An experimental study on dynamic processes of ephemeral gully erosion in loess landscapes

An experimental study on dynamic processes of ephemeral gully erosion in loess landscapesJ.G.Gong a ,⁎,Y.W.Jia a ,Z.H.Zhou a ,Y.Wang b ,W.L.Wang c ,H.Peng aa Department of Water Resources,China Institute of Water Resources and Hydropower Research,Beijing 100038,Chinab State Key Laboratory of Earth Surface Processes and Resource Ecology,College of Geography and Remote Sensing,Beijing Normal University,Beijing 100875,ChinacState Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau,Institute of Soil and Water Conservation,CAS and MWR,Yangling,Shaanxi 712100,Chinaa b s t r a c ta r t i c l e i n f o Article history:Received 19June 2010Received in revised form 21September 2010Accepted 22September 2010Available online 29September 2010Keywords:ErosionHydrodynamics RunoffEphemeral gully Loess PlateauEphemeral gully erosion is widespread on the Loess Plateau of China.To provide theoretical support for constructing numerical models and soil-water conservation planning,the hydrodynamic characteristics of ephemeral gully flows were studied by laboratory experiments with a physical model.We firstly concluded that,with the in fluence of “step-slope-pool ”(or “step-pool ”)terrain on the bottom of gully channels,no obvious or consistent pattern changes were evident in the hydrodynamic parameters along the flow direction.Secondly the change of hydrodynamic parameters during erosion could be classi fied into an initially fast changing interval followed by a stable period,and the initial adjustment period would become shorter with increasing slope and rainfall intensity.Thirdly ephemeral gully erosion flows were turbulent and changed frequently in space and time between supercritical and subcritical flows.Throughout the experiment,the Reynolds number fluctuated and increased with time.With increasing rainfall intensity and gully slope,the frequency of larger Reynolds numbers increased.In addition,the Froude number also fluctuated,but decreased with time,and the mean Froude number eventually stabilized at ~0.5at different slope angles and rainfall intensities.Fourthly the distribution of erosional energy was in fluenced mainly by topography in loess slopes.In the case of 20°slopes,the inverse ratios of dissipation as soil erosion,sediment transport,and flow kinetic energy were relatively stable in time and space during ephemeral gully erosion.Moreover,flow velocity,shear stress,the Darcy –Weisbach friction factor,and the Manning coef ficient were in fluenced by rainfall intensity to a lesser degree during erosion.In the stable interval,for 15°and 25°slopes,shear stress,the Darcy –Weisbach friction factor and Manning coef ficient of ephemeral gully flow both increased with increasing rainfall intensity.Flow velocity on the 15°slope decreased initially then increased with increasing rainfall intensity,but flow velocity on the 25°slope decreased with increasing rainfall intensity.Finally the regularity seen in hydrodynamic parameters of ephemeral gully flows occurred despite disturbance from lateral con fluences,gravity erosion of the channel bank,and changes in terrain.The sediment transport capacity of ephemeral gully flows increased with USP by a linear function (r=0.64,n=99,P b 0.01).©2010Elsevier B.V.All rights reserved.1.IntroductionIn recent years,the importance of soil erosion processes has been widely recognized.Based on accurate surveys and detailed study of gully erosion processes near Milledgeville,Georgia,from 1840to 1938,Ireland (1939)showed that retreat of gully heads had slowed over time,because the heads were within 200–300ft of the drainage divide and received much less water than they did previously.Classi fication of water erosion includes splash,rill,ephemeral gully,and gully erosion.The term “ephemeral gully ”was coined by American scholars in the twentieth century as a then newly recognized type of erosion.The of ficial website of the Soil ScienceSociety of America (2010)de fines ephemeral gullies as “small channels eroded by concentrated flow that can be easily filled by normal tillage,only to reform again in the same location by additional runoff events.”On the Loess Plateau of China,some researchers (Huang,1953;Zhu and Zhang,1955)in the 1950s observed that there were many shallow gullies without steep walls,the traces of which cannot be removed after contour plowing.Shallow gully erosion is a transitional erosion type between rill and gully erosion.More recently,research-ers (Liu et al.,1988;Zhang et al.,1991;Wang et al.,2003a,b )have emphasized that a shallow gully is an erosion trench formed at the bottom of weak slope incisions scoured by surface runoff.They noted that shallow gullies occur mainly on 15°tilled slopes,and while they have no impact on plowing,they could develop into gullies.Thus,shallow gullies can be treated as part of the extended “ephemeral gullies ”group.Geomorphology 125(2011)203–213⁎Corresponding author.Tel.:+861068785505;fax:+861068785625.E-mail address:jiaguogong@ (J.G.Gong).0169-555X/$–see front matter ©2010Elsevier B.V.All rights reserved.doi:10.1016/j.geomorph.2010.09.016Contents lists available at ScienceDirectGeomorphologyj o u r n a l h om e p a g e :w w w.e l s e v i e r.c o m /l oc a t e /g e o m o r p hOn the Loess Plateau,especially in hilly areas,ephemeral gullies are the main erosion type and widespread(Zhang and Tang,1992). They typically occur on slopes between20and60m below the watershed divide and gully erosion zone.In slope gully systems, ephemeral gullies are the transitional links between rills and gullies (Wang et al.,2003a,b).Ephemeral gullies amount to~70%of the land surface area between gully areas,and they contribute to35–70%of the slope erosion mass(Tang,2004).Ephemeral gullies can broaden the erosion area,increase the ephemeral gully catchment area,and speed up theflow concentration of slopeflow.As a result,flow can be collected easily,and erosion energy can be enhanced.Ephemeral gullies provide the energy for full erosion and gully-head develop-ment(Wang et al.,2003b).Ephemeral gully incisions are the main channels of sediment delivery derived from raindrop splash erosion,surface erosion,and rill erosion,and also are the main source of eroded sediments.The hydrodynamic processes of ephemeral gully gouges are important in slope gully systems.According to Wang et al.(2003b),the hydrodynamics of ephemeral gully waterflows is similar to that of open channel waterflows.The study of hydrodynamic parameters of ephemeral gully waterflow has developed widely around the world. Hydromechanical models based on these hydrodynamic parameters can be used to forecast erosion.These studies lend themselves to experimental analysis where estimates of soil erosion can be made in order to investigate hydrodynamic parameters.The pertinent hydro-dynamic parameters includeflow depth(Merz,1990),total discharge, discharge per unit width(Meyer et al.,1975;Line and Meyer,1989),flow shear stress,effectiveflow shear stress(Lyle and Smerdon,1965; Torri,1987;Ghebreiyessus et al.,1994;Nearing et al.,1997),runoff kinetic energy(Bagnold,1977;Hairsine and Rose,1992;Elliot and Laflen,1993;Zhang et al.,2003),effective runoff kinetic energy (Govers,1992),unit stream power(Yang,1972;Moore and Burch, 1986),and the Froude number(Fr)(De Ploey,1983).Other models include the runoff kinetic energy model GUEST(Misra and Rose, 1996),and KYERMO(Hirschi and Barfield,1988).The U.S.Department of Agriculture developed the ephemeral gully erosion model(EGEM) (Foster,1990),the only conceptual tool tailored specifically for ephemeral gully erosion.The EGEM comprises a hydrological module and an erosional module.It simulates spatial and temporal changes in gullying and forecasts annual average soil erosion of a single gully,but its adaptability to different regions is low(Casalíet al.,1999;Capra and Scicolone,2002;Valcárcel et al.,2003;Capra et al.,2005).Despite decades of research on ephemeral gullies around the world,many unsolved problems still persist in many regions.The Loess Plateau is a plateau that covers an area of640,000km²in the upper and middle reaches of China's Yellow River,and in China proper.Since the silty loess soil is highly prone to erosion,it has been called the“most highly erodible soil on earth”(Laflen,2000).Because field observations can be difficult and hazardous in this part of China, the number offield-based studies on the dynamic process of ephemeral gully erosion on the Loess Plateau is limited.Based on previousfield observations,we conducted a simulation experiment that investigated changes inflow patterns,kinematic behavior,and frictional behavior of ephemeral gullyflow.Hydrodynamic processes also were analyzed.This study is intended to provide theoretical support for establishing an ephemeral gully erosion model based on hydrodynamic processes in the Loess Plateau,and in other regions of similar soil types.2.Experimental designEphemeral gully formation on the Loess Plateau proceeds as follows.On sloping farmland,rainfall leads to sheetflow,which initiates sheet and rill erosion and concentratedflows.Points of initial incision evolve into erosion gullies in the downslope direction.Since the land is used for agriculture,the gullies then arefilled and leveled during plowing.With subsequent rainfall events,thefilled gullies are re-initiated at the sites of the original gullies.This alternating erosion and plowing over time produces the unique topography of the Loess Plateau hilly area,termed“imbricated landform”(Fig.1)(Zhang and Tang,1992).The factors influencing ephemeral gully formation and development are soil type and texture,rainfall,land slope and shape, and land use.The experimental loess was located in the hilly region of the Loess Plateau,Ansai County.Initially we built up10-cm depth samples of fine sand on the bottom of the experimentalflume.The loess was passed through a1-cm sieve,then placed in the experimentalflume to a depth of50cm(built up infive layers).The two surface layers simulated the plow zone,and were packed at a bulk density of 1.1g cm−3.The three lower layers were packed at a bulk density of 1.25g cm−3.The soil particle size distribution is presented in Table1.The experimental parameters are presented in Table2(Zhang et al.,1991;Zhang and Zhu,2006;Xiao et al.,2009).Runoff from the upstream catchment area was simulated by controlled release of water.The simulated slope length was8m(Fig.2).After the soil sample was set up in theflume,and to maintain soil moisture consistency between different experiments,synthetic rain was applied at15-mm h−1intensity until surface runoff on the slope occurred.The soil sample was then left undisturbed for24h.To adjust the rainfall intensity,we covered theflume by placing a plasticfilm over the experiment.Then,we uncovered thefilm,and set the“zero”time as the start offlow out of theflume.At the same time,water discharged from above at a setflow rate.Three observation sections were located at2,4and6m in the down slope direction.Observation times were at1,3,6,9,12,15,18,21,24,27,30,33,36and39min after the experiment commenced(Fig.3).Every experiment was repeated twice,and we took the average of the observed data within 1–30min.Observed variables wereflow rate(Q,m3s−1),sediment concen-tration(S,kg m−3),flow velocity(v,m s−1),flow surface width(w, m)and depth(d,m),gully width and bottom depth(m),and temperature(T,°C)at the outlet.3.ResultsThe hydrodynamic parameters studied were the Reynolds Number (Re),Froude Number(Fr),shearing stress(τ,N m−2),unit stream power(USP,m s−1),Darcy–Weisbach friction factor(f),and Manning coefficient(n).The equations were as follows:Re=vR=ηð1ÞFr=v=ffiffiffiffiffiffigdpð2Þτ=γRJð3ÞFig.1.Typical slope in the hilly region of the Chinese Loess Plateau(Tang,2004).204J.G.Gong et al./Geomorphology125(2011)203–213UPS=vJð4Þf=8RJg=v2ð5Þn=R2=3J1=2=vð6Þwhere v is theflow velocity(m s−1);R is the hydraulic radius(m);ηis the water kinematic viscosity coefficient(m2s−1),η=0.01775/ (1+0.0337T+0.000221T2);Āis the area of average waterflow section(m2),R=Ā/Wp;Wp is the wetted perimeter(m),Wp=w+ 2d;g is the acceleration due to gravity(m s−2);d is theflow depth (m);γis the water density(kg m−3);and J is the hydraulic gradient (m m−1).3.1.Variation offlow typesOpen channelflows either should be turbulent or laminarflows (linked to the Reynolds number).For turbulentflows,frictional energy loss is much greater than that in laminarflows.Flows also can be classified into supercritical or subcritical types(linked to theFroude number).Supercriticalflows are rapid and have a higher erosion capability compared to subcriticalflows.Thus,checking the spatial and temporal changes of the Reynolds and Froude numbers in the experiment is important.3.1.1.Temporal and spatial variation of the Reynolds numberThe Reynolds runoff number(Re)characterizes the ratio offlow inertial and viscous forces.It is an important index for determining whether waterflow is laminar or turbulent.When Re is less than a critical number,laminarflow occurs that is characterized by rectilinear motion without mixing.When Re is greater than a critical number,turbulentflow occurs that is characterized by mixing and disorder.In laminarflow,the effect of theflow viscous force is greater than theflow inertial force,so that theflow moves in stable layers. Turbulentflow is the opposite of laminarflow(Lv et al.,2002).Open channelflows are laminar when Re b500and turbulent when Re N1000.The range between500and~1000is transitional.For ephemeral gully waterflow,we assume that theflow is turbulent when Re N500because of frequent changes in large channel bed slope andflow directions.Based on our experimental results,Re on a15°slope increased with increasing rainfall intensity(Fig.4A).On average,Re was 2.0N1.5N1.0mm min−1during the experiment.As the experiment progressed,Re increased moderately under1.0mm min−1rainfall intensity,fluctuated mildly under 1.5mm min−1,andfluctuated significantly under2.0mm min−1.At slopes of20°(Fig.4B)and25°(Fig.4C),Re for all rainfall intensitiesfluctuated consistently without evident increases or declines,although Re showed an overall increase for25°at1.0mm min−1.Re increased on15°and20°slopes under1.0 and1.5mm min−1rainfall intensities,but with initial increases and then decreases(Table3).Re on a25°slope increased initially,then decreased under1.0and1.5mm min−1rainfall intensities.Under the 2.0mm min−1rainfall,Re declined initially and then increased.In summary,Re changed gradually on low slope gradients under low rainfall intensity.With increasing slope gradients and rainfall intensities,the variation in runoff response was much greater.In all the cases,flow was turbulent at lowest Re=2,726and highest Re=56,037.3.1.2.Temporal and spatial variation in Froude numberThe Froude number(Fr)is the ratio of waterflow inertial force to gravity,and is an important index of waterflow state.The ephemeral gully's Fr declined gradually as the experiment progressed.For a15°slope,the rate of decline decreased with increasing rainfall intensity,where Fr at1.0N1.5N2.0mm min−1(Fig.5A).On a20°slope,the Fr decreased gradually and was evident within10min (Fig.5B).As the experiment progressed,Fr remained steady.On a25°slope,Fr declined gradually,which again was evident within10min, and thereafter remained steady(with an exception:where rainfall intensity was 1.0mm min−1,somefluctuations were larger).In summary,under different slope angles and rainfall intensities Fr, declined in thefirst10min,remained mostly steady thereafter,but displayed some greater variation on the steepest slope gradient.Fr increased down the gully on a15°slope and under1.0mm min−1 rainfall intensity,decreased on a15°slope under1.5and2.0mm min−1 rainfall intensity,and decreased also on a20°slope under1.5mm min−1 rainfall intensity(Table4).Fr decreased initially,and then increased on a 20°slope under1.0and2.0mm min−1rainfall intensities,and it also decreased on a25°slope under1.0,1.5,and2.0mm min−1rainfall intensities.Interestingly supercriticalflows were observed at the beginning of most experiments,and they all ended as subcriticalflows.Table1Particle size classes of the experimental soil.Particle size(mm)b0.0010.001–0.0050.005–0.010.01–0.050.05–0.250.25–1Percentage(%) 3.5610.477.9348.6328.34 1.07Table2Experimental plots characteristics.Slope gradient Intergullydistance(m)Upper catchmentarea(m2)Rainfall intensity(mm/min)Upper discharge a(L/min)17.531525.66500 1.511.29215.0619.432019.94500 1.514.14218.85111.722515.46500 1.517.59223.45a Drainageflow=actual gully spacing×rainfall intensity×upper catchment area×cos(slope gradient)×runoff yield coefficient;runoff yield coefficient is0.4(Yang et al., 2003;Xia et al.,2007).Fig.2.Sketch of experimental apparatus.205 J.G.Gong et al./Geomorphology125(2011)203–2133.2.Variation inflow dynamics3.2.1.Temporal and spatial variation inflow velocityFlow erosion is a powerful driver of terrain evolution,andflow velocity is an important parameter that characterizesflow kinetic energy.Furthermore,the gravitational force along slope direction increases with increasing slope gradient,which results in increasing flow velocity acceleration,and vice versa.In addition,irregular variations in gully slope and cross section make it difficult to establish a definite law offlow velocity.In our experiments,flow velocity declined gradually on a15°slope under1.0and1.5mm min−1rainfall intensity(Fig.6A).Under a rainfall intensity of2.0mm min−1,flow velocity was constant,but thefluctuation range increased.Flow velocity decreased gradually on a20°slope under all rainfall intensities(Fig.6B),and theflow velocity decreased gradually in thefirst10min,and then remained constant on25°slopes under all rainfall intensities(Fig.6C).In summary,flow velocity stabilized when the slope gradient was high and the rainfall intensity was low,or when the slope gradient was low and the rainfall intensity was high.Under other conditions,flow velocity decreased gradually as erosion proceeded.Flow velocity declined gradually in thefirst10min,and then stabilized on different slope gradients and under different rainfall intensities.(A) Pre-experiment(B) Experiment(C) Post-experimentFig.3.Progressive incision from erosion processes through the experiment.(A) 15° slope(B) 20° slope(C) 25° slopeFig.4.Changes in Reynolds number with time under different experimental treatments.206J.G.Gong et al./Geomorphology125(2011)203–213In terms of spatial variations,flow velocity increased down the gully on a 15°slope under rainfall intensity of 1.0mm min −1,and on a 20°slope under rainfall intensity of 2.0mm min −1(Table 5).The variation decreased at first and then increased on a 15°slope under rainfall intensity of 1.5mm min −1,on a 20°slope under a 1.0mm min −1rainfall intensity,and on a 25°slope under all rainfall intensities.Flow velocity increased initially and then decreased down the gully on a 15°slope under 2.0mm min −1rainfall intensity and on a 20°slope under 1.5mm min −1rainfall intensity.3.2.2.Temporal and spatial variation in flow shear stressShear stress is an important driver in soil particle removal by the flow.When shear stress exceeds the cohesive properties of soil particles,the soil is detached and transported down slope by the runoff.Flow shear stress is affected by flow density,hydraulic radius,and hydraulic gradient on sloping land.When the hill slope gradient isT a b l e 3C h a n g e s i n R e y n o l d s n u m b e r u n d e r d i f f e r e n t e x p e r i m e n t a l c o n d i t i o n s .D i s t a n c e f r o m t o p o f c h a n n e l (m )S l o p e g r a d i e n t15°20°25°R a i n f a l l i n t e n s i t y m m m i n −11.01.52.01.01.52.01.01.52.02A v e r a g e 27264081865377099035578410,92410,61621,391R a n g e 1944–35591437–62321941–20,5141690–12,8563245–22,7961494–23,4604413–22,9821285–25,41710,306–50,8734A v e r a g e 2898487018,1189218963916,15420,38221,3638214R a n g e 963–37183329–65112898–49,1623216–22,0654030–13,2754312–27,8486564–29,27111,963–56,0372466–23,2076A v e r a g e 3866723717,26412,58512,13914,150516817,7898908R a n g e1978–73444121–12,3911300–51,2282837–19,8745792–21,6498353–24,5791323–13,9493571–33,1402720–27,944(A) 15° slope(B) 20° slope(C) 25° slopeFig.5.Changes in Froude number with time under different experimental treatments.207J.G.Gong et al./Geomorphology 125(2011)203–213constant,hydraulic gradient effects are weak.Flow density is linked closely with sediment content,and the hydraulic radius is determined by bothflow erosion and substrate.Changes inflow shear stress result from the dynamic interplay of slope gradient,rainfall intensity,and catchment area.In our study,flow shear stress increased gradually withfluctuations on a15°slope as the experiment proceeded(Fig.7A).Flow shear stress and itsfluctuation range also increased with increasing rainfall intensity. On a20°slope,flow shear stress increased with greaterfluctuations in thefirst6min,but then the rate of increase lessened(Fig.7B).On a20°slope,flow shear stress increased whilefluctuating in thefirst10min and stabilized thereafter at a relatively larger value(Fig.7C).The shear stress of ephemeral gullyflow ranged from19.7to 530.9N m−2,with a mean value of156.5N m−2.The maximum occurred under a1.5mm min−1rainfall intensity on a25°slope,and the minimum occurred under rainfall intensity of1.0mm min−1on a 15°slope.The combined results indicate that shear stress values and associatedfluctuations increased with increasing rainfall intensity and slope gradient.In terms of spatial variations,runoff shear stress decreased and then increased down the gully on a15°slope under a rainfall intensity of1.0mm min−1(Table6).Shear stress increased on a15°slope under rainfall intensities of1.5and2.0mm min−1,and also increased on a20°slope under rainfall intensity of1.5mm min−1.Shear stress increased and then decreased on a20°slope under rainfall intensities of1.0and2.0mm min−1;and the same occurred on a25°slope under rainfall intensities of1.0and1.5mm min−1.On a25°slope under a2.0mm min−1rainfall intensity,the runoff shear stress decreased.3.2.3.Temporal and spatial variation in the unit stream powerUSP includesflow velocity and slope.Many researchers have described sheet erosion and rill erosion on hillslopes based on USP (Yang,1972;Moore and Burch,1986).Since ephemeral gullyflows are bigger and deeper than rillflows,concentratedflows aid ephemeral gullyflows.At the same time,lateral confluences and sediment from inter-gullies and gravitational erosion of the banks of gullies make temporal and spatial variations in the unit stream power more complex.From Eq.(4),we can see that variations in the unit stream power had the sameflow velocities on the same slope,although USP increased with increasing slope gradient.This trend became weak with increasing rainfall intensity(Fig.8).During the experiment,USP slightly became smaller,especially under1.0mm min−1conditions (Fig.8A).Changes in2.0mm min−1conditions(Fig.8C)could be classified into an initially fast changing interval followed by a relatively stable period.At that point,the changes in the1.5mm min−1conditions(Fig.8B)were between the 1.0and2.0mm min−1condition.3.3.Changes inflow resistance features3.3.1.Temporal and spatial variation in the Darcy–Weisbachfriction factorThe Darcy–Weisbach friction factor evaluates resistance linked withflow kinetic energy.The larger the factor is,the higher the dissipation ratio offlow kinetic energy.Table4Changes in Froude number under different experimental conditions.Distance from top of channel (m)Slope gradient15°20°25°Rainfall intensity mm min−1 1.0 1.5 2.0 1.0 1.5 2.0 1.0 1.5 2.02Average0.730.890.840.750.780.770.630.710.50 Range0.63–0.900.40–2.120.45–1.550.3–2.250.49–1.510.29–1.610.34–0.950.34–1.720.26–0.98 4Average 1.100.540.710.560.690.460.460.380.48 Range0.54–2.880.25–0.970.38–2.150.37–1.850.53–1.030.24–0.780.28–0.920.29–0.510.24–0.95 6Average 1.440.510.650.840.530.62 1.300.720.67 Range0.32–3.120.37–0.680.28–2.730.49–1.300.39–0.990.36–0.880.36–2.170.31–1.690.30–1.53(A) 15° slope(B) 20° slope(C) 25° slopeFig.6.Changes inflow velocity with time under different experimental treatments.208J.G.Gong et al./Geomorphology125(2011)203–213On a 15°slope,the Darcy –Weisbach friction factor increased gradually while fluctuating under all rainfall intensities (Fig.9A).Both flow shear stress and the fluctuation range increased with increasing rainfall intensity.The friction factor increased on a 20°slope under allrainfall intensities,in the first 6min of the experiment,before the rate of increase slowed with increasing fluctuations (Fig.9B).Considering Fig.9C,we can see that on a 25°slope,the Darcy –Weisbach friction factor increased under all rainfall intensities in the first 9min of the experiment.After this,under a 1.0mm min −1rainfall intensity,the friction factor increased greatly and consistently with an increasing fluctuation range.Under rainfall intensities of 1.5and 2.0mm min −1,the friction factor rapidly reached ~20,and then decreased.In terms of spatial variations,the Darcy –Weisbach friction factor decreased and then increased on a 15°slope under 1.0mm min −1rainfall intensities (Table 7).The variations increased uniformly on a 15°slope under both 1.5and 2.0mm min −1rainfall intensities,and increased on a 20°slope under 1.5mm min −1rainfall intensity.The factor decreased uniformly on a 25°slope under 1.0and 2.0mm min −1rainfall intensities.On a 20°slope under 2.0mm min −1rainfall intensity and on a 25°slope under 1.0and 1.5mm min −1intensities,the Darcy –Weisbach friction factor increased initially before decreasing.3.3.2.Temporal and spatial variation in the Manning coef ficientThe Manning coef ficient is a comprehensive index that measures the roughness condition of a wetted area.Under fixed cross section conditions,the value remains constant.For intensive substrate changes from erosion,the Manning coef ficient of ephemeral gully water flow re flects a geomorphic change of gully incision.In our experiments,the Manning coef ficient (n )closely related to the Darcy –Weisbach friction factor (f )(r =0.97).Thus,temporal and spatial variations in the Manning coef ficient were basically the same as the Darcy –Weisbach friction factor.4.DiscussionDuring the course of the experiments,flow states were signi fi-cantly different in dynamics and resistance between the initial period of 6–9min and the remainder of the simulation in the 9–30min period.The flow dynamic characteristics exhibited self adjustment in the initial erosion runoff period.Subsequently,the dynamic flow characteristics usually stabilized over different slope lengths and under different rainfall intensities.4.1.Flow regimes of the ephemeral gully channelUnder the experimental conditions,the Re of ephemeral gully flows ranged from 2192to 34,307,and was much greater than 500,thereby indicating signi ficant turbulent flows.At the same time,the Re of the ephemeral gully trench increased with increasing rainfall intensity and slope gradient.The combination of low rainfall intensity and low slope produced the minimum average,and the maximum average occurred from the combination of high rainfall intensity and low slope angle.Since the channel water depth was comparatively large in the ephemeral gully,to erosion was strong.Channel morphology changed constantly,and channel topography had higherTable 5Changes in flow velocity under different experimental conditions.Distance from top of channel (m)Slope gradient15°20°25°Rainfall intensity mm min −11.01.52.01.01.52.01.01.52.02Average 0.300.330.360.300.360.300.340.340.36Range 0.26–0.330.25–0.470.28–0.420.22–0.470.27–0.470.22–0.520.26–0.410.30–0.450.25–0.504Average 0.350.310.400.290.360.310.330.300.26Range 0.29–0.450.28–0.380.27–0.550.25–0.490.28–0.530.24–0.380.29–0.390.27–0.380.20–0.436Average 0.430.330.350.440.320.380.400.370.31Range 0.22–0.620.26–0.430.25–0.490.33–0.700.29–0.390.29–0.560.27–0.570.26–0.520.20–0.49(A) 15° slope(B) 20° slope(C) 25° slopeFig.7.Changes in flow shear stress with time under different experimental treatments.209J.G.Gong et al./Geomorphology 125(2011)203–213。