent owstructuresthat aresensedaslong-wave oscillations by the Fourier-transformed long-term signal ofthe MPPS.Twokinds of noise levels canbe identiedinthe spectra.Although the recording was obtained by applying a low-pass l-ter, highfrequencies still producealiasingnoise. Theresultingpeakscanbeseeninabandof1030Hzinthespectraofthesensors at y=22; 38 mm, where the signal was too small toabsorb these interferences. The second source of noise is the un-avoidablewhitenoise. Inthespectrait canbeidentiedat ap-proximately102Pa2/ Hz. Consequently, aspectral separationof the uctuating pressure signal can be made as follows:p,tot2= p,t2+ p,w2+ N28wherep,tot2denotes thetotal variance; p,t2=part duetoturbu-lence; p,w2=part due to long wave oscillations; and N2=part dueFig. 9. One-sided power spectra for single pressure signals at differ-ent vertical positions#uni6. Theareaunderthecurvesequalsthevariances 2. Line widths from thick to thin correspond toy=+10; +5; 7; 22; 38 mm, indicatingtheuctuatingpart ofthedragandlift as D; L; D; D; D recall Fig. 5. Here, thesensors indicating drag uctuations are vertically aligned; the sensorindicating lift uctuations is atz=80 mm relative to the other sen-sorslightgrayline,seealsoFig.5. Thedashedcurvedenotesthepossible inuence of long waves in the outer ow Eqs. 6 and 7.The vertical line highlights the response time of 10 ms guaranteed bythemanufacturer. Thedottedhorizontallinerefersapproximatelytothewhitenoiselevel. Theinuenceofthelow-passlterwiththecutoff frequency at 500 Hz becomes prominent forf 200 Hz.Fig. 10. Vertical proles of the standard deviation of the drag and lift,D andL, for runs #unii plotted with ks. a Scaled with open-channelow variableo. b Scaled with seepage ow variableghu/ kf. The position of the roughness crest yt=0 is indicated by the horizontal line.Filled symbols refer toD; unlled symbols refer toL. The measured signals are ltered from white noisesee level in Fig. 9.786 / JOURNAL OF HYDRAULIC ENGINEERING ASCE / OCTOBER 2010J. Hydraul. Eng. 2010.136:779-789.Downloaded from ascelibrary.org by INDIAN INST OF TECHNOLOGY - ROORKEE on 08/14/14. Copyright ASCE. For personal use only; all rights reserved.to noise. Since N2is independent of the ow conditions, the mea-sured signals at low turbulence intensities are subjected to a lowsignal-to-noise ratio. Especially for measurements within the bedfor #sphiand #uni3, the signicance ofp,t2andp,w2is low.Thepower spectrainFig. 9givedetailedinsights intothegenesis, damping, anddissipationof pressureuctuationsfor aporous bedunderlyingopenchannel ow. This informationisimportant for the verication of time resolved numerical simula-tionse.g., large eddy simulation.Turbulence Intensity ProlesIn Fig. 10, vertical proles of the standard deviation of the pres-sure uctuations indicating drag and lift, DandL, for all runsof #unii are given. Fig. 10a shows that D and L can be scaledwitho. Theturbulenceintensitiesobtainedatthedifferentowconditions match appropriately in the roughness layer and in theouter ow. However, within the subsurface layer deeper than1ksaconstant nonzerovalueisreachedfor bothDandL.Thus, deeper in the gravel layer the variances are independent ofFig. 11.VerticalprolesofturbulentdragintensitiesD/ oleftcolumnandturbulentliftintensitiesL/ orightcolumnfora#unii;b#rhi9; and c #sphi. The given data points have had removed the contributions from both long-wave oscillations in the seepage ow and whitenoise. The ts of Eqs. 10 and 9 are given by dashed and continuous lines, respectively. Roughness crest and grain diameter d are shown in thebackground. Filledunlled symbols refer toD L. The thinner parallel lines give a vertical range of0.25y/ ks.JOURNAL OF HYDRAULIC ENGINEERING ASCE / OCTOBER 2010 / 787J. Hydraul. Eng. 2010.136:779-789.Downloaded from ascelibrary.org by INDIAN INST OF TECHNOLOGY - ROORKEE on 08/14/14. Copyright ASCE. For personal use only; all rights reserved.the orientation of the pressure pickup. Here, an appropriate scal-ing is performed with respect to seepage ow, as can be seen inFig. 10b. The normalizationwas done usinga seepage owvariableghu/ kf, where1 thehydrostaticpressuretermghincorporates the inuence of large-scale structures that scale withwater depth h e.g., Bakker et al. 1994. However, as h was hardlyvaried in these experiments, the inuence cannot be seen directly.2 The constant kf considers seepage ow. 3 u accounts for theouter ow. uis proportional tothe bulkvelocityandconse-quently also to a convection velocity, providing a further indica-tionthat thelong-waveoscillationsinthesubsurfacelayer aredominated by pressure elds that are convected in the outer ow.TodoaseparateexaminationofDandLforthethreedif-ferent bedmaterials, thevariancesshowninFigs. 11achavehad removed the contribution from the long-wave oscillations inthe seepage ow assumed to be constant, see Fig. 10 and whitenoiseseelevelinFig. 9byapplyingEq. 8.Thus, solelytheturbulent uctuations are considered. At y5 mm marginal dif-ferences are recognized between D and L, which is most likelydue to the effect that the drag-indicating sensors are not protrud-inganymoreout of thegravel crest. Consequently, plotsof Dalso containL below this horizon and vice versa.For all three bed types, an exponential decay within the rough-nesslayerbecomesobvious.Thisndingsubstantiatesthend-ings of Vollmer et al. 2002 and Breugem et al. 2006, where thepressureuctuationswerealsofoundtodecreaseexponentiallyinside the bed. At the interface of the free ow to the porous bed,Breugemet al. 2006 foundvalues p/ o=1.6Re=176, =0.60 andp/ o=3.0Re=500, =0.95, indicatingthat p= fRe. A ReynoldsdependencywasalsoproposedbyFarabeeand Casarella 1991, and a comparable tendency is found in theactual data. Whereas the reference values for #unii scatter aroundD/ o=9andL/ o=3,therespectiveratiosarelargerfor#rhi9and smaller for #sphi. However, the statistical scatter is too largeto allow a detailed analysis of a Reynolds dependency. Therefore,acurvettingonlywas conductedfor thedataof #unii. Thevertical decay ofL could be matched well by an exponential tL/o = 2.88 expyks/2.0 9Incontrast,theverticaldecayofDisnotwelldescribedbyanexponential t. A simple linear description was appliedD/o = 6.89 + 11.84 y/ks10BothrelationsareplottedinFigs. 11ac. Withrespect totheshortcomingsindeningaswellasindetectingtheorigininy,thelinesparallel toEqs. 9 and10 giveavertical rangeof0.25y/ ks. Inprinciple, the shapes of Dand Lappear ad-equatelyapproximatedbyEqs. 9and10, independentofthetype of the analyzed granular bed. After showing the PDF of theextremevaluesandtherelatedfrequencydistributions, Eqs. 9and 10 allowestimating the size of the destabilizing loads.Based on Eqs.9 and10 prediction formulas for sediment en-trainment or washout effectsof nesediment canbeimprovednow.ConclusionsInthisstudy, theturbulent pressureuctuationsleadingtodragandlift forcesat thewater-sediment interfacehavebeendeter-minedexperimentally. Thesmall dimensionaswell asthehighsensitivity and accuracy of MPPSs give a powerful tool to high-light turbulent forces onsinglegrains at river beds. Themainoutcomes are as follows: Vertical prolesofthepressureuctuationsat different owconditionsscaleappropriatelywiththeactual shearstressoand equivalent grain roughness ks. Open-channel ow turbulence strongly inuences the standarddeviationofthepressuresignal, p, aboveandintherough-ness layer, where the lift uctuations decay exponentially withincreasing depth of cover. Withinthesubsurfacelayer, preachesanonzeroconstant,however, mainly dominated by long-wave pressure elds thatare convected in the outer ow.These ndings help to understand the physical processeswithinaporous gravel bed. Theycanbeusedtoimprovetheprediction of sediment entrainment by analytical approaches. Es-peciallytheformulationdescribingthedecayofliftuctuationswithincreasingdepthof cover will behelpful toestimatethewashout effects of ne sediments from the pores of a stable gravellayer.AcknowledgmentsThesupportbytheBaden-WrttembergResearchProgramSe-curing a Sustainable Living Environment BWPLUS Grant No.BWR25003withfundsoftheStateofBaden-Wrttembergisgratefully acknowledged.NotationThe following symbols are used in this paper:a wave amplitude;Bwidth of the ume;Ddrag indicator in units of pressure;d characteristic grain diameter;digrain size quantiles of i%sieve screening;FDdrag force;FLlift force;f frequency;g gravitational acceleration;h water depth;i , j integer numbers or dummy variable;k wave number;kfpermeability coefcient;ksequivalent grain roughness after Nikuradse;Llift indicator in units of pressure;n integer number;p pressure;Qow rate;Rehbulk Reynolds number =Uh/ ;Reboundary layers Reynolds number =u/ ;Sppautospectra ofp;t time;Ubulk velocity =Q/ Bh;u streamwise velocity;ubnear-bed velocity;ushear velocity =o/ 0.5;Vototal volume;Vfvolume of uid;x coordinate in the streamwise ow direction;788 / JOURNAL OF HYDRAULIC ENGINEERING ASCE / OCTOBER 2010J. Hydraul. Eng. 2010.136:779-789.Downloaded from ascelibrary.org by INDIAN INST OF TECHNOLOGY - ROORKEE on 08/14/14. Copyright ASCE. For personal use only; all rights reserved.y vertical coordinate, zero crossing gained byextrapolating the log law;ytvertical coordinate, zero crossing at theroughness tops;z transverse coordinate;empirical constant; channel half-width, here=boundary layerthickness;hlocation of the maximum velocity in distanceto the bed;noncentrality parameter;wavelength;fitt parameter; kinematic viscosity; density of water;sdensity of stone;pstandard deviation of pressure;Dstandard deviation of the drag-indicatingsignal D;Lstandard deviation of the lift indicating signalL;ubstandard deviation of ub;fitt parameter;p,tot2total variance;p,t2part ofp,tot2due to turbulence;p,w2part ofp,tot2due tolong wave oscillations;N2part ofp,tot2due to noise;oboundary shear stress;roughness geometry function=Vf / Vo, with10;. . .temporal average of;. . . spatial average of ;. . . temporal uctuating part of ;. . .maxmaximum of ; andVnabla operator =/ x, / y, / z in 3D.ReferencesAberle, J., and Nikora, V. 2006. 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For personal use only; all rights reserved.