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PHYSICAL AND ECOLOGICAL ASPECTS OF MOBILE SEDIMENTS Effects of biofilm on turbulence characteristics and the transport of fine sediment Wei Cheng 1,2 & Hongwei Fang 1 & Haojie Lai 1 & Lei Huang 1 & Subhasish Dey 3 Received: 6 December 2016 /Accepted: 21 October 2017 /Published online: 10 November 2017 # Springer-Verlag GmbH Germany 2017 Abstract Purpose Biofilm growth changes the sediment properties and the characteristics of the bed, which further influences the interactions between the flow and the sediment bed, such as the turbulence characteristics of the flow and the erosion re- sponse of the sediment to hydrodynamic forces. In this study, the effects of biofilm on the turbulence characteristics of the flow and bio-sediment suspension are investigated. Materials and methods Cohesive sediments were collected from the bottom of the Three Gorges Reservoir, which have a median size of less than 0.1 mm. Flume experiments were conducted for the erosion of the sediment bed with and with- out biofilm under the same flow rate. Acoustic Doppler Velocimetry (ADV) was used to measure the velocities along the depth, based on which the distribution of Reynolds shear stress, time-average velocity, turbulence intensities, turbu- lence kinetic energy flux and budgets, and bursting events of the flow were determined. Meanwhile, the biofilm effects on the physical characteristics of sediments, such as the diameter, density, and falling velocity, were summarized from previous studies. Then, the changes of the vertical distribution of suspended sediment concentration and the near-bed concen- tration were evaluated. Results and discussion After biofilm growth, the time- averaged velocity increases by approximately 6.7% under the low flow rate condition with a flat bed, and by more than 20% under the high flow rate condition with a deformed bed. The vertical distribution of the turbulence intensity becomes more uniform under the high flow rate condition. However, the changes of the turbulence kinetic energy flux and budgets due to biofilm are hardly observed by the scattered measurement data, and more experiments need to be conducted in the future. Conclusions Biofilm exerts an influence on the turbulence characteristics, mostly by affecting the deformation extent of the sediment bed. Meanwhile, the changes of the physical properties of sediments due to biofilm significantly influence the transport of suspended sediment. Keywords Biofilm . Near-bed concentration . Suspended bio-sediment . Turbulence characteristics 1 Introduction With the development of society and industry, more and more waste water, including industrial waste water, domestic sew- age, and rainwater carrying fertilizers from agricultural fields, is discharged into rivers and then accumulates in lakes and reservoirs (Liu et al. 2007; Le et al. 2010; Cao et al. 2011). This substantial amount of waste water provides abundant nutrients for the growth and reproduction of microorganisms, which usually live as biofilms coating the bed surface or per- meating into the bed and binding particles (Headley et al. 1998; Gerbersdorf et al. 2008; Stone et al. 2011). Biofilms growth on the sediment bed change the micro-topography, Responsible editor: Sabine Ulrike Gerbersdorf * Hongwei Fang [email protected] Lei Huang [email protected] 1 State Key Laboratory of Hydro-Science and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China 2 Beijing Engineering Corporation, POWERCHINA, Chaoyang District, Beijing 100024, China 3 Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India J Soils Sediments (2018) 18:30553069 https://doi.org/10.1007/s11368-017-1859-1

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Page 1: Effects of biofilm on turbulence characteristics and …...PHYSICAL AND ECOLOGICAL ASPECTS OF MOBILE SEDIMENTS Effects of biofilm on turbulence characteristics and the transport of

PHYSICAL AND ECOLOGICAL ASPECTS OF MOBILE SEDIMENTS

Effects of biofilm on turbulence characteristics and the transportof fine sediment

Wei Cheng1,2 & Hongwei Fang1 & Haojie Lai1 & Lei Huang1 & Subhasish Dey3

Received: 6 December 2016 /Accepted: 21 October 2017 /Published online: 10 November 2017# Springer-Verlag GmbH Germany 2017

AbstractPurpose Biofilm growth changes the sediment properties andthe characteristics of the bed, which further influences theinteractions between the flow and the sediment bed, such asthe turbulence characteristics of the flow and the erosion re-sponse of the sediment to hydrodynamic forces. In this study,the effects of biofilm on the turbulence characteristics of theflow and bio-sediment suspension are investigated.Materials and methods Cohesive sediments were collectedfrom the bottom of the Three Gorges Reservoir, which havea median size of less than 0.1 mm. Flume experiments wereconducted for the erosion of the sediment bed with and with-out biofilm under the same flow rate. Acoustic DopplerVelocimetry (ADV) was used to measure the velocities alongthe depth, based on which the distribution of Reynolds shearstress, time-average velocity, turbulence intensities, turbu-lence kinetic energy flux and budgets, and bursting events ofthe flow were determined. Meanwhile, the biofilm effects onthe physical characteristics of sediments, such as the diameter,density, and falling velocity, were summarized from previous

studies. Then, the changes of the vertical distribution ofsuspended sediment concentration and the near-bed concen-tration were evaluated.Results and discussion After biofilm growth, the time-averaged velocity increases by approximately 6.7% under thelow flow rate condition with a flat bed, and by more than 20%under the high flow rate condition with a deformed bed. Thevertical distribution of the turbulence intensity becomes moreuniform under the high flow rate condition. However, thechanges of the turbulence kinetic energy flux and budgets dueto biofilm are hardly observed by the scattered measurementdata, and more experiments need to be conducted in the future.Conclusions Biofilm exerts an influence on the turbulencecharacteristics, mostly by affecting the deformation extent ofthe sediment bed. Meanwhile, the changes of the physicalproperties of sediments due to biofilm significantly influencethe transport of suspended sediment.

Keywords Biofilm . Near-bed concentration . Suspendedbio-sediment . Turbulence characteristics

1 Introduction

With the development of society and industry, more and morewaste water, including industrial waste water, domestic sew-age, and rainwater carrying fertilizers from agricultural fields,is discharged into rivers and then accumulates in lakes andreservoirs (Liu et al. 2007; Le et al. 2010; Cao et al. 2011).This substantial amount of waste water provides abundantnutrients for the growth and reproduction of microorganisms,which usually live as biofilms coating the bed surface or per-meating into the bed and binding particles (Headley et al.1998; Gerbersdorf et al. 2008; Stone et al. 2011). Biofilmsgrowth on the sediment bed change the micro-topography,

Responsible editor: Sabine Ulrike Gerbersdorf

* Hongwei [email protected]

Lei [email protected]

1 State Key Laboratory of Hydro-Science and Engineering,Department of Hydraulic Engineering, Tsinghua University,Beijing 100084, China

2 Beijing Engineering Corporation, POWERCHINA, ChaoyangDistrict, Beijing 100024, China

3 Department of Civil Engineering, Indian Institute of TechnologyKharagpur, Kharagpur, West Bengal 721302, India

J Soils Sediments (2018) 18:3055–3069https://doi.org/10.1007/s11368-017-1859-1

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sediment properties, and the interparticle forces (Grabowskiet al. 2011), subsequently changing the erosion response ofsediment to the flow, as well as the bedform and sedimenttransport (Gerbersdorf and Wieprecht 2015). The turbulencecharacteristics of flow after biofilm growth are different fromthose corresponding to sediment bed without biofilm, whichaffects the mass exchange at the sediment-water interface andinfluences the ecosystem significantly (Graba et al. 2010;More et al. 2014).

At present, most studies that analyzing the biofilm ef-fects on turbulence characteristics are performed in openchannels with rough beds which consist of coarse non-cohesive sediments, gravels or artificial roughness, andfocus on the interaction between the flow and biofilm inthe benthic zone. It is concluded that the presence, age,and structure of biofilm are important factors influencingthe local hydrodynamic characteristics, such as the fric-tion velocity, equivalent roughness, turbulence shearstress, and turbulence intensity (Moulin et al. 2008;Graba et al. 2010). The measurements by Laser DopplerVelocimetry (LDV) or Particle Image Velocimetry (PIV)generally show an acceleration of longitudinal mean ve-locity in the upper half-part of flow and a decrease ofvelocity near the bottom after biofilm growth. The pres-ence of biofilm shifts the origin of the sediment bed up-wards; thus, the position of the first measured value abovethe biofilm is also shifted vertically. The changes ofboundary layer parameters derived from logarithmic pro-files, however, are not consistent in different studies.Some studies find that the friction velocity derived fromthe turbulence quantities increases with the biofilmgrowth, leading to an increase of the roughness length(Nikora et al. 1997; Labiod et al. 2007). In contrast, adecrease in the friction velocity and equivalent roughnessis observed by some other studies (Moulin et al. 2008;Graba et al. 2010; Vignaga 2012). These contradictoryresults are induced by the different growth patterns ofbiofilm under different hydrodynamic conditions(Moulin et al. 2008) and the methods used to interpretthe biofilm thickness (Godillot et al. 2001). Nikora et al.(2002) investigated the changes of turbulence characteris-tics due to biofilm using Acoustic Doppler Velocimetry(ADV). Results show that in the interfacial sublayer(i.e., under the top of the bed roughness), the biofilmgrowth suppresses the mean velocity, turbulence shearstress, turbulence intensities, and vertical turbulence ener-gy flux. The penetration of large-scale eddies from theouter flow to the interfacial sublayer is weakened afterbiofilm growth, which would change the sweep eventsand influence the mass transfer from the flow to the sed-iment bed.

These studies reveal the complexity of the mutual interac-tions between the flow and biofilm when the bed is fixed.

Many studies have also been conducted to investigate theeffects of biofilm on the sediment motion. It is revealed thatthe sediment stability is enhanced due to biofilm growth thusincreasing the incipient velocity of sediments (Paterson 1989;Righetti and Lucarelli 2007; Gerbersdorf et al. 2008; Fanget al. 2014). The presence of biofilm would cause one orderdecrease of the sediment transport rate in the surface biofilmlayer (Watanabe et al. 2008; Stone et al. 2011). Moreover, theerosionmode of the sediment bed is also significantly changed(Hagadorn and Mcdowell 2012; Thom et al. 2015), and thebedform dimensions of fine sediment bed are reduced com-paring to the sediment bed without biofilm under the sameflow conditions (Malarkey et al. 2015; Parsons et al. 2016).Furthermore, some experiments have been performed to in-vestigate the settlement of river sediment influenced by bio-film, trying to establish a general method for calculating thebed load and suspended load transport rate of bio-sediment(Shang et al. 2014; Fang et al. 2016).

However, few attention are paid to the biofilm-inducedchanges of turbulence characteristics on fine sediment bedand their subsequent effects on the suspended sediment trans-port. Therefore, the objectives of the present study are to re-veal (1) the change of turbulence characteristics caused bybiofilm growth on the cohesive sediment bed and (2) the re-sultant change of sediment transport properties such as thesuspended sediment distribution and the sediment entrainmentflux.

2 Experiment setup and procedure

The experiment was conducted using a circulated flume of theState Key Lab of Hydro-Science and Engineering at TsinghuaUniversity. The flume was 16 m long, 0.5 m wide, and 0.5 mhigh, as shown in Fig. 1, with the side walls and bottomconsisted of plexiglass and ceramic tiles, respectively. Thewater was circulated within the flume by a pump system,and the discharge could be measured by an electromagneticflowmeter. The flow was controlled by the flume slope thatcan be adjusted by a lifted device and the tailgate to be uni-form or quasi-uniform, and stabilizing equipment was alsoplaced at the entrance of the flume. A recess, which was0.5 m long, 0.5 m wide, and 2 cm deep, was located at10.05 m from the entrance to place the sediment.

Sediments used in the experiment were collected from thebottom of Three Gorges Reservoir (TGR), which were firstlyfiltered by the sieve with a pore size of 1.0 mm and thenwashed by the deionized water to remove the impurities.Thus, these sediment samples were regarded as clean sedi-ment. The median size d50 of the sediment sample was0.065 mm, with a clay content of 4.7% and a sorting coeffi-cient φ [=(d75/d25)

0.5] of 1.75. Before the biofilm formation,the sediment sample was first mixed with clear water and

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settled for 12 h. Afterwards, the saturated sediments weredeposited in the recess and scraped flat at the bed surface level.Two blocks were then placed and sealed in the flume near therecess, and natural water from the pond at TsinghuaUniversity was added to a depth of 10 cm for the colonizationof microorganisms. Nutrients were also added into the exper-imental water as Zhao et al. (2011) and Fang et al. (2014) toensure a relatively high trophic level, which included not onlythe necessary C, N, P, and S sources but also sufficient traceelements such as Na, Mg, Ca, and Si. The temperature wasapproximately 20 °C during the biofilm formation, and a halfof experimental water was refreshed every day. Sunlight pen-etrated through the lab windows with no special treatment;thus, the light intensity was relatively weak during the day-time. Previous observations have showed that the microorgan-isms would colonize on the sediment bed in 3 days, and thebiomass increased rapidly over 10 days, especially in the first5 days (Fang et al. 2015).

After 10 days of biofilm formation, the experimental waterwas drained and the blocks were removed. Clear water wasthen added to the flume and the flow discharge was increasedgradually by controlling the output power of the pump. Theflow conditions in the experiment are presented in Table 1.The low flow rate condition, corresponding to a flat bed, isselected to investigate the direct effect of biofilm on turbu-lence characteristics (i.e., affecting the micro-morphology ofbed surface), while the high flow rate condition is designed toestimate the indirect effect of biofilm (i.e., affecting the for-mation of bedform). The specific values of the flow discharge

were firstly determined by the Shields curve presented byFang et al. (2014, 2016, 2017) and then adjusted by observa-tions in a series of testing experiments. The water depth alongthe flume was measured by point gauges, and the velocity wasmeasured by Sontek MicroADV (16 MHz) vertically in thecenterline of the testing area, as shown in Fig. 2. Themeasuredline was 30 cm away from the start of the sediment bed in thehorizontal direction. The interval of the adjacent measuredpoints increased with the increasing distance from the bed inthe vertical direction, i.e., the interval ranged from 2 to 5 mmwhen the distance was less than 0.2 h, and above that it rangedfrom 5 to 10 mm. The number of measured points dependedon the flow depth in the experiment, and the measurementtime for each point lasted for 3~4 min, which referred to thetime applied by Nikora et al. (2002). As the sampling volumeof ADV is 5 cm below the probe, the points within 5 cm awayfrom the water surface were not measured. The softwareHorizonADV was used to collect and review the data with asampling frequency of 50 Hz. Then, the measured data werefiltered by an acceleration threshold algorithm to obtain thefluctuating velocities (Goring and Nikora 2002; Dey and Das2012).

After the velocity measurements, the flow was stoppedgradually and the bed topography was then measured by theADV with an error margin of 0.1 mm. Moreover, the flowcharacteristics of the sediment bed without biofilm were alsomeasured for comparison. The corresponding discharges andwater depths are also presented in Table 1, i.e., the same flowconditions with the experiments of sediment bed with biofilm.

Fig. 1 The profile of the experimental flume

Table 1 Flow parameters of four experiments with variable dischargeQ and biofilm (B with biofilm, P without biofilm). h represents the water depth,u*s is the friction velocity derived from energy slope, u*τ is the friction velocity derived from distribution of the Reynolds shear stress,Δz is the depth ofvirtual bed from the measured point, and z0 is the roughness length

Test no. Q/m3 h−1 h/cm u*s/cm s−1 u*τ/cm s−1 Δz/cm z0 (× 10−3)/cm

P-1 69.0 15.25 1.28 1.28 0.055 0.70

P-2 136.0 13.63 2.90 2.78 0.407 1.70

B-1 69.0 15.03 1.25 1.27 0.006 0.45

B-2 136.0 13.62 2.99 2.60 0.162 0.45

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3 Results

3.1 Reynolds shear stress distribution

Figure 3a presents the vertical distributions of the non-dimensional Reynolds shear stress (RSS) τ zð Þ for the sedi-ment bed with and without biofilm under different flow dis-

charges. The RSS τ(¼ ‐ρu0w0 ) is scaled by the bed shear stressτ0(¼ ρu2* ), and the vertical distance z is scaled by the flowdepth h, i.e., τ = τ/τ0and z = z/h. For the two-dimensional openchannel flow, the vertical distribution of RSS follows a linearlaw, i.e., τ ¼ 1−z, out of the viscosity affected layer near thewall (Nezu and Nakagawa 1993; Dey et al. 2012). As the two-dimensional flow is driven by gravity, the linear distribution isalso called gravity line, see Fig. 3a. Based on the verticaldistribution of RSS, the shear stress of flow exerting on thebed τ0 can be obtained by extending the linear fitted line to thebed with data between the inflection point and free surfaceFig. 2 Sketch of the measurement settings in the experiment

Fig. 3 Vertical distributions ofnon-dimensional RSS τ (a), time-averaged velocities (b), and tur-bulence intensities (c) for the bedwith (triangle) and without(quadrate) biofilm under the low-er and higher discharge

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layer (z/h < 0.6). The corresponding shear velocity u*τ (=ffiffiffiffiffiffiffiffiffiffiτ0=ρ

p) for different cases are shown in Table 1.

It can be observed that the RSS follows a linear distributionin the case of a lower flow discharge, but a slight deviationfrom the gravity line when z > 0:1 due to the non-uniformityof the flow. In the case of a higher flow discharge, the datacollapse to the gravity line when z > 0:1. Comparing the dis-tribution of non-dimenional RSS on sediment beds with andwithout biofilm, it can be found that there is no significantchange under the same flow discharge, which reflects thatthe biofilm effect on the RSS distribution is negligible.However, the magnitude of RSS near the bed (representedby u*τ) is changed after biofilm growth, especially in the caseof a higher flow discharge with a variation of about 6.5%, asshown in Table 1.

3.2 Time-averaged velocity distribution

Figure 3b shows the vertical distribution of non-dimensionaltime-averaged longitudinal velocity for the sediment bed withand without biofilm under these two levels of flow discharge.The time-averaged velocity u is scaled by the friction velocityu* (= u*τ), and the distance from the virtual bed level z +Δz isscaled by the water depth h, i.e., here, z ¼ zþΔzð Þ =h. It isobserved that the mean flow velocity for the bed with biofilmare larger than that without biofilm irrespective of the flowdischarge, i.e., the presence of biofilm would increase themean velocity. However, the increments of the mean velocityare especially different under different flow conditions, whichare approximately 6.7 and 26% under the low and high flowrate conditions, respectively, in the wall region.

In general, the logarithmic law for the mean longitudinalvelocities u is valid in the wall region where (z +Δz)/h < 0.2,i.e.,

uu*

¼ 1

κln

zþΔzz0

� �ð1Þ

where κ is the von Kármán coefficient, Δz is the depth ofvirtual bed from the bed surface, and z0 is the zero-velocitylevel or the roughness length. Previous studies show that κvaries with the sediment transport (Chien and Wan 1999;Nikora and Goring 2000; Dey et al. 2012). However, the sed-iment transport is very weak in the present study, thus κ isassumed to be equal to the value in clear flow, i.e., 0.41 (Nezuand Rodi 1986). The estimated values of the parameters in Eq.(1) are shown in Table 1, indicating that both Δz and theroughness length z0 decrease with the presence of biofilmunder the same flow rate. Under the low flow rate condition,Δz decreases by 11% of the magnitude compared to the cleansediment bed and z0 decreases by 36%. Meanwhile, under thehigh flow rate condition,Δz and z0 decreases by 60 and 74%,respectively. Nevertheless, the magnitude of the parameters is

in a small order,thus, the presence of biofilm plays a role in asmall scale.

3.3 Turbulence intensity distribution

Figure 3c presents the vertical distributions of the relativeturbulence intensities σu zð Þh i and σw zð Þh i for all cases.

The turbulence intensities σu(¼ffiffiffiffiffiffiu02

q) andσw(¼

ffiffiffiffiffiffiffiw02

q)

are also scaled by the friction velocity u* (=u*τ) and z =(z +Δz)/h. Results show that the turbulence intensity inthe longitudinal direction ⟨σu⟩ decreases as the distance tothe bed z increases, and the vertical component ⟨σw⟩ alsodecreases with the increasing z in the upper flow layerwhile increases in the region of z < 0:1 with the maxi-mum value of approximately 0.86 at z = 0.1. These resultsare consistent with previous studies on the flow oversmooth and rough beds (Nezu and Rodi 1986; Kironotoand Graf 1994; Song and Chiew 2001). The empiricalformula for the distribution of turbulence intensity sug-gested by Nezu and Rodi (1986) is also plotted in Fig.3c, i.e.,

σuh i ¼ffiffiffiffiffiffiu02

qu*

¼ 2:26exp −0:88zð Þ ð2Þ

σwh i ¼ffiffiffiffiffiffiffiw02

qu*

¼ 1:23exp −0:67zð Þ ð3Þ

Comparing the turbulence intensities above the sedimentbedwith and without biofilm, no significant differences can befound under the low flow rate condition. In the case of highflow rate, however, the vertical component of turbulence in-tensity ⟨σw⟩ decreases in the wall region of z < 0.2 due to thepresence of biofilm, and it is more uniformly distributed in thevertical direction. The maximum reduction is approximately18% near z = 0.1. In contrast, the distribution of the longitu-dinal component ⟨σu⟩ does not change significantly after bio-film growth, and there is only a slight reduction near the bed.Therefore, biofilm growth mainly affects the vertical compo-nent of turbulence intensity.

3.4 Turbulence kinetic energy (TKE) flux and budgetdistributions

The vertical distributions of the non-dimensional turbulence

kinetic energy flux (TKE flux), i.e., Fku ¼ f ku=u3* (where f ku

¼ 0:5 u0u0u0 þ u0w0w0� �

) and Fkw ¼ f kw=u3* (where f ku ¼ 0

:5 u0w0w0 þ w0w0w0� �

) for the longitudinal and vertical com-

ponents, are shown in Fig. 4. Under the low flow rate condi-tion, the Fku starts with a small positive value for the sediment

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bed without biofilm, i.e., Fku(z =0.04) ≈ 0.16, which decreaseswith the increasing z and changes the sign at z ≈ 0.05. Thevalue of Fku further decreases with the increasing z until z ≈0.2, where Fku ≈ −1.37, and then turns to increase with afurther increase of z. Dey et al. (2012) noted that a positiveFku implies a streamwise transport of TKE flux, while a neg-ative value indicates that the TKE flux transports against thestreamwise direction. The vertical TKE flux Fkw begins with asmall positive value and increases with the increasing z until z≈ 0.2, where Fkw ≈ 0.42, and then turns to decrease slightly asz further increases. It is observed that Fkw remains positivethroughout the water depth, indicating an upward transportof the TKE flux. Furthermore, no regular difference on thevertical distribution of TKE flux can be observed for sedimentbed with and without biofilm.

Under the high flow rate condition, however, the verticaldistributions of TKE flux are different from those under thelow flow condition. The Fku starts with a positive value anddecreases with an increase in z, which changes the sign at z ≈0.1. The negative magnitude of Fku increases with z up to z ≈0.2 and then decrease until z ≈ 0.4. Finally, Fku remains neg-ative with a small magnitude in the flow layer of z > 0.4. Incontrast, the Fkw starts with a negative value and increaseswith the increasing z, which also changes the sign at z ≈ 0.1.In the upper flow layer of z > 0.1, Fkw is positive and increaseswith z up to z ≈ 0.2, while decreases with a further increase in zuntil z ≈ 0.4. Then, Fkw retains a small positive value in theflow layer of z > 0.4. Overall, few differences between thevertical distribution of TKE flux for sediment beds with andwithout biofilm are observed by these scattered measurement

data. However, as the friction velocity on the bio-sedimentbed is 6.5% less than that without biofilm, the TKE flux com-ponents in the longitudinal and vertical directions decreasedue to biofilm growth.

The TKE budget for a uniform open-channel flow is givenas follows (Nezu and Nakagawa 1993):

where Tp is the TKE production rate, ε is the TKE dissipationrate, TD is the TKE-diffusion rate, PD is the pressure energydiffusion rate, and vD is the viscous diffusion rate. p′ is thepressure fluctuations and k is the TKE defined as

0:5 u02 þ w02� �

. The viscous diffusion rate νD is relatively

small and negligible in the present study. The TKE dissipationrate ε is calculated using Kolmogorov’s second hypothesis, andthe details are described in Dey et al. (2012). Then, the pressureenergy diffusion rate PD can be calculated from Eq. (4) asPD = TP – ε –TD. The parameters Tp, ε, TD, and PD are scaled

by h=u3* to be non-dimensional values as T p, ED, TD, and PD.The vertical distributions of the TKE budget components reflectthe TKE production and transfer of the turbulence.

Figure 5 shows the vertical distribution of TKE budgetcomponents under the low flow rate. The TKE production

rate T p corresponds to the conversion of energy from thetime-averaged flow to the turbulence, which presents near-bed amplification and decreases with the increasing z.

Fig. 4 Vertical distributions ofnon-dimensional TKE flux com-ponents (Fku and Fkw) for the bedwith (triangle) and without(quadrate) biofilm under the low-er and higher discharge

(4)

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Negative values of T p are observed at some points, implyingan inverse conversion of energy due to the flow fluctuation.

The dissipation rate ED also decreases with z in a similar way

to the variation of T p. It can be observed that ED is almost

equal to the T p in the wall region, implying that most of theturbulence kinetic energy dissipates locally. In the upper flowlayer of z > 0.2, however, the TKE production rate is less thanthe dissipation rate, revealing that the TKE has been

transported or produced in other ways. The variation of TD

with z is scattered in the near-bed region (z < 0.3), and bothnegative and positive values can be observed. However, itbecomes almost zero in the upper flow layer, i.e., invariant

with z. The PD decreases with z in the negative magnitude,while the values are also scattered and some positive values

can be observed. The negative values of TD and PD suggest again in turbulence production, which balances the TKE pro-

duction rate T p and the TKE dissipation rate ED. It is also

observed that there are little differences between the distribu-tions of TKE budget components for the sediment bed withand without biofilm. Therefore, the biofilm effect on the TKEbudgets is negligible under the low flow discharge.

Figure 6 illustrates the vertical distribution of TKE budgetcomponents under the high flow rate condition. The variations

of T p, ED, and TD with z are similar to those under the low

flow rate condition, while the PD inverts and becomes almostzero in the flow layer of z > 0.3. In the wall region, the TKE

dissipation rates ED are much smaller than the production rate

T p, and the maximum of T p is approximately 3.5 times of ED,which implies that most of TKE are transferred by turbulencekinetic or pressure diffusion to the upper or lower flow layer.

However, T p is almost equal to ED in the upper flow layer of z> 0.3. Similar to the low flow rate condition, regular changes

of the TKE production rate T p, diffusion rate TD and pressure

energy diffusion rate PD due to biofilm are hardly observed bythese scattered measured data. However, the change of the

dissipation rate ED is relatively significant, which decreasesby approximately 12% in the near-bed region of z < 0.3, asshown in Fig. 6b.

3.5 Conditional RSS distributions

Bursting events caused by the motion of coherent eddiesare categorized by the conditional RSS production, andthey are the governing mechanisms for the production ofReynolds shear stress, determining the momentum andenergy transfer between the near-bed region and the out-er flow (Nikora and Goring 2000), and hence determin-ing the mass transport in the flow such as the sedimententrainment and bedload transport (Dey et al. 2011,2012). The characteristics of bursting events can be de-tected by the quadrant analysis for the velocity fluctua-tions u′ and w′ (Lu and Willmarth 1973), and four typesof events are identified: (i) outward interactions E1:i = 1, u′ > 0, w′ > 0; (ii) ejection E2: i = 2, u′ < 0, w′ > 0;(iii) inward interactions E3: i = 3,u′ < 0, w′ < 0; and (iv)

Fig. 5 Vertical distributions of

TKE budget components [TP (a),ED (b), TD (c), and PD (d)] for thebed with (triangle) and without(quadrate) biofilm under the low-er flow discharge

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sweep E4: i = 4, u′ > 0, w′ < 0. The fractional contributionfrom the event Ei (i = 1, 2, 3, or 4) towards the RSSproduction is given by

Si;H zð Þ ¼ 1

u0w0⋅ limT→∞

1

T∫T0 u

0tð Þw0

tð Þλi;H z; tð Þdt ð5Þ

where T is the sampling duration, t is the time, λi,H(t) isthe detecting function, and λi,H(t) = 1 if the (u′, w′) pair isin quadrant i with |u′w′| ≥Hσu ⋅ σw; otherwise, λi,H(t) = 0.Here, H is the hole size, which draws a clear distinctionbetween the strong events outside the hole and the weakones inside it. The changes in the fractional contributionsof bursting events towards the RSS reflect the biofilmeffects on the turbulence structure. Here, the data ofSi,H(z ) with H = 0 are plotted in Fig. 7.

Under the low flow rate condition, for the sediment bedwithout biofilm, E2 and E4 events contribute approximately65 and 63% to the total RSS production at the nearest point tothe bed, respectively, and the fractional contributions of E2events increasingly exceed those of E4 events with the increas-ing z. This implies that the high speed fluid parcel from theupper flow region revokes the arrival of the low speed parcelfrom the near bed zone. On the other hand, E1 events contributeminimally to the total RSS production, i.e., 13% near the bed,while the contributions of E3 events exceed it slightly with apercent of 15%. The vertical distribution of the contributions ofE1 events is almost the same as that of E3 events, and thevariation amplitude is especially small from the bed to the upper

flow layer (i.e., less than 10%). Overall, the biofilm effect onthe fractional contributions of the bursting events is not appar-ent for the flat bed. For the sediment with biofilm, at the nearestpoint to the bed, E2 and E4 events contribute approximately 68and 62%, respectively, which are almost the same as those forthe sediment bed without biofilm. The contributions of the E1and E3 events almost remain constant in the vertical direction,i.e., approximately 15 and 16%, respectively.

Under the high flow rate condition, for the sediment bedwithout biofilm, the contributions of E4 events exceed thoseof E2 events in the near bed region of z ≤ 0.1, which contribute67 and 64% to the total RSS production at the point nearest tothe bed, respectively. This may be due to the bed erosion,which causes roughness with a scale larger than the particlesand also weak sediment transport on the bed (Nikora andGoring 2000; Dey et al. 2012). In the upper flow layer of z> 0.1, however, the contributions of E2 become larger thanthose of E4 events and the difference increases with the in-creasing z. E1 events still provide minimal contributions andthe contributions of E3 events are almost the same as E1events, i.e., approximately 15% throughout the water depth.The changes in the fractional contributions of the burstingevents are apparent in the presence of biofilm. It can be ob-served that in the near-bed zone of z ≤ 0.1, the contributions ofE4 events are almost the same as those of E2 events, whichincrease to 74 and 71% at the nearest point to the bed, respec-tively, compared to the sediment bed without biofilm.Meanwhile, the contributions of E1 and E3 events also in-crease to 21 and 24%, respectively. The contributions of E2

Fig. 6 Vertical distributions of

TKE budget components [TP (a),ED (b), TD (c), and PD (d)] for thebed with (triangle) and without(quadrate) biofilm under thehigher flow discharge

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and E4 events decrease, however, compared to the contribu-tions of the clean sediment bed at the same relative position,suggesting that the influence of the sweep and ejection eventsis relatively weaker for the sediment bed with biofilm. Manyresearchers have found that the E4 events are the governingmechanisms for sediment transport (Nikora and Goring 2000;Dey et al. 2011, 2012). Therefore, the biofilm growth on thesediment bed would change the bursting events, which in-hibits the sediment motion and increases the bed stability.

3.6 Bed morphology

As mentioned in the introduction, the presence of biofilm onthe sediment bed not only influences the flow properties, butalso influences the bed morphology. Figure 8 shows the bedmorphology in these four experiments. It is observed that thebed surface under the low flow discharge is almost flat, as theshear stress exerting on the bed is smaller than the criticalvalue of sediment incipient. However, under the high flowrate condition, the sediment beds with and without biofilmare both eroded. The average erosion depth for the clean sed-iment bed is about 6 mm, while it is about 2.5 mm for the bio-sediment bed.

4 Discussion

4.1 Biofilm effects on the hydrodynamics

In the preceding sections, the hydrodynamic characteristics onsediment beds with and without biofilm are compared. It is

noted that the biofilm affects the turbulence characteristics bychanging the boundary condition in two ways: one is chang-ing the interaction between the flow and sediment throughcovering the bed surface under the lower flow discharge,and the other is changing the bedform characteristics and thesediment transport under the higher flow discharge.

Under the lower flow discharge, the bed is almost flat andthe turbulence characteristics including the vertical distribu-tions of RSS, relative turbulent intensity, TKE flux, TKE bud-get components, and bursting events are almost not changed.However, the change of the time-averaged velocity is visible,and the variations of roughness length and virtual bed heightare observed in a millimeter scale, indicating that the presenceof biofilm on the fixed sediment bed reduces the bedresistance. Nikora et al. (1997, 2002) concluded that the bio-film growing on the gravel bed increases the roughness lengthas well as the resistance to the flow. However, some otherstudies, which are also performed on rough beds consistingof gravels, cobbles, and artificial roughness elements, showthat the presence of biofilm decreases the roughness lengthand bed resistance (Labiod et al. 2007; Graba et al. 2010).Moreover, it is also stated that the structures of biofilm, suchas the compactness and the size of filaments, play an impor-tant role on changing the hydrodynamic parameters (Moulinet al. 2008). In the present study, it is observed that the biofilmcovering the sediment bed is in a millimeter scale which bindstightly with the sediment. Thus, the direct disturbance on theflow is quite limited and the turbulence characteristics arehardly changed.

Under the higher flow discharge, the changes of bed mor-phology due to biofilm growth are significant, indicating that

Fig. 7 Vertical distributions ofSi,0 for the bed without (a, c) andwith (b, d) biofilm under thelower and higher flow discharge

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the biofilm has a great impact on the bed stability that reducesthe erodibility of sediment. Moreover, the changes on theRSS, time-averaged velocity, roughness length, turbulent in-tensity, and even bursting events are larger than those of theflow over the flat bed, implying that the indirect impact ofbiofilm on the turbulence characteristics through changingthe bedform is greater than its direct influence through cover-ing the sediment bed. Unfortunately, due to the limited accu-racy of experimental data, no statistical results can be obtainedfor the changes of TKE flux and TKE budget components inthe near bed region, and further studies are still needed.

It should be noted that the turbulence characteristics of flowon the mobile bed is quite different from that on the fixed bed inthe near bed region (Dey et al. 2012), such as the excessivedamping effect of RSS, the reduction of flow resistance, andthe changes of the positive and negative sign of TKE flux. Inthis study, sediment transport occurs under the higher flow dis-charge. However, the vertical distribution of the non-dimensional RSS shows no excessive damping effect, indicat-ing a weak sediment transport in the near bed region.Nevertheless, the biofilm effect on the erosion mode and trans-port characteristics of sediment is prominent in the experiment,which will be further discussed in the following section.

4.2 Biofilm effects on the sediment transport

4.2.1 Suspended bio-sediment distribution

Previous studies show that the biofilm growing on the substrateis consisted of bio-particles with the diameters 100 to 200 times

larger than the original particles (Nicolella et al. 1999; Andalibet al. 2010; Shang et al. 2014), and the increment of particle sizeis inversely proportional to the original diameter. Shang et al.(2014) proposed an empirical relationship between the diame-ters of clean sediment and bio-sediment particles (or flocs)based on the biofilm cultivation experiments using sedimentwith diameters of 0.01~2 mm as the substrate, i.e.,

d f ¼ d0 1þ adm0

� �ð6Þ

where df and d0 are the diameters of the bio-particle and theoriginal sediment particle, respectively, with the unit of milli-meters and the values of the parameters a and m are 0.6 and1.21, respectively.

Furthermore, based on the experimental results of bio-sediment settling, Shang et al. (2014) obtained a relationshipbetween the resistance coefficient CDf and particle Reynoldsnumber Re* for bio-sediment, expressed as

CDf ¼ 63:36Re−0:754*

Re* ¼ ω f ⋅d f

ν

ð7Þ

Substituting Eq. (6) and Eq. (7) into Eq. (8), i.e., the forcebalance equation for the falling particles or aggregates, thetheoretical expression of the falling velocity ωf for bio-sediment is then obtained as Eq. (9):

π6

ρ f −ρ� �

gd3f −CDfπd2f4

ρω2f

2¼ 0 ð8Þ

Fig. 8 Topography of the bed with clean sediment (a, c) and bio-sediment (b, d) under the lower (a, b) and higher discharge (c, d)

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ω f ¼ 0:021 ρ f =ρ−1� �

gd fd f

ν

� �0:754" #1=1:246

ð9Þ

where ρf is the density of bio-sediment, and here, it takes thevalue of 1100 kg/m3; ρ is the density of the water and ν is theviscosity coefficient (=1.0 × 10−6 m2/s).

Table 2 presents the falling velocities of the sediment par-ticles with three different diameters, i.e., d30, d50, and d90,which are selected according to the particle size distributionof the applied sediment sample. The Zhang Ruijin method isused to calculate the falling velocity of the clean sediment(Fang and Wang 2000), i.e.,

ω0 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi13:95

νd0

� �2

þ 1:09⋅sgd0

s−13:95

νd0

ð10Þ

where s = ρs/ρ-1, and ρs is the density of the clean sedimentparticle; g is the gravity acceleration (= 9.81 m/s2).

It can be observed from Table 2 that the falling velocity ofbio-sediment is an order of magnitude larger than that of cleansediment, and the finer the clean particle is, the greater thechange is. Therefore, under the same flow condition (i.e., thesame bed shear stress), the suspension index β = ω/κu∗ of thebio-sediment is much larger than that of clean sediment. Thesuspension indices β and βf for clean and bio-sediment withu* = 2.60 cm/s are presented in Table 2, which shows that theβf is 3 to 10 times larger than β. Generally, the vertical distri-bution of the relative suspended sediment concentration isdescribed by the Rouse formula derived from the turbulencediffusion theory of fluid parcels, which is written as (Celik andRodi 1988):

SSb

¼ h=z−1h=a−1

� �ω=κu* ð11Þ

where Sb is the reference concentration near the bed and a isthe corresponding position that is usually set as 0.05 h.Figure 9a shows the distribution of the relative suspendedsediment concentration for clean and bio-sediment using theparameters in Table 2. Apparent changes in the sediment dis-tribution are observed, and the biofilm growth causes the sed-iment concentrating towards the bottom. In the zone of z/

h < 0.4, the bio-sediment concentration decreases drasticallywith the increasing z/h, with an especially small concentrationin the upper layer.

As stated in Section 3, biofilm growth would change theflow resistance of the eroded bed under the high flow ratecondition. Thus, besides the falling velocity, the change offriction velocity u* also influences the sediment suspension.Table 3 gives the suspension index for the clean and bio-sediment with d0 = 0.065 mm, corresponding to the flowconditions in Table 1. The vertical distributions of the relativesuspended sediment concentration are plotted in Fig. 9b, and itcan be found that the variation of friction velocity also chang-es the distribution of suspended sediment concentration.Considering the clean sediment, the relative sediment concen-tration decreases approximately 5.7% with a decrease in u* atthe point of z/h = 0.4. For the bio-sediment, however, therelative concentration decreases approximately 25.7% at thesame relative height, which is much greater than that of cleansediment, suggesting that the distribution of suspended bio-sediment is more sensitive to the variation of flow conditioncompared to the clean sediment.

According to Eq. (11), the reference concentration near thebed Sb is a critical factor determining the magnitude ofsuspended sediment concentration, which is generallyregarded as the turbulence flow capacity of the sediment anddetermined by both the flow and sediment characteristics. Asthe physical characteristics of the bio-sediment are quite dif-ferent from that of clean sediment, the Sb of the bio-sedimentshould also be changed. Fang et al. (2016) adapted van Rijn’smethod (1984) to study the near-bed sediment concentrationfor bio-sediment and proposed a new formula, i.e.,

SbB ¼ 0:0363d f

aT1:5d0:2f * ð12Þ

where T [=Θ/Θc − 1] is the transport stage of the flow,Θ is theShield parameter given by u2*=sgd0, and Θc is the criticalShields parameter for sediment entrainment or movement.Here, df∗ = df(s

′g/ν2)1/3, and s′ = ρf/ρ − 1. Figure 10 shows theShields curve for the clean and bio-sediment with d∗ = d0(sg/ν2)1/3.

The method proposed by van Rijn (1984) to calculate thenear-bed concentration of the clean sediment is given by

Sb ¼ 0:015d50a

T1:5

d0:3*

ð13Þ

The vertical distribution of the suspended bio-sedimentconcentration can be obtained by employing Eqs. (6), (9),(11), and (12), and that of the clean sediment by Eqs. (10),(11), and (13), which are plotted in Fig. 11. Compared to thedistribution of clean sediment concentration, the bio-sedimentconcentration is much larger in the near-bed zone of z/h ≤ 0.2,and the concentration in the upper layer decreases more

Table 2 Falling parameters for the clean and bio-sediment particles. d0,ω0, and β represent the diameter, falling velocity, and suspended index forclean sediment, respectively, df, ωf, and βf represent that of the bio-sediment

d0/mm df/mm ωf/m s−1 ω0/m s−1 βf β

0.043 1.20 0.0148 0.00117 1.419 0.112

0.065 1.13 0.0135 0.00266 1.297 0.255

0.086 1.09 0.0128 0.00461 1.233 0.443

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sharply with the increasing z/h. At the reference height nearthe bed, the concentration of the bio-sediment is approximate-ly seven times as large as that of clean sediment, and a largeroriginal particle size d0 corresponds to a greater increment ofthe concentration. In the upper flow layer of z/h > 0.4, how-ever, the bio-sediment concentration is smaller than that ofclean sediment. These differences will influence the transportrate of suspended sediment significantly.

4.2.2 Entrainment flux of bio-sediment

Cao (1997) proposed an entrainment function based on thecharacteristics of the turbulence bursting events, i.e.,

En ¼ P⋅d1:50 Θ=Θc−1ð ÞΘ ð14Þ

P ¼ λ⋅C0⋅ s⋅gð Þ0:5ν⋅Tþ

Bð15Þ

where λ is the average area of all bursts per unit bed area,here given the value of 0.02; C0 is the volumetric concen-tration of sediment, and the most dense packing of whichis 0.6; Tþ

B is the non-dimensional period of the burstevents equaling to 100. Equation (14) implies that theentrainment flux En is determined by both the particle sizeand the stream power P, and there is a greater entrainmentflux for larger particles under the same flow condition.Considering the changes in the physical characteristicsof sediment due to biofilm growth, including the diameter

and density, the non-dimensional entrainment flux can bewritten as

E0n ¼ P

0⋅d f ⋅d0:50 ⋅ Θ=Θ

0c−1

� �Θ ð16Þ

P0 ¼ λ⋅C0⋅ s⋅gð Þ0:5

ν⋅TþB

ρ f

ρsð17Þ

where Θ0c is the critical Shields parameter for bio-sediment.

Figure 12 shows the entrainment flux of the clean and bio-sediment under different flow conditions (i.e., different flowShields parameter Θ). It can be observed that the entrainmentflux of the bio-sediment is less than that of clean sedimentwhen the flow Shields parameter Θ is low, while it becomeslarger than that of clean sediment when Θ exceeds a criticalvalue. For example, the bio-sediment entrainment flux is twotimes as large as that of clean sediment with d50 = 0.065 mmwhen Θ = 1.0. Moreover, the difference between the entrain-ment flux of bio-sediment and clean sediment increases withan increase in Θ, but the increment becomes smaller.Figure 12 also shows that the entrainment flux increases withthe increasing particle size under the same flow power Θ forboth the bio-sediment and clean sediment, while the criticalShields parameter decreases, exceeding which the bio-

Fig. 9 Vertical distributions ofthe relative concentration forsuspended clean and bio-sediment in the flow with thesame (a, where u* = 2.60 cm s−1)and different (b, where u* = 2.78and 2.60 cm s−1) friction velocity

Fig. 10 Shields curves for clean and bio-sediment (Fang et al. 2014)

Table 3 Suspension indices for clean and bio-sediment in the flowwithdifferent friction velocities. u* represents the friction velocity, and β andβf represent the suspended indices for clean and bio-sediment,respectively

u*/cm s−1 2.78 2.60 Remark

β 0.239 0.255 Clean sediment

βf 1.213 1.297 Bio-sediment

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sediment entrainment flux is larger than that of clean sedi-ment. This is attributed to the increase of the critical Shieldsparameter as well as the decrease in the sediment diameter.Under the same flow condition, the ratio between the entrain-ment fluxes of bio-sediment and clean sediment decreaseswith an increase in d50. For example, when Θ = 1.0, the bio-sediment entrainment flux is 2.3 times larger than that of cleansediment with d50 = 0.043 mm, while only 1.7 times largerwith d50 = 0.086 mm.

4.3 Implication

Biofilm growth on the sediment bed will change the physicalproperties of sediments, such as the bulk density and the in-terparticle forces (Zhao 2009). Consequently, the erosion re-sponse of the bio-sediment will be different from that of cleansediment, which behaves as the change of incipient form fromparticles to flocs (Thom et al. 2015) as well as the change of

bedform characteristics (Fang et al. 2017). The changes offlow characteristics influence the transport of sediment andother substances such as nutrients in the water, but do notdetermine the transport capacity. Thus, the properties of bio-sediment play a more important role on the sediment dynam-ics. Therefore, more experiments concentrating on the bio-sediment properties, such as the floc size, density, and settlingvelocity in the turbulent flow, are expected to be conducted inthe future. Moreover, based on the present study, a preliminarymathematical model can be further established by combingbio-sediment transport with the hydrodynamic model.

5 Conclusions

In the present study, flume experiments were conducted toinvestigate the effects of biofilm growth on the turbulencecharacteristics of the flow, such as the RSS, time-averagedvelocity, turbulence intensity, TKE flux and budget, and burst-ing events. Furthermore, the near-bed entrainment flux and thedistribution of suspended bio-sediment were analyzed. Themain conclusions are as follows:

1. For the flow over a flat bed, there is few changes in theRSS along the water depth due to the biofilm. For the flowover an eroded bed, however, the magnitude of the RSSchanges in the presence of biofilm, although the verticaldistribution only changes slightly. The bed shear stressexerted on the sediment bed with biofilm becomes smallerthan that without biofilm.

2. The time-averaged velocity profile appears to change afterbiofilm growth, and the increment of the mean velocity isproportional to the flow discharge. Under the low flowrate condition (i.e., a flat bed), the increment of the non-dimensional mean velocity is approximately 6.7%, whileit is more than 20% under the high flow rate condition(i.e., an eroded bed), which implies a decrease of the bedresistance to the flow. Moreover, the logarithmic velocitydistribution in the wall region shows an upward shift ofthe virtual bed level and a decrease of the roughness dueto biofilm.

3. The presence of biofilm changes the distribution of theturbulence intensity only in the flow over an eroded bed,resulting in a more uniform distribution along the waterdepth. The changes of TKE flux and TKE budget arehardly observed by these scattered measured data.Moreover, the changes of the bursting events contributeto the total RSS in the flow by inhibiting sediment incip-ient and transport.

4. Compared to the distribution of clean sediment, thesuspended bio-sediment concentration is much higher inthe wall region but lower in the upper layer. Furthermore,the entrainment flux of the bio-sediment increases when

Fig. 11 Vertical distributions of the suspended clean and bio-sedimentunder the same flow condition (u* = 2.60 cm s−1)

Fig. 12 Entrainment flux of clean and bio-sediment under differentstream powers

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the flow Shields parameter exceeds a critical value, whichis attributed to the decrease of density and the increase ofparticle size.

Funding information This investigation was supported by the NationalNatural Science Foundation of China (No. 91647210) and National KeyResearch and Development Program of China (No. 2016YFC0402506).

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