Turbulent flows in straight compound open-channel with a transverse embankment on the floodplain

Transcription

1 Turbulent flows in straight compoun open-channel with a transverse embankment on the flooplain Y. Peltier, S. Proust, N. Rivière, A. Paquier, K. Shiono To cite this version: Y. Peltier, S. Proust, N. Rivière, A. Paquier, K. Shiono. Turbulent flows in straight compoun openchannel with a transverse embankment on the flooplain. Journal of Hyraulic Research, 2013, 51 (4), p p < / >. <hal > HAL I: hal Submitte on 9 Oct 2014 HAL is a multi-isciplinary open access archive for the eposit an issemination of scientific research ocuments, whether they are publishe or not. The ocuments may come from teaching an research institutions in France or abroa, or from public or private research centers. L archive ouverte pluriisciplinaire HAL, est estinée au épôt et à la iffusion e ocuments scientifiques e niveau recherche, publiés ou non, émanant es établissements enseignement et e recherche français ou étrangers, es laboratoires publics ou privés.

2 1 2 Turbulent flows in straight compoun open-channel with a transverse embankment on the flooplain YANN PELTIER (IAHR Member), Ph. D., Laboratoire e Mécanique es Fluies et Acoustique (LMFA, CNRS UMR5509, Université e Lyon), INSA e Lyon, Bât. Jacquar, 20 av. A. Einstein, 69621, Villeurbanne, France. Previously, Irstea, UR HHLY, Hyrology- Hyraulics, 5 rue e la Doua, CS 70077, VILLEURBANNE Ceex, France. yann.peltier90@gmail.com (Corresponing Author) SEBASTIEN PROUST (IAHR Member), Researcher, Irstea, UR HHLY, Hyrology- Hyraulics, 5 rue e la Doua, CS 70077, VILLEURBANNE Ceex, France. sebastien.proust@irstea.fr NICOLAS RIVIERE (IAHR Member), Professor, Laboratoire e Mécanique es Fluies et Acoustique (LMFA, CNRS UMR5509, Université e Lyon), INSA e Lyon, Bât. Jacquar, 20 av. A. Einstein, 69621, Villeurbanne, France. nicolas.riviere@insa-lyon.fr ANDRE PAQUIER (IAHR Member), Senior Researcher, Irstea, UR HHLY, Hyrology- Hyraulics, 5 rue e la Doua, CS 70077, VILLEURBANNE Ceex, France. anre.paquier@irstea.fr KOJI SHIONO (IAHR Member), Professor, Department of Civil an Builing Engineering, Loughborough University, Leicestershire,UKLE11 3TU, Unite Kingom. k.shiono@lboro.ac.uk 21 Page 1 of 24

3 22 23 Turbulent flows in straight compoun open-channel with a transverse embankment on the flooplain ABSTRACT The present stuy eals with turbulent flows in an asymmetrical compoun channel with an embankment set on the flooplain, perpenicularly to the longituinal irection. The main purpose of this stuy was to assess how a rapily varie flow affects interaction between the flooplain flow an the main channel flow. In aition to rapi changes in the water level an velocity across the compoun channel that have a great influence on the bounary shear stress istribution, the embankment, through two recirculation zones eveloping upstream an ownstream, is also responsible for strong lateral mass exchange between the main channel an the flooplains (channel sub-sections). The lateral velocity can inee reach 50 % of the longituinal velocity, which moifies the characteristics of the mixing layer eveloping between the channel sub-sections. Depth-average Reynols shear stresses 5 times greater than those measure for reference flows are recore within the mixing layer, which inicates that the turbulent exchange is also impacte by the lateral mass exchange Keywors: Floo moelling, Flow-structure interactions, Laboratory stuies, Separate flows, Turbulent mixing layers Introuction In natural or engineere rivers, the flow is containe in the main channel (m), limite by the river banks, most of the time. During heavy snow melting events or significant rainfalls, the river main channel cannot convey all the runoff an consequently overflows on its ajacent flooplains (f). The resulting flow is ientifie as a compoun channel flow. Uner uniform flow conitions, the fast an eep flow in the main channel interacts with the slow an shallow flow on the flooplains. This results in the formation of a mixing layer at the interface between the sub-sections (the main channel an the flooplains), which transfers momentum ue to turbulent exchange between them (Sellin 1964). This turbulent exchange leas to the ecrease in the main channel conveyance an to the increase on the flooplain one. Moreover, the overall conveyance of the compoun channel is reuce relative to the one of a single channel of same hyraulic raius (Knight an Demetriou 1983, Knight an Hame 1984). Knight an Shiono (1990) an Shiono an Knight (1991) showe that for such flow conitions, the epth-average Reynols shear stress representative of the turbulent exchange, T xy = ρu v ( u an v the horizontal components of the fluctuating velocity, the Page 2 of 24

4 epth-averaging operator an the time-averaging operator), is maximal at the junction between the sub-sections. They also foun that for a given flooplain with, the lateral extent of the high shear region between the channel sub-sections an the maximum of T xy, are inversely proportional to the relative flow epth, H r = H f /H m (H f an H m, the mean water epth on the flooplain an in the main channel respectively), while they increase with the flooplain with an a constant H r. Accoring to van Prooijen et al. (2005), the behaviour of T xy within the mixing layer must be linke to the ifference in velocity between the subsections, U m U f (U m an U f are the longituinal mean velocity in the main channel an on the flooplain respectively), an to the lateral graient of the epth-average longituinal velocity, U / y. The turbulent exchange between the sub-sections also epens on channel geometries accoring to results of three types of geometries, which were stuie in the past: Prismatic geometry with a isequilibrium in the upstream ischarge istribution (Bousmar et al. 2005, Proust et al. 2011, 2013), Non prismatic geometry with a continuous variation in the flooplain with, the overall with being constant along the channel, as skewe compoun channels (Elliot an Sellin 1990, Chlebek an Knight 2008) an compoun meanering channels (Shiono an Muto 1998), Non prismatic geometry with a variable overall with, as symmetrically converging flooplains (Bousmar et al. 2004), symmetrically iverging flooplains (ivergence angle smaller than 5.8 ; Proust 2005, Bousmar et al. 2006) an compoun channel with an abrupt flooplain contraction (convergence angle of 22 ; Proust et al. 2006). These flows were efine as graually varie flows. In these experiments, each channel either yiels or receives water from its ajacent channel(s); this exchange of mass, along with nonnegligible lateral velocities, generates noticeable aitional lateral exchange of streamwise momentum that superimposes to the turbulent exchange between the sub-sections (Proust et al. 2009, 2010). Accoring to Proust et al. (2013), the irection an the intensity of the lateral 82 velocity inuce changes in the lateral istribution of the local Reynols shear stress, ρu v ρ u v, by stretching the coherent structures that evelop insie the mixing layer. When mass is transferre from the flooplain to the main channel, the region of high turbulent shear is isplace towars the main channel. Both the maximum of T xy an the lateral extent of the high shear region are lowere. When mass is transferre towars the flooplains, the high shear region wiely extens on the flooplains an the peak of T xy at the sub-sections junction is enhance. In natural or manmae rivers, the flooplains may rapily vary with obstacles either natural (natural levees, rock slie) or artificial (embankments for railways an motorways). Page 3 of 24

5 This has various implications for risk assessment an river geomorphology. The consiere embankment here acts as an asymmetric, partial am which causes an elevation of the water epth in the whole upstream channel. The flow on the flooplain is then constricte by the obstacle, which promotes the evelopment of two recirculation zones, one upstream from the obstacle an one ownstream. Silting can occur in these slack-flows. Oppositely, the flow has to skirt the embankment an its acceleration, causes scouring an can possibly blow away goos or people. When focusing on the flow escription, it results in significant variations of the flow section an in the generation of strong lateral mass exchange (relatively to graually varie flows) between the sub-sections (Proust 2005, Bourat 2007, Peltier et al. 2008, 2009). This type of flow commonly occurs in the fiels, but has been rarely stuie. Among the few stuies ealing with overbank flows with an obstacle on the flooplain (Proust 2005, Peltier et al. 2008), the results inicate that 2D-H numerical moelling has some ifficulties in capturing the recirculating flows an that the physics of the mixing layers in the channel is still not well unerstoo. Aitional etaile measurements of the turbulence characteristics an of bounary shear stress are require, along with some theoretical evelopments. The unerstaning of overbank flows in compoun channel with a transversal obstacle blocking off the flooplain is inee paramount for floo moellers. The accurate estimation of the characteristics of the one hunre year return perio floo, for instance, is necessary for esigning unsinkable motorway an railway embankments (Lefort an Tanguy 2009). Moreover, as part of the establishment of floo hazar prevention plans, flooe area in the vicinity of embankments must be etermine with minimal uncertainties. The present stuy then aims at assessing the effects on the hyraulic parameters of the superposition of two types of flows: (i) a rapily varie flow in the vicinity of a thin embankment an (ii) a compoun channel flow. We notably estimate the effects of the lateral mass exchange on the interaction between the flows in the sub-sections Experimental setup The compoun channel The present experiments were conucte in an experimental flume locate at the Laboratoire e Mécanique es Fluies et 'Acoustique (LMFA, Lyon, France). The flume has a length, L, of 8 m an a total with, B, of 1.2 m. This flume is straight with an asymmetrical crosssection an has a longituinal be-slope, S ox, of 0.18 %. The main channel cross-section is rectangular (Figure 1) an is 0.4 m wie. The bank-full height, b, is of 5.1 cm an the flooplain is 0.8 m wie. The flooplain an the main channel are PVC mae an their surface state is smooth. Page 4 of 24

6 Following the recommenations of Bousmar et al. (2005), separate inlet tanks for the main channel an the flooplain were installe (see schematic top view in Figure 1). They are use to istribute the require ischarges in the sub-sections, which enables to quickly establish a uniform flow relative to in a flume with a single inlet. The flow is then canalise by a succession of gris an the free surface oscillations are attenuate by a float. The outlet consists of two inepenent ajustable tailgates, one for each sub-section. The separate tailgates enable a better ajustment of the ownstream bounary conitions by reucing the backwater effects an the lateral mass exchange between the sub-sections at the far en of the flume. In the present paper, we use a Cartesian coorinate system in which x, y an z are the longituinal, lateral an vertical irections, respectively (as presente in Figure 1). x = 0 immeiately ownstream from the inlet tanks an y = 0 at the lateral bank of the flooplain. z is taken along a plan following the mean slope of the flume an obtaine by the root mean square metho. The origin of the plan is taken in the main channel Measurements evices Water epth an level The water epths an the water levels were measure using an ultrasonic probe (Baumer Electric, UNDK 20I 6912 S35A). The uncertainty of the probe was estimate to ±0.42 mm for a recoring time greater than 20 s Mean an instantaneous velocity A micro-propeller (Nixon, Streamflo Velocity Meter 403) was couple to a vane an an encoing angle evice for simultaneously measuring the flow irection an the mean velocities. The recoring time was set to between 60 s an 90 s epening on the lateral position in the flume to ensure an accurate estimation of the mean an stanar eviation of the velocity. With such recoring time, the uncertainties were estimate to 1.5 % of the mean velocity. Measurements of instantaneous velocities were performe using a 2D sie-looking Acoustic Doppler Velocimeter (micro-adv, Nortek, Vectrino+). The sampling frequency was set to 100 Hz with a signal-to-noise ratio greater than 20 B in orer to have weak influences of the noise (McLellan an Nicholas 2000). The recoring time was set at least to 3 min to ensure an accurate estimation of the mean an stanar eviation of the signal. Page 5 of 24

7 The uncertainties for the estimate Reynols stresses from the instantaneous velocities were minimise. The measure velocity signals were espike using the metho of Goring an Nikora (2002) an the probe misalignment was estimate an correcte using the methos presente in Peltier (2011) Bounary shear stress The bounary shear stress was measure with a Preston tube (outer iameter of 2.72 mm) using the calibration law specifie by Patel (1965). For each experiment, the Preston tube was aligne with respect to the longituinal irection an the uncertainty was within 6 % of the measure bounary shear stress (Preston 1954). In case of large lateral velocities, a correction coefficient was applie to the pressure measurements for taking into account the fact that the Preston is no longer aligne with the main flow irection. The correction coefficient was worke out by measuring the resulting pressure when the Preston tube was turne by a known angle in a uniform flow Measurement gri The measuring evices were mounte on a movable carriage moving on a metal frame in the vicinity of the flume. This metal frame is inepenent of the flume an has the same longituinal mean slope as the flume. The carriage was programmable an was move through a DC motor with an accuracy of ±0.2 mm in both x- an y-irections. Along the y-axis, the gri-step of the measurements was 5 or 10 cm from y = 0.05 m to y = 0.75 m, 1 cm from y = 0.75 m to y = 0.85 m (the junction between the sub-sections is at y = 0.8 m) an 2.5 or 5 cm from y = 0.85 m to y = 1.15 m. The gri-step along the x-axis was not regular an epens on the measuring evice use. The water epth an the mean velocity were measure at every 0.5 m from x = 1.5 m to x = 3.5 m (the embankment is place at x e = 2.5 m) an then at every 1 m until the en of the flume. The instantaneous velocity an the bounary shear stress were measure in four cross-sections: one upstream from the embankment at x = 2 m, one in the embankment cross-section at x = x e = 2.5 m an two ownstream from the embankment at x = 4.5 m an 6.5 m. Along the z-axis, the velocity was measure at least at 2 vertical positions on the flooplain for the shallowest case an at 6 vertical positions for the eepest case Flow conitions The total ischarge an the length of the embankment were chosen in orer to examine a large range of flow conitions, with in particular a large mass exchange between sub-sections. In these experiments, the mass exchange was generate by a transverse embankment set on Page 6 of 24

8 the flooplain an the intensity of the lateral mass exchange was inversely proportional to the longituinal length of the recirculation zones eveloping on both sies of the embankment (upstream: u L x an ownstream: L x ). The recirculation zones were ientifie by Large Scale Particle Image Velocimetry (LSPIV); they are boune by the flooplain wall an the separation streamline corresponing to zero-ischarge in the recirculation zone. The flow conitions are summarize in Table 1. Three reference flows with no embankment were first investigate. The three values of the total ischarge, Q t, an ischarge ratio on the flooplain, Q f /Q t, were those to have uniform flows with the relative flow epths H r = 0.2, 0.3 an 0.4, respectively. The ownstream tailgates were ajuste so that the mean slope of the water surface was equal to the longituinal be-slope. Six flows with a thin obstacle, representing an embankment on the flooplain, were further investigate. The embankment was set at x e = 2.5 m, perpenicularly to the longituinal irection. Various lengths of embankment,, were investigate (see the fourth column in Table 1), with the bounary conitions use for the reference flows, i.e. the same upstream ischarge istributions an height of the tailgates. To analyse the flow conitions, we first consier the longituinal lengths of the recirculation zones that evelop upstream ( L u x ) an ownstream ( L x ) from the embankment (see the fifth an sixth columns in Table 1). zone an the lateral extent L y (x) is never larger than. By contrast, u L x is close to for the upstream recirculation L x increases with the total ischarge an the embankment length, an the lateral extent L y (x) of the ownstream recirculation zone can reach 1.1 between x = 2.75 m an x = 3.25 m for the six flow-cases with an embankment (not shown in Table 1). This generates a constricte cross-section in the x flow. Regaring the normalise length L /, it ecreases with increasing /B f or ecreasing Q t, therefore emphasising the role of the be-generate turbulence in the evelopment of the recirculation zone (Chu et al. 2004, Rivière et al. 2004, 2011). Consiering the Reynols number in the sub-sections, R i = 4R i U i /ν (ν the kinematic viscosity, U i an R i respectively the mean velocity an the hyraulic raius in a subsection), the values in the main channel are one orer of magnitue greater than those on the flooplain (see seventh an eight columns in Table 1). However, the Reynols numbers in both sub-sections are sufficiently high to neglect viscosity effect in the computation of the stresses. Finally the minimal an the maximal relative flow epths (last column in Table 1) inicate very weak longituinal variations in the flow epth for the reference flows, while significant variations are observe for the flow- cases with an embankment: for such flow conitions, the epth on the flooplain can be twice higher than that measure without an embankment. Page 7 of 24

9 In the following sections, the flow-cases are reference in the form Q/, where Q is the total ischarge an the embankment length. Reference cases have = 0.0 (see in Table 1) A rapily varie flow In this section, we show how the embankment set on the flooplain generates a rapily varie flow on the flooplain an in a lesser extent in the main channel Water epth an level The left plots in Figure 2 show the longituinal variations in the flooplain water epth, H f. Putting asie the most ownstream position an the three first meters for flow-case 17.3/0.0, a constant flow epth (to the uncertainty) is observe in the flume for the reference flows. The increase in epth at the en of the flume is ue to a slight backwater effect cause by the ifference in level between the bottom of the flume an the bottom of the tailgates. Regaring the ecrease in epth at the inlets (particularly marke for 17.3/0.0), it is ue to the gris in the reservoir that inuce a strong hea loss an a plunging flow at the channel entrance. For the embankment-cases, the embankment inuces strong variations in the water epth an the istortions (relative to the reference flows) are felt until the en of the flume. On the flooplain near the embankment the longituinal mean slope of the free surface, S wx, is one orer of magnitue greater than the longituinal mean slope of the be (S ox = 0.18 %) an the steepness of this slope increases with both the embankment length (S wx 1.5 % for 24.7/0.3 an S wx 3 % for 24.7/0.5) an the total ischarge (S wx 1 % for 17.3/0.3 an S wx 4 % for 36.2/0.3). It is interesting to see that the water epth at the en of the flume is equivalent to the uniform one for most flows with an embankment. This seems to inicate that, in our short flume, the recirculation is harly affecte by any backwater effects coming from the ownstream conition, though a uniform lateral velocity profile is not recovere. The lateral istribution of the water level, Z, is shown in four cross-sections in Figure 2 (right plots) for flow-cases 24.7/0.3, 24.7/0.5 an 36.2/0.3. The lateral mean slope of the free surface, S wy, can be of the same orer of magnitue as S ox in the zone of large lateral velocities. This slope increases with both the embankment length (S wy 0.25 % for 24.7/0.3 an S wy 1 % for 24.7/0.5) an the total ischarge (S wy 0.2 % for 17.3/0.3 an S wy 0.8 % for 36.2/0.3). A transverse flow is observe from high water level areas to low water areas, except at x = 4.5 m for 36.2/0.3, where the presence of a normal unulate hyraulic jump at this station makes locally rise the water level (see subsection 3.3). Page 8 of 24

10 Depth-average velocity Figure 3 shows the 2D fiels of the longituinal an lateral epth-average velocities (U, V ). The embankment an the resulting recirculation zones (Table 1) are responsible for large variations in the flow section, therefore leaing to significant lateral epth-average velocities V. In the vicinity of the embankment tip, V can be up to 50 % of the longituinal epthaverage velocities U. The flow in the main channel is less influence by the obstacle an V is rather close to 10 % of U. The sign of V must be reference relative to the contracte cross-section locate between x = 2.75 m an x = 3.25 m (where L y (x) = see in Figure 3): upstream from the contraction, the lateral velocities are positive an the flow converges from the flooplain towars the main channel; ownstream, the flow iverges from the main channel towars the flooplain. The comparison of the istribution of the longituinal epth-average velocity with the reference flow emphasises that as long as a recirculation zone is present in the measurement cross-section the velocity ifference, U m U f, ecreases while the maximum of the velocity graient within the mixing layer, U / y, increases. Inee U / y also epens on the with of the mixing layer that evelops between the channel sub-sections. This with is also moifie by the embankment, as shown in section Froue number A typical istribution of the local Froue number, F = 2 2 / U + V gh (h the local water epth), is presente in Figure 4 (flow-case 24.7/0.3). Because of the large velocities (see in Figure 3) an the relatively low water epths on the flooplain (see H f in Figure 2), Froue numbers higher than 0.5 are foun for all flow-cases with the embankment. Moreover, the flow becomes supercritical from the contraction until at least the half of the ownstream recirculation zone. This supercritical zone expans with both the total ischarge an the embankment length. The transition from the supercritical to the subcritical regime is operate through a normal unulate jump consistent with the maximal Froue number smaller than 1.7 (Graf an Altinakar 2000). By contrast, the flow in the main channel is always subcritical Lateral mass exchange Figure 5(a) shows the longituinal variation in the flooplain ischarge compare to that for ref the reference flows, ( ) ref 100 Q Q / Q. The exchange of mass between the sub-sections f f f occurs until the en of the flume for each case an the longituinal variation in the flooplain ischarge increases with the embankment length, but ecreases with the total ischarge. The minimal flooplain ischarge is reache near the contracte cross-section: the flooplain can Page 9 of 24

11 here lose up to 65 % of its ischarge (flow-case 24.7/0.5). To get a eeper insight into the lateral mass exchange, the Figure 5(b) shows the longituinal variations in the normalise intensity of the lateral mass exchange per unit length: q n Q f = (1) Q efine at the junction between the sub-sections (a mass exchange from the flooplain towars the main channel correspons to q n > 0). In the present experiments, the maximum of q n ranges from 0.2 to 0.8, while for non-uniform flows in a straight compoun channel, it oes not excee 0.2 for the most extreme case (Proust et al. 2011, 2013): the initial objective of working with larger mass exchanges is then achieve. The strongest exchanges are observe in the cross-sections near the embankment an the absolute value of q n increases with the embankment length. By contrast, given the uncertainty on the computation of q n (δq n = ±0.07), it seems that the total ischarge has little effect on the variations of q n. f Time-average local velocity The time-average longituinal velocity, u, is isplaye in Figure 6 for the flow-case 24.7/0.0 at x = 5.5 m (where the reference flow is almost establishe; Peltier 2011) an for the flow-cases 24.7/0.5 at x = 2 m (upstream from the embankment), x = 2.5 m (in the embankment cross-section) an x = 4.5 m (ownstream from the embankment). Notice that missing ata in some of the contour plots in Figure 6, is ue to the metrological consierations: intrusive evice an low water epths in some cross-sections. Regaring the flow-case 24.7/0.0, the inflection of the isovels in the main channel clearly emphasises the presence of seconary currents of Prantl's secon kin (Tominaga an Nezu 1991). These seconary current cells are ue to the presence of the two vertical soli bounaries in the main channel. By contrast, the presence of seconary current cells for the flow-cases with an embankment is not so clear. The lateral mass exchange between the channel sub-sections is responsible for the weakening of these structures. In the case of the lateral mass exchange from the flooplain towars the main channel (flow-case 24.7/0.5 at x = 2 m an x = 2.5 m in Figure 6), some slow water enters the upwar part of the main channel until the centreline (above the bank-full level) an also the ownwars part of the main channel near the flooplain ege, which estroy the seconary currents. The penetration of this slow flow, is obviously proportional to q n (see Figure 5). In the case of the lateral mass exchange coming from the main channel towars the flooplain (flow-case 24.7/0.5 at x = 4.5 m in Figure 6), the flow in the main channel an on the flooplain is homogenise by the mass exchange an Page 10 of 24

12 only bounary layers at the walls can be observe. Once the reattachment point of the ownstream recirculation zone is reache an q n is close to zero, the flow in both sub-section starts establishing a typical compoun channel flow Interaction between a rapily varie flow an a compoun channel flow In this section, we iscuss how the parameters usually stuie in compoun channel flows are affecte by the lateral mass exchange inuce by the embankment on the flooplain Bounary shear stress Figure 7 first shows typical istributions of bounary shear stress, τ b, measure uner uniform flow conitions with no embankment on the flooplain (at x = 4.5 m). The bounary shear stress on the flooplain is always smaller than that in the main channel an it increases with the total ischarge. The changes in τ b are smaller in the main channel, since the changes in the velocity are smaller in the main channel than in the flooplain. Figure 7 then shows τ b for the flow-cases with the embankment 24.7/0.3, 24.7/0.5 an 36.2/0.3. The bounary shear stress on the flooplain at x = 2 m (upstream from the embankment an q n > 0) ecreases compare to those measure for reference flows, because of the rise in the water epth an of the flow eceleration. This ecrease is even larger when the embankment length is longer or the ischarge is higher. By contrast, in the embankment cross-section, at x = 2.5 m, the bounary shear stress rapily increases, as the flow here is plunging an is strongly accelerate close to the bottom. Downstream from the embankment where q n < 0, the bounary shear stresses measure at x = 4.5 m an x = 6.5 m out of the ownstream recirculation zone can be 375 % greater than those measure on the flooplain uner uniform flow conitions. These changes are ue to the strong flow acceleration an the very shallow flow relate to the supercritical flow regime (Figure 4). It can be notice that the istribution of bounary shear stress on the flooplain oes not coincie with the reference- flow one as long as the ownstream recirculation zone has not reattache (see flow-cases 36.2/0.0 an 36.2/0.3 at x = 6.5 m in Figure 7) Mixing layer between the sub-sections U 1 an U 2 are the mean longituinal velocities worke out with the epth-average velocities locate in the outsie of the mixing layer in the main channel an in the flooplain respectively. We can efine the lateral location y α (x) for 0 < α < 1 such that the longituinal epth-average velocity, U, writes: ( α ) 2 α 1 2 U x, y ( x) = U + ( U U ) (2) Page 11 of 24

13 The with of the mixing layer, δ(x), can be efine as follows (van Prooijen et al. 2005): ( ) δ ( x) = 2 y ( x) y ( x) (3) an the centre of the mixing layer, y c, is efine as being equal to y 0.5. The Figure 8(a) shows the longituinal variations in the mixing layer with, δ(x), for the embankment-cases, compare to the with, δ ( x), of the reference flows. As long as the ref 359 recirculation zone is present in the measurement cross-section (from e u x x x L until e x ref x x + L ), δ(x) is smaller than δ ( x), because the velocity ifference, U m U f (see in Figure 3), is smaller than that for the reference flows (not shown here); e.g. the flow contraction inuces an increase in the flooplain velocity higher than the increase in the main channel velocity. Upstream an ownstream from this zone, δ(x) is either equivalent to δ ref (x) or greater, because U m U f is equal or greater than for the reference flow. The Figure 8(b) then shows that the centre of the mixing layer, y c (x), oes not always follow the geometrical forcing create by the flooplain ege. On the one han, y c (x) is shifte in the main channel when the normalise intensity of the lateral mass exchange per unit length q n > 0 an the shift is proportional to q n. On the other han, it seems to remain on the flooplain ege for q n < 0 as observe by Proust et al. (2013) in a straight compoun channel with a similar value of q n. The shape of the mixing layers that evelop in the flow-cases 24.7/0.0, 24.7/0.3 an 24.7/0.5 are isplaye in Figure 8(c). The part of the mixing layer on the flooplain is highly impacte by the lateral mass exchange an for the most extreme cases (see flow-case 24.7/0.5), the mixing layer can even isappear where q n is maximum Reynols shear stress The Figure 9(a) shows the lateral istribution of the epth-average Reynols shear stress, T xy, for the three reference-cases at the ownstream position x = 5.5 m, where the flows were establishe in term of water epth an longituinal epth-average velocity. The lateral extent of the high shear region between the channel sub-sections is close to δ ref (x) (not shown here) an as observe in the literature for vertical banks, the maximum of T xy is locate at the subsections junction. The magnitue of the maximum of T xy is inversely proportional to the relative flow epth H r an is proportional to the velocity ifference between the sub-sections U m U f : max(t xy ) = 1.28 Pa an 0.57 Pa, U m U f = 0.33 m s -1 an 0.17 m.s -1, an H r = 0.2 an 0.4 for cases 17.3/0.0 an 36.2/0.0 respectively. These results confirm the relationship between T xy an H r uner uniform flow conitions with a constant flooplain with (Shiono an Knight 1991). Page 12 of 24

14 The lateral istribution of the epth-average Reynols shear stress, T xy, is strongly correlate to the lateral graient of the epth-average longituinal velocity, U / y. Figure 9(b-) put into relation T xy an U / y for the reference flow-cases. U / y is multiplie by a calibrate constant turbulent ey viscosity, ν t, equal to m²s -1 in orer to respect the imension of T xy. The lateral variations in both parameters are similar, therefore qualitatively confirming the Boussinesq relationship for the reference flows. The lateral profiles of T xy for the flow-cases 24.7/0.3, 24.7/0.5 an 36.2/0.3 are isplaye in Figure 10 at various locations along the channel. Similarly to the reference flows (Figure 9(a)), the position of the maximum of T xy coincies with y c (x) (see in Figure 8(b)). By contrast, the magnitues of the maximum of T xy can be 3 or 5 times greater or smaller than those measure for the reference flows. It can be notice that a seconary maximum is also observe on the flooplain ownstream from the embankment (see at x = 4.5 m for 24.7/0.5 in Figure 10(c)) an exists as long as the ownstream recirculation has not reattache. This seconary maximum is ue to the mixing layer that evelops between the recirculation zone an the main flow. The lateral extent of the high shear region also coincies with the one of δ(x). When q n > 0 (Figure 10(a)), the lateral extent reuces with an increase in the embankment length or in the total ischarge. By contrast, when q n < 0, the variations in the lateral extent are not so clear (see at x = 4.5 m in Figure 10(c)), because the secon mixing layer that evelops between the ownstream recirculation zone an the main flow constrains the flooplain flow an prevents the mixing layer between the sub-sections from spreaing too far on the flooplain. All the moifications unergone by the turbulent exchange within the mixing layer are ue to the changes impose by the lateral mass exchange to the istribution of the longituinal velocity in the flume. The right plots in Figure 10 show the lateral istribution of the epth-average longituinal velocity, U, in the same cross-sections as those for T xy. As shown in Figure 10(a-b: upstream an in the embankment cross-section), the lateral extent of the high shear region is proportional to the velocity graient, U / y, an the maximum of T xy is proportional to U m U f. When consiering the stations ownstream from the embankment (see at x = 4.5 m in Figure 10(c)), the lateral extents of the high shear region can be smaller than that measure upstream from the embankment although U / y is the same (flow-case 24.7/0.3). This is ue to the presence of the velocity ip in the istribution of U near the sub-sections junction, as emonstrate by Nezu et al. (1999). This behaviour is observe from the contraction to at least the half of the ownstream recirculation (i.e. while both mixing layers can interact). Finally, the very large peak of Reynols stress at the sub- Page 13 of 24

15 sections junction at x = 4.5 m for case 24.7/0.5, which is relate to an almost iscontinuity of velocity, highlights an extremely high turbulent iffusion that can lea to bank erosion Conclusion The present paper investigates experiments in a compoun open-channel with a transverse embankment on the flooplain. The embankment creates a rapily varie flow on the flooplain, which subsequently interacts with the flow in the main channel. Each varie flow is compare to the reference flow obtaine uner uniform flow conitions in the same flume. The embankment an the recirculation zones that evelop upstream an ownstream are responsible for a strong lateral mass exchange, which inuces significant changes in the water epth an the velocity istribution across the compoun channel, when compare to the reference flows. The mean slopes of the free surface (lateral an longituinal) can be one orer greater than the mean be-slope an the lateral epth-average velocity near the embankment can reach 50 % of the longituinal epth-average velocity. Moreover, because of the low water epth an the high velocity on the flooplain ownstream from the embankment, a supercritical flow occurs until at least the half length of the ownstream recirculation zone. These changes have also great impacts on the parameters more specific to compoun channel flows. It confirms the implication for floo risk assessment an geomorphology mentione in the introuction. While the increase in water epth can reach about 50% in the flooplain upstream the embankment, the 3D flow at the tip of the embankment an the acceleration in the supercritical zone ownstream, inuce bounary shear stresses up to 375 % greater than those of the reference flows. The mixing layer eveloping at the interface between the sub-sections is also highly affecte by the embankment, the recirculation zones an the lateral mass exchange. As long as a recirculation zone is present in the measurement cross-section, the mixing layer with remains smaller than the reference flows one an the turbulent exchange (i.e. epth-average Reynols shear stress) is strongly affecte. The magnitue of the peak of epth-average Reynols shear stress can be up to 5 times greater than that for the reference flows, while the lateral extent of the high shear region is 100 % smaller. The peak is besies not always locate at the junction: it is shifte in the main channel when mass is transferre from the flooplain towars the main channel an remains at the sub-sections junction in the opposite irection. Nevertheless, the Boussinesq hypothesis can still be use in first approach for escribing the evolution of the high shear region. Page 14 of 24

16 Thanks to the present ata-set (epth, velocity, bounary shear stress, Reynols stress), further work coul be evote to numerically moel such rapily varie compoun channel flows in 1D an 2D-H (Line et al. 2012). Concerning 1D moelling, the escription of the turbulent exchange at the interface between the sub-sections is paramount for calculating the ischarge istribution between sub-sections. The present results are of interest to moellers for improving its moelling, since for now only the shear at the interface between the sub-sections is consiere (apparent shear stress, mixing length moel ), an assume to be maximum (Nicollet an Uan 1979, Proust et al. 2009). Concerning 2D moelling, we showe that the Boussinesq hypothesis is still vali for flows with embankment, which is interesting for low-cost moelling in an operational point of view. We also highlighte the behaviour of the seconary currents in the presence of an embankment, which coul be use to correct the shallow water equations by aing terms taking into account the ispersion on the vertical of the horizontal velocities (Peltier 2011) Acknowlegements The research was fune by IRSTEA an by the Rhône-Alpes region (SRESR - EXPLORA'DOC 2008 Bourse Cluster 6). The authors are grateful to F. Thollet an M. Lagouy for their technical support. The authors also thank the anonymous reviewers for their avices Notation b = Bank-full height (m) B = Total with of the flume (m) B f = With of the flooplain (m) B m = With of the main channel (m) = Length of the embankment (m) F = Froue number (-) g = Gravity constant (m.s -2 ) h = Local water epth (m) H f = Water epth on the flooplain (m) H m = Water epth in the main channel (m) H r = Relative flow epth (-) L = Longituinal length of the flume (m) L x = Longituinal length of the ownstream recirculation zone (m) Page 15 of 24

17 u L x = Longituinal length of the upstream recirculation zone (m) L y (x) = Lateral extent of the recirculation zones (m) q n = Normalise intensity of lateral mass exchange per unit length (-) Q f = Discharge on the flooplain (m 3.s -1 ) Q t = Total ischarge (m 3.s -1 ) R i = hyraulic raius of sub-section i (m) R = Reynols number (-) S ox = Longituinal mean be-slope (-) S wx = Longituinal mean free surface slope (-) S wy = Lateral mean free surface slope (-) T bi = Mean bounary shear stress in the sub-section i (Pa) ρu v = Reynols shear stress (Pa) T xy = Depth-average Reynols shear stress (Pa) u = Time-average longituinal velocity (m.s -1 ) u = Fluctuating longituinal velocity (m.s -1 ) U = Longituinal epth-average velocity (m.s -1 ) U f = Longituinal mean velocity on the flooplain (m.s -1 ) U m = Longituinal mean velocity in the main channel (m.s -1 ) v = Fluctuating lateral velocity (m.s -1 ) V = Lateral epth-average velocity (m.s -1 ) x = Longituinal irection (m) x e = Position of the embankment with respect to the inlets (m) y = Lateral irection (m) y c = Centre of the mixing layer between the sub-sections (m) z = Vertical irection (m) δ(x) = With of the mixing layer between the sub-sections (m) ν = Kinematic viscosity (m - ².s -1 ) ν t = Turbulent ey viscosity (m.s - ²) ρ = Flui ensity (kg.m -3 ) τ b = Bounary shear stress (Pa) References Bourat, A. (2007). Déborements es cours eau en présence e remblais routiers ans les lits majeurs. Master s thesis. HHLY, Cemagref, France. Page 16 of 24

18 Bousmar, D., Wilkin, N., Jacquemart, J. H. an Zech, Y. (2004). Overbank flow in symmetrically narrowing flooplains. J. Hyraulic Eng. 130(4), Bousmar, D., Rivière, N., Proust, S., Paquier, A., Morel, R. an Zech, Y. (2005). Upstream ischarge istribution in compoun channel flumes. J. Hyraulic Eng. 131, Bousmar, D., Proust, S. an Zech, Y. (2006). Experiments on the flow in a enlarging compoun channel. In River Flow 2006: 3 r International Conference on Fluvial Hyraulics. 6-8 September, Lisbon, Portugal. Chlebek, J., an Knigtht, D. W. (2008). Observations on flow in channels with skewe flooplains. In River Flow 2008: 4 th International Conference on Fluvial Hyraulics. 3-5 September 2008, Cesme-Izmir, Turkey. Chu, V. H., Liu, F. an Altai, W. (2004). Friction an confinement effects on a shallow recirculating flow. J. Envir. an Eng. Sciences. 3, Elliot, S. C. A. an Sellin, R. H. J. (1990). Serc floo channel facility: skewe flow experiments. J. Hyraulic Res. 28(2), Goring, D. G., an Nikora, V. I. (2002). Despiking acoustic oppler velocimeter ata. J. Hyraulic Eng. 128(1), Graf, W. H., an Altinakar, M. S. (2000). Hyraulique fluviale: écoulement et phénomènes e transport ans les canaux à géométrie simple. PPUR presses polytechniques. Hauet, A., Kruger, A., Krajewski, W. F., Braley, A., Muste, M., Creutin, J. D. an Wilson, M. (2008). Experimental system for real-time ischarge estimation using an imagebase metho. J. Hyrologic Eng. 13(2), Knight, D. W., an Demetriou, J. D. (1983). Flooplain an main channel flow interaction. J. Hyraulic Eng. 109(8), Knight, D. W., an Hame, M. E. (1984). Bounary shear in symmetrical compoun channels. J. Hyraulic Eng. 110 (10), Knight, D. W., an Shiono, K. (1990). Turbulence measurements in as shear layer region of a compoun channel. J. Hyraulic Res. 28(2), Lefort, P. an Tanguy, J. M. (2009). Mécanisme e l écoulement à surface libre. In De la goutte e pluie jusqu à la mer : traité hyraulique environnementale. Tome 1 : processus hyrologiques et fluviaux. J. M. Tanguy, es. Lavoisier, Paris, France, Line, F., Paquier, A., Proust, S., an Peltier, Y. (2012). Errors in 2-D moelling using a 0th orer turbulence closure for compoun channel flows. In River Flow 2012: 6 th Int. Conf. on Fluvial Hyraulics. 5-7 September, San José, Costa-Rica McLellan, S. J., an Nicholas, A. P. (2000). A new metho for evaluating errors in highfrequency ADV measurements. Hyrological Processes. 14, Page 17 of 24

19 Nezu, I., Onitsuka, K. an Iketani, K. (1999). Coherent horizontal vortices in compoun open channel flows. In Hyraulic moeling. V. P. Singh, I. W. Seo an J. H. Sonu es. Water Resources Publications, Colorao, USA, Nicollet, G., an Uan, M. (1979). Ecoulements permanents à surface libre en lit composés. La Houille Blanche. pp Patel, V. C. (1965). Calibration of the Preston tube an limitations on its use in pressure graients. J. Flui Mech. 23, Peltier, Y. (2011). Physical moelling of overbank flows with a groyne set on the flooplain, Ph. D. thesis. Université e Lyon, Lyon, France. Peltier, Y., Proust, S., Bourat, A., Thollet, F., Rivière, N. an Paquier, A. (2008). Physical an numerical moelling of overbank flow with a groyne on the flooplain. In River Flow 2008: 4 th Int. Conf. on Fluvial Hyraulics. 3-5 September 2008, Cesme-Izmir, Turkey. Peltier, Y., Proust, S., Thollet, F., Rivière, N. an Paquier, A. (2009). Measurement of momentum transfer cause by a groyne in compoun channel. In 33 r IAHR Congress: Water Engineering for a Sustainable Environment August 2009, Vancouver, Canaa. Preston, J. H. (1954). The etermination of turbulent skin frictions by means of pitot tubes. J. Royal Aero. Society, 58, Proust, S. (2005). Ecoulements non-uniformes en lits composés : effets e variations e largeur u lit majeur. Ph. D. thesis. INSA e Lyon, Lyon, France. Proust, S., Rivière, N., Bousmar, D., Paquier, A., Zech, Y. an Morel, R. (2006). Flow in compoun channel with abrupt flooplain contraction. J Hyraulic Eng. 132(9), Proust, S., Bousmar, D., Rivière, N., Paquier, A. an Zech, Y. (2009). Non-uniform flow in compoun channel: a 1D metho for assessing water level an ischarge istribution, Water Resour. Res. 45(12), Proust, S., Bousmar, D., Rivière, N., Paquier, A. an Zech, Y. (2010). Energy losses in compoun open channels. Av. Water Res. 33(1), Proust, S., Peltier, Y., Fernanes, J. N., Leal, J. B., Thollet, F., Lagouy, M. an Rivière, N. (2011). Effect of ifferent inlet flow conitions on turbulence in a straight compoun open channel. In 34 th IAHR Congress: Balance an Uncertainty; Water in a Changing Worl. 26 June-01 July 2011, Brisbane, Australia. Proust, S., Fernanes, J. N., Peltier, Y., Leal, J. B., Rivière, N. an Caroso, A. H. (2013). Turbulent non-uniform flows in straight compoun open-channels. Submitte to J. Hyraulic Res. Page 18 of 24

20 Rivière, N., Proust, S. an Paquier, A. (2004). Recirculating flow behin groynes for compoun channel geometries. In River Flow 2004: 2 n Int. Conf. on Fluvial Hyraulics june 2004, Napoly, Italy. Rivière, N., Gautier, S. an Mignot, E. (2011). Experimental characterization of flow reattachment ownstream open channel expansions. In 34 th IAHR Congress: Balance an Uncertainty; Water in a Changing Worl. 26 June-01 July 2011, Brisbane, Australia. Sellin, R. H. J. (1964). A laboratory investigation into the interaction between the flow in the channel of a river an that over its floo plain. La Houille Blanche Shiono, K., an Knight, D. W. (1991). Turbulent open channel flows with variable epth across the channel. J Flui Mech. 222, Shiono, K., an Muto, Y. (1998). Complex flow mechanisms in compoun meanering channels with overbank flows. J. Flui Mech. 376, Tominaga, A., an Nezu, I. (1991). Turbulent structure in compoun open channel flow. J. Hyraulic Eng. 117(1), van Prooijen, B. C., Battjes, J. A., an Uijttewaal, W. S. J. (2005). Momentum exchange in straight uniform compoun channel flow. J. Hyraulic Eng. 131(3), Page 19 of 24

21 620 2 Tabl le 1 Mai in char racteristics of the experimental ata-set: referencee flows (note Q/ /0.0), emb bankment-cases (note Q/) a b x = 1.5 m an x = 7.5 m. c 17..3/ / / / / / / /0.2 Q t (L.s - -1 ) Q f /Q Q t (%) B f /B (-) u L x 36..2/ The lengths of the recirculation zones were assesse by Large Scale Particle Imaging Velocimetry Minimumm an maxi mumm relative flow epth between x = 1.5 m an x = 7.5 m. / (-) a L x (-) / b R f 10 4 (-) R b m 10 5 (-)) c H r (-)) (Hauet et al. 2008) using vieo-sequences of at leas st 2 min long. Minimumm an maximumm Reynols number in the main channel an on the flooplain between Figu ure 1 Definition sketch of the flume in the LM MFA: cross-sectional an plan views (scheme is not to scale). Page 20 of 24

22 Figure 2 (Left plots) Longituinal variations in the water epth on the flooplain, H f, for the nine flow-cases. The black plain line correspons to the x-wise position of the embankment. (Right plots). Lateral istribution of water level, Z. The ashe line correspons to the junction of the sub-sections. Uncertainty: δh = ±0.42 mm an δz = ±0.42 mm Figure 3 2D epth-average velocity fiels for flow cases (a) 17.3/0.3, (b) 24.7/0.3, (c) 24.7/0.5 an () 36.2/0.3 (presente in Table 1). The coloure surfaces represent the velocity intensity. The separation line between the recirculation zones an the main flow is ientifie by the bol black line. Uncertainty: δu /U = ±1.5 % an δv /V = ±1.5 % Figure 4 Froue number istribution for flow-case 24.7/0.3 (presente in Table 1). The black ashe line correspons to F = 1. Page 21 of 24