Predicting the flow in the floodplains with evolving land occupations during extreme flood events \(FlowRes ANR project\)

Flood hazards (flow depth and velocity) must be accurately assessed in high-risk areas during extreme flood events. However, the prediction of the very high flows is not an easy task due to the lack of field data and to the strong link between flow resistance and the land occupation of the floodplain. Confinement and inhomogeneity in lateral and longitudinal directions of hydraulic roughness strongly vary with return period T. The physical processes are complex, some still largely unexplored, and the assumptions linked to numerical modelling cannot be validated without field data. The FlowRes project (2015-2018), funded by the French National Research Agency (ANR), aims at improving the flood hazard assessment in floodplains in: 1) investigating in laboratory the hydrodynamic structure associated with extreme flood flows for various land occupations and flow discharge magnitudes; 2) assessing if the existing numerical modelling practices used for T ~ 100 years are still valid for extreme events with T > 1000 years, relying on the experimental data and on one field case. This paper reports some results obtained during the first year


Introduction
The FlowRes project (2015-2018), funded by the French National Research Agency (ANR), addresses the effect of evolving land occupations (i.e.varying Flow Resistance) on extreme flows over the floodplains where vulnerability and risk are located.Both the specific physical processes related to the very high flows and their numerical modeling are handled.
The project focuses on the flow resistance caused by three types of hydraulic roughness elements commonly encountered on floodplains: meadows, trees and houses.Depending on the flow rate magnitude, these roughness elements can be modeled as bed-induced roughness, emergent or weakly submerged macro-roughness.
The project distinguishes two different flow domains: (a) the compound channel, in the case of a strong interaction between the flow in the Main Channel (MC) of the river and the flow in the Floodplains (FP); (b) the FP considered as a single rectangular cross-section channel, in the case of a negligible MC/FP interaction (far from the interface with the MC and/or when the FP flow is mainly driven by the FP roughness elements).
The consortium of the FlowRes project is composed of eleven partners, mentioned above in the affiliations of the co-authors.The project is divided into two main tasks, as shown in Table 1: experiments in laboratory flumes (Task 1), and assessment and improvement of the modelling practices (Task 2).The laboratory experiments focus on the effects on flow structure of: longitudinal and lateral transitions in hydraulic roughness, of the confinement degree of the roughness elements, and of the spatial distribution and density of these elements.The experiments are carried out in five flumes, under uniform or non-uniform flow conditions in the streamwise direction, relying on the state-of-the-art measurements on both large and small scales (i.e. the river reach scale or the roughness elements scale).For the second task, the previous experimental database is compared  simulations performed with industrial and research codes (1D to 3D modelling).The classical methods to model flow resistance with an increasing complexity are assessed and improved to capture the physics for the entire span of studied flow rates.The codes and methods are then applied to the floods at Besançon, France.Events with a return period T~100, 1000 and 10000-year are simulated with both classical and improved methods, and the discrepancies will be calculated.This project will permit to quantify uncertainties on water levels and velocities computed for extreme events.The present paper focuses on the work carried out during the first year of the project (2015), mostly measurements in laboratory flumes and preliminary numerical results.The existence of a universal profile for the turbulent boundary layer over a rough bed, especially a log-law profile, has been predicted theoretically and verified by many experiments, at least for flow conditions where the boundary layer thickness is large in comparison with the rough bed geometrical scales.Models to predict the hydraulic roughness k s have been developed for urban canopies formed of cubic-like roughness elements (see e.g.McDonald (2000) [1]), based upon a parametrisation of the drag behind individual roughness elements of height h and of the mixing layer profiles in the canopy (region with elevation z < h).This approach also applies to emergent roughness elements.The same framework was applied to plant canopies by Nepf and Vivoni (2000) [2] to model the drag and velocity profiles of canopies formed by very elongated individual roughness elements.

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Recently, the question of the persistence of a log-law profile in very confined flow with h/D<1 (where D is the flow depth) in the limit h/Do1 has been addressed by different authors, following the claim by Jiménez (2004) [3] that log-law should disappear for h/D>0.025.All agree on the necessity to use the double-averaging methodology proposed by Nikora et al. (2007) [4] in order to describe the flow inside the roughness sublayer, but few experiments achieve enough spatial convergence to obtain correct estimates of double-average quantities, as discussed in Florens et al. (2013) [5].Surprisingly, it was found that profiles above the canopy (z>h) still exhibit log-law behaviours for values of h/D as large as 0.66, see Rouzès et al. (2016) [6].
The experimental study proposed as part of this project aims at performing measurements both above and inside the canopy for flow regimes around the transition between emergent (h/D>1) and submerged (h/D<1) roughness elements.The measurements must provide both spatially and temporally converged double-averaged flow quantities.The roughness elements shape must allow a comparative study of urban-like canopies (with h|l, where l is the element width) formed by cubic roughness elements and plant-like canopies formed by elongated roughness elements (with h>> l).

Experimental set-up
Experiments are carried out at the Institut de Mécanique des Fluides de Toulouse (IMFT) in a 26-mlong, 1.10-m-wide and 0.50-m-deep open-channel flume with a 13-m-long section made out of glass and a slope of 0.3 %.Water level can be adjusted with a downstream weir.The bottom of the open-channel was filled up with a 10-m-long rough bed placed 10 m after the tranquilization section, in order to obtain both fully developed boundary layer and uniform flow conditions at the centre of the rough bed.The rough bed was formed by 4 cm cubes arranged in square configuration, separated by a distance L=9 cm, yielding a frontal density Ȝ f =h.l/L 2 =0.20.This configuration is the same as S1 in Eiff et al. (2014) [7], except for the length scale l which is doubled.
In the measurement section, glass cubes were used to allow optical access.Longitudinal vertical laser sheets were generated from below through the bottom of the channel, using a special optic system (parallel laser sheet generator) in order to generate a 10 cm wide parallel laser sheet.Almost no shadows were then generated when propagation occurred through the glass cubes.Images were recorded from the flume side, the camera looking through water or an alley of transparent glass cubes.A telecentric lens was used to prevent any parallax.All PIV measurements were performed in vertical planes near the centre of the flume.See Figure 1 for a view of the measurement system.This set-up allows access to the whole flow region, from z=0 to z=D, as can be seen in Figure 2 (right), with a spatial resolution of 2 mm as inferred from preliminary PIV calculations.
For the more submerged flow regime (h/D=0.24),9 vertical planes located in the periodic pattern were used (to be compared to the 3 planes used by Florens et al. (2013) [5] and Eiff et al., 2014 [7], as shown in Figure 2  (left).Only 5 planes were used for the other flow regimes.
The Table 2 contains the flow regimes investigated with the rough bed of cubes, along with the measurement conditions.In the case of a compound section, the MC and each of the two 1 m wide lateral FP.The dense meadow over the FP is modeled with artificial plastic grass, whose blades are 5 mm high.The bank full height in the MC is of 115 mm (from MC bottom to the top of the blades of the plastic grass).The emergent trees are modeled by wooden rigid cylindrical stems, with a staggered distribution, as shown in Figure 3 (bottom).The cylinder diameter, I, is of 10 mm, and the stem density, N, is of 81 stems/m².

From bed-friction to emergent macro roughness drag, or vice versa
In the case of a single section, the right-hand FP is isolated from the MC by a vertical sidewall (see Dupuis et al. (2015) [11], Dupuis et al. 2016 [12] ).

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,QOHW FRQGLWLRQV In Table 3, the corresponding flow cases are denoted µ0HDGRZ ¶ DQG µ7UHHV ¶, respectively.Two non-uniform geometries were investigated: FP with (1) a transition from meadow to trees installed on the meadow (denoted ³0HDGow / Trees³ RU YLFH YHUVD ³Trees0HDGRZ´ The change in roughness is located at mid-length of the flume, where the origin of the longitudinal x-axis was chosen (x = 0).In the presence of a roughness transition, the inlet FP discharge, Q f ; was modified as shown in Table 3.
The flow depth was measured with an ultrasonic sensor with an accuracy of ± 0.5 mm (acquisition rate of 50 Hz during 3 minutes).A side-looking ADV probe (Vectrino Plus, Nortek) was used to measure the velocity (acquisition rate = 100 Hz, recording time = 180 s).
Velocity is measured with a lateral step 'y in the range 1 cm to 10 cm (smaller values inside the mixing layer), and with 20 to 25 points for each vertical profile in the MC, or 9 to 13 in the FP.

Flow depth and discharge in the floodplain
We present here some experimental results at the reach scale for the flows in a compound channel with a transition 0HDGRZ 7UHHV DQG 7UHHV 0HDGRZ )LJXUH 7RS The evolution along the longitudinal direction of flow depth D f and discharge Q f in the FP is depicted in Figure 4 (Q f is calculated by integration of velocity profiles).
The results show that, in the upstream reach (x<0), the flow is strongly driven by the upstream discharge distribution between MC and FP, while in the downstream reach (x0), the flow is primarily driven by the downstream water level.In particular, in the upper reach, the lateral mean flow between MC and FP can be enhanced or cancelled depending on the value of FP inflow, denoted Q f , inlet .This may alter the shear-layer turbulence developing at the junction between MC and FP, as previously shown by Proust et al. (2013) [13] for non-uniform flows in straight compound channel with smooth FP.

Experiments at IMFT
Experiments were carried out in the same flume as for the study of the submergence / emergence transition (see section 2.1).The bottom of the open-channel was filled up with a 21.4-m-long rough bed placed 2.60m after the tranquilization section.The half left and right sides of the flume were filled up with 2 cm cubes arranged in respectively staggered and square configurations, with frontal densities Ȝ f =0.20 and Ȝ f =0.40 (the configurations S1 and S2 of Eiff et al., 2014 [7]).The roughness discontinuity is then located along the centre of the channel (see Figure 6).Preliminary analysis of the interfacial measurements (namely in S1int planes) show that secondary currents persist deep inside the roughness sublayer even for high values of h/D, as visible in Figure 7.
Stereoscopic PIV measurements in the transverse vertical plane located at X5 (see Figure X) were done at high frequency.Under the frozen turbulence assumption, time-series of u(y,z,t), v(y,z,t) and w(y,z,t) are transformed into a 3D-3C velocity field u(x,y,z), v(x,y,z) and w(x,y,z) providing useful experimental data for coherent structure analysis beside classical statistical approach.
Following Vermaas et al. (2011) [15], both sets of experimental data will be used to quantify the contributions of the different processes responsible for the transverse fluxes of momentum: net mass exchanges between the two regions, the presence of a horizontal mixing layer, and the secondary current generated around the discontinuity.The statistical approach will be completed by an analysis of coherent flow structures.

Figure 7. Time-averaged transverse velocity field V(x,z)
normalized by friction velocity u* above the discontinuity (vertical plane S1int at X5 of Figure 6) for decreasing submergence.The flow depth is denoted here d (d=D).The upper color table applies to h/D=0.33 flow regime.The lower color table applies to h/D=0.50 and 0.66 flow regimes.

Hydraulic roughness of interspersed families of roughness elements
The sub-task 1.4 of the FlowRes project (Table 1) will be dedicated to the study of interspersed families of roughness elements, namely to the interaction between a uniform bed-induced roughness and emerged obstacles.

Experimental set-up
To address these objectives, this study proposes an experimental setup based on 42 test cases.The experiments are carried out in a 1.20 m width and 8 m long rectangular laboratory flume with a fixed slope of S 0 = 0.18 %.The bottom of the flume is covered by an artificial grass layer, onto which the emergent obstacles are placed (Figure 8).The obstacles consist of prismatic bricks with dimensions: 0.054 u 0.054 m² along both horizontal directions and remain emergent in all cases.The flume is equipped with a robotic arm that allows displacements in the three directions: X, Y, and Z (Figure 8).This robotic arm allows us to measure water depth by means of an ultrasonic limnimeter and velocities by using a micro-ADV.
In this study, only fully turbulent flows with low Froude number (Fr < 0.30) are considered.These considerations allow us to neglect the effects of the Reynolds number (Re) and of the Froude number (Fr), reducing to 4 the number of non-dimensional parameters, namely B/L, Ȝ f , D/L, and H/D, where B is the channel width (B = 1.20 m), L stands for the distance between the centers of two consecutive obstacles in both directions (X and Y) (Figure 8), the ratio B/L thus denotes the number of bricks per cross-section, İ is the bed roughness height (İ = 0.007 m), and the ratio İ/D denotes the relative roughness.The spatial distribution of the bricks is parameterized by the frontal density Ȝ f = l.D/L² (emergent elements), with l = 0.054 m.
In this study we will consider values of the filling ratio B/L ranging from 5 to 11 (typically 7 cases).For each value of B/L, three values of Ȝ f and three values of D/L will be studied.).An ultrasonic limnimeter with an accuracy of ± 1 mm is used to measure the water surface and a side-looking Nortek-Vectrino (micro-ADV) is used to measure the 3D velocity field.
The purpose is to obtain the evolution of the ratio ) G / ) E for increasing values of Ȝ f and D / L. Also, the interaction between bed-friction and drag forces is studied by analysing on the one hand, the influence of the bed friction on the drag coefficient and on the other hand, the influence of the obstacles on the bed-friction coefficient.As a conclusion, this study is expected: (1) to characterize the flow resistance of a FP with varying density of buildings, which represents the increase of human settlement; (2) to quantify the ratio between bedfriction forces and drag forces acting on the flow as the building density increases; (3) to characterize the transition from a flow whose resistance is governed by the bottom friction (for a limited built land occupation), towards a flow whose resistance is governed by the drag forces on buildings (for a high built land occupation).

Assessment and improvement of the modelling practices
The second objective of the FlowRes project is to assess if the existing modelling practices that are commonly used for events with return period T up to 100year are still valid to predict the floodplain flow for T 1000-year.The main stake is to quantify uncertainties on computed water levels and velocities that are directly linked to the modelling of the various contributions to flow resistance.To this end, two different investigations will be carried out.

Numerical simulations against experimental data
The experimental data related to Task 1 will be compared to simulations with both industrial and research codes (1D, 1D+, 2D and 3D).The aim is twofold: (i) to evaluate the classical methodologies used by practitioners to model the different contributions to flow resistance (Manning-like coefficients, global drag coefficients, porous-media approach, topographic singularity) and (ii) to improve these methodologies to better capture the physics found in the laboratory experiments, irrespective of the return period T. We present here some results using a 1D+ approach, 2D modelling, and 3D modelling with a porous media approach.

1D+ simulation of non-uniform overbank flows with emergent rigid vegetation
The non-uniform flows experimentally investigated during sub-task 1.2 (see section 2.2) were simulated with a 1D+ model called the Independent Sub-sections Method ±ISM-, see Proust et al. (2016) [19].
The ISM consists in a system of 4 ordinary differential equations (3 momentum and 1 mass conservation equations) that computes the water level and the 3 sub-section-averaged velocities in the right-hand FP, MC and left-hand FP.The ISM is original among the 1D approaches because x 7KH ZDWHU VXUIDFH SURILOH LV VROYHG LQ HDFK VXE VHFWLRQ ' x 7KH sub-section head loss gradients can differ from one sub-section to another (S Hm 6 Hf ) x 7KH actual upstream discharges Q m and Q f and the downstream water level can be simultaneously accounted for x The lateral discharge per unit length q and the depth-averaged lateral Reynolds-stress W int , at the interface between MC and FP are explicitly computed.The volume drag force exerted by the stems is modelled by a formula of Nepf (1999) [16].The head loss in a sub-section i due to drag reads where U i = sub-section-averaged mean velocity, the frontal surface per unit volume a = NI = 0.81 m -1 , and C D = drag coefficient related to each stem.
According to Nepf (1999) [16], the lateral and longitudinal distances between two stems are here (Figure 3    The FlowRes project should lead to a valuable tool: a recommendation guide for the numerical simulation of extreme flood flows.This guide will rely on the comparison experimental database / numerical simulations (sub-task 2.1 in Table 1), but also on the simulation of floods at Besancon (sub-task 2.2), to address the issues related to changes in scale from laboratory to field in the high flow context.This guide will be designed for operational users and control authority.It should propose scientific responses to integrate all types of hydraulic roughness encountered in the field, depending on the flow magnitude, the land occupation of the FP, and on the type of numerical modelling (from 1D to 3D).In particular, the uncertainties associated to the different types of flow resistance modelling will be quantified.Lastly, it is also planned to share the experimental data collected during Task 1 in the various flumes with the international scientific community (the database could also be used for benchmarking).

Figure 1 .
Figure 1.PIV measurement system for measurements inside the canopy.The upper system is the camera with its telecentric lens to avoid any parallax effect.The lower system is a 200 mJ pulsed Nd-Yag laser connected to a parallel laser sheet generator.A 45° inclined mirror reflects the laser sheet vertically through the bottom of the flume.

Figure 2 .
Figure 2. Position of the measurement plane near the centre of the flume (left) and typical image of particles recorded by the camera (right) for plane 9.The specific optical setup shown in Figure 1 allows recording of particles even in the part of the flow that would be hidden by cubes.

Figure 4 .
Figure 4. Experiments of Dupuis (2016) [10], sub-task 1.2, compound channel with a longitudinal roughness transition over the FP.Flow depth D f and discharge Q f in the FP against downstream position x.
One of the experiments related to sub-task 1.3 is conducted at Laboratorio Nacional de Engenharia Civil (LNEC), in collaboration with the Instituto Superior Técnico, Lisbon, and Eidgenössische Technische Hochschule Zürich, Switzerland.The experimental work is being carried out in a compound-channel facility (Figure 5 ± Top).The channel is a 10 m long and 2 m wide symmetrical compound-channel, comprising a 0.6 m wide and 0.10 m deep MC and two adjacent FP 0.7 m wide.It is made of polished concrete with a bottom longitudinal slope of 0.0011 m/m.The two FP are covered with synthetic grass.Before the experimental tests with multiple obstacles in the FP, initial tests were conducted to investigate the effects of a single emerging cylindrical obstacle with 5 cm diameter, placed on the middle of the FP, on the characteristic flow processes.3D instant-velocity recordings are made by means of ADV measurements, with a sample frequency rate of 200 Hz and sampling duration of 180 s, towards the extraction of mean-flow characteristics including the velocity field (Figure 5bottom), flow-wise vs span-wise Reynolds Shear Stresses, turbulent intensities and variation of the apparent shear stress at the vertical interface of the abrupt velocity discrepancies.Following this experimental test, 3D structures and momentum-exchange processes at the interface of the MC and the FP will be characterized based on experimental tests with the cylindrical obstacle placed in the interface.

Figure 5 .
Figure 5. Experiments at LNEC (sub-task 1.3), compound section with dense meadow over the FP: (Top) test with a single circular cylinder; (bottom) normalized mean flow-wise velocity at the wake of a circular cylinder

Figure 6 .
Figure 6.Top view of the flume with positions of the SPIV vertical measurement planes, from Rouzès (2015) [14].Three different flow regimes were studied, generated with discharge rates Q of around 2.2 Ls -1 , 5.4 Ls -1 and 15.8 Ls -1 in order to reach water depth D equal respectively to 6 cm, 4 cm and 2 cm.These flow conditions yield values of the relative submergence h/D equal respectively to 0.33, 0.5 and 0.66.Measurements in the centre of the rough bed S1 for completely developed flow conditions (at position X5) were used to investigate the turbulent boundary layer structure above the canopy for high values of h/D, focusing in particular on the roughness sublayer extent and the log law parameters.These measurements and results are analysed in a separate publication (seeRouzès et al. (2016) [6]).Measurements in longitudinal vertical planes near the discontinuity of bed roughness (noted S1int in figure1) were used to investigate the flow structure at the interface between the two flow regions S1 and S2, and its development along the flume.Stereoscopic measurements give access to the three components of the flow in the laser sheet plane, allowing calculations of the different transverse fluxes of momentum.Preliminary analysis of the interfacial measurements (namely in S1int planes) show that secondary currents persist deep inside the roughness sublayer even for high values of h/D, as visible in Figure7.Stereoscopic PIV measurements in the transverse vertical plane located at X5 (see FigureX) were done at high frequency.Under the frozen turbulence assumption, time-series of u(y,z,t), v(y,z,t) and w(y,z,t) are transformed into a 3D-3C velocity field u(x,y,z), v(x,y,z) and w(x,y,z) providing useful experimental data for coherent structure analysis beside classical statistical approach.Following Vermaas et al. (2011)[15], both sets of experimental data will be used to quantify the contributions of the different processes responsible for

Figure 8 .
Figure 8. Experiments of sub-task 1.4: downstream view of the laboratory flume located at LMFA.

Figure 9 .
Figure 9. Experiments of sub-task 1.4: lateral view of the hydrodynamic balance.
± bottom) such that the interaction between the DOI: 10.1051/ 04004 (2016) , 6 E3S Web of Conferences e3sconf/201 FLOODrisk 2016 -3 rd European Conference on Flood Risk Management 7 0704004 cylinder wakes is negligible, resulting in a constant drag coefficientC D = 1.2.The results of the ISM simulations are shown in Figure10.Computations are carried out in considering or neglecting the horizontal turbulent mixing between the MC and the FP.The estimate of the flow depth D f and FP discharge Q f are in good agreement with the measurements for both the high (Top plot) and the medium (bottom plot) overbank flows.A higher discrepancy is observed for the interfacial Reynolds stress, W int , but as turbulent mixing is modeled by a simple mixing length model in the horizontal plane, results appear to be satisfactory.7KLVPHWKRG LV QRZ EHLQJ GHYHORSHG IRU ILHOG DSSOLFDWLRQV FRPSOH[ JHRPHWULHV XQVWHDG\ IORZV« 7KH ,60 LV EHLQJ LPSOHPHQWHG LQ WKH ' FRGH 0$*( ,UVWHD /\RQ 7KH VLPXODWLRQV ZRUN IRU ERWK LQEDQN DQG RYHUEDQN XQVWHDG\ IORZV ZKHQ FRQVLGHULQJ D XQLTXH ULYHU UHDFK 7KH WUDQVLWLRQ EHWZHHQ WZR VWHDG\ VWDWHV LV DOVR ZHOO PDQDJHG 7KH QH[W VWHSV DUH WKH FRPSDULVRQ ZLWK GDWD RI 7DVN WKH WUDQVLWLRQ IURP LQEDQN WR RYHUEDQN IORZV DQG WR DGGUHVV WKH LVVXH RI PXOWLSOH UHDFKHV FRQIOXHQFHV 3.1.2Simulation with Telemac 2D of non-uniform overbank flows with smooth floodplains Before coping with emergent of weakly submersed roughness elements, some preliminary 2D simulations of overbank flows with smooth FP are being carried out.The experimental data of Proust et al. (2013) [13] were used.The compound channel flume is 8m long, 1.2 m wide, with an asymmetrical cross-section (a 0.4m wide MC and 0.8m wide unique FP).The bank full height in the MC is 53 mm with a vertical bank between MC and FP.The non-uniform flows are caused by disequilibrium in the upstream discharge distribution between the MC and the FP.The simulations are carried out with the open source code TELEMAC 2D.The actual vertical bank is replaced by a sloping bank (horizontal: 50 mm / vertical: 53 mm).The mesh is composed of 2.5-long-edge triangles.A constant turbulent eddy viscosity is used, equal to 0.43u10 -3 m²/s, which is the depth-averaged value measured by Proust et al. (2013) [13] at downstream position x = 5.5 m at the interface MC/FP.At the upstream boundary condition (x = 2.5m), the sub-sectionaveraged velocities in the MC and FP, U m and U f , are imposed and equal to the experimental values.At the downstream boundary condition (x = 7m), a constant water level is imposed (measured value).A simulation of the lateral distribution of depthaveraged streamwise velocity, U d , and depth-averaged lateral Reynolds-stress, T xy , at downstream distance x=6.5m (last experimental measuring section) is shown in Figure11.The results clearly show that the 0 th order turbulence model cannot accurately predict the turbulent mixing between the two flows (MC and FP), except the peak Reynolds stress.By contrast, the simulated velocities are in good agreement with the measured ones.

Table 4
contains the typical ranges of the different non-dimensional parameters planned in the experiments.