IAHR Member Yann Peltier
email: yann.peltier90@gmail.com

Sébastien Proust

N Rivière

André Paquier
email: andre.paquier@irstea.fr

Koji Shiono
email: k.shiono@lboro.ac.uk

Sebastien Proust
email: sebastien.proust@irstea.fr

Nicolas Riviere
email: nicolas.riviere@insa-lyon.fr

Turbulent flows in

Keywords: Flood modelling, Flow-structure interactions, Laboratory studies, Separated flows, Turbulent mixing layers

come

Introduction

In natural or engineered rivers, the flow is contained in the main channel (m), limited 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 and consequently overflows on its adjacent floodplains (f). The resulting flow is identified as a compound channel flow.

Under uniform flow conditions, the fast and deep flow in the main channel interacts with the slow and shallow flow on the floodplains. This results in the formation of a mixing layer at the interface between the sub-sections (the main channel and the floodplains), which transfers momentum due to turbulent exchange between them [START_REF] Sellin | A laboratory investigation into the interaction between the flow in the channel of a river and that over its flood plain[END_REF]. This turbulent exchange leads to the decrease in the main channel conveyance and to the increase on the floodplain one. Moreover, the overall conveyance of the compound channel is reduced relative to the one of a single channel of same hydraulic radius (Knight and[START_REF] Knight | Floodplain and main channel flow interaction[END_REF][START_REF] Knight | Boundary shear in symmetrical compound channels[END_REF]. [START_REF] Knight | Turbulence measurements in as shear layer region of a compound channel[END_REF] and [START_REF] Shiono | Turbulent open channel flows with variable depth across the channel[END_REF] showed that for such flow conditions, the depth-averaged Reynolds shear stress representative of the turbulent exchange, T xy = u v ρ -′ ′ ( u′ and v′ the horizontal components of the fluctuating velocity, the depth-averaging operator and ഥ the time-averaging operator), is maximal at the junction between the sub-sections. They also found that for a given floodplain width, the lateral extent of the high shear region between the channel sub-sections and the maximum of T xy , are inversely proportional to the relative flow depth, H r = H f /H m (H f and H m , the mean water depth on the floodplain and in the main channel respectively), while they increase with the floodplain width and a constant H r . According to [START_REF] Van Prooijen | Momentum exchange in straight uniform compound channel flow[END_REF], the behaviour of T xy within the mixing layer must be linked to the difference in velocity between the subsections, U m -U f (U m and U f are the longitudinal mean velocity in the main channel and on the floodplain respectively), and to the lateral gradient of the depth-averaged longitudinal velocity, /

d U y ∂ ∂ .
The turbulent exchange between the sub-sections also depends on channel geometries according to results of three types of geometries, which were studied in the past:

• Prismatic geometry with a disequilibrium in the upstream discharge distribution [START_REF] Bousmar | Upstream discharge distribution in compound channel flumes[END_REF][START_REF] Proust | Effect of different inlet flow conditions on turbulence in a straight compound open channel[END_REF], 2013),

• Non prismatic geometry with a continuous variation in the floodplain width, the overall width being constant along the channel, as skewed compound channels [START_REF] Elliot | Serc flood channel facility: skewed flow experiments[END_REF]Sellin 1990, Chlebek andKnight 2008) and compound meandering channels [START_REF] Shiono | Complex flow mechanisms in compound meandering channels with overbank flows[END_REF],

• Non prismatic geometry with a variable overall width, as symmetrically converging floodplains [START_REF] Bousmar | Overbank flow in symmetrically narrowing floodplains[END_REF], symmetrically diverging floodplains (divergence angle smaller than 5.8°; [START_REF] Proust | Ecoulements non-uniformes en lits composés : effets de variations de largeur du lit majeur[END_REF], Bousmar et al. 2006) and compound channel with an abrupt floodplain contraction (convergence angle of 22°; [START_REF] Proust | Flow in compound channel with abrupt floodplain contraction[END_REF].

These flows were defined as gradually varied flows. In these experiments, each channel either yields or receives water from its adjacent channel(s); this exchange of mass, along with nonnegligible lateral velocities, generates noticeable additional lateral exchange of streamwise momentum that superimposes to the turbulent exchange between the sub-sections (Proust et al. 2009[START_REF] Proust | Energy losses in compound open channels[END_REF]. According to [START_REF] Proust | Turbulent non-uniform flows in straight compound open-channels[END_REF], the direction and the intensity of the lateral velocity induce changes in the lateral distribution of the local Reynolds shear stress,

u v ρ - ′ ′ u v ρ ′ ′ -
, by stretching the coherent structures that develop inside the mixing layer. When mass is transferred from the floodplain to the main channel, the region of high turbulent shear is displaced towards the main channel. Both the maximum of T xy and the lateral extent of the high shear region are lowered. When mass is transferred towards the floodplains, the high shear region widely extends on the floodplains and the peak of T xy at the sub-sections junction is enhanced.

In natural or manmade rivers, the floodplains may rapidly vary with obstacles either natural (natural levees, rock slide) or artificial (embankments for railways and motorways).

Author-produced version of the article published in Journal of Hydraulic Research (2013), 51,4, p. 446-458 The original publication is available at http://www.tandfonline.com/, DOI: 10.1080DOI: 10. /00221686.2013.796499 .796499 This has various implications for risk assessment and river geomorphology. The considered embankment here acts as an asymmetric, partial dam which causes an elevation of the water depth in the whole upstream channel. The flow on the floodplain is then constricted by the obstacle, which promotes the development of two recirculation zones, one upstream from the obstacle and one downstream. Silting can occur in these slack-flows. Oppositely, the flow has to skirt the embankment and its acceleration, causes scouring and can possibly blow away goods or people. When focusing on the flow description, it results in significant variations of the flow section and in the generation of strong lateral mass exchange (relatively to gradually varied flows) between the sub-sections [START_REF] Proust | Ecoulements non-uniformes en lits composés : effets de variations de largeur du lit majeur[END_REF][START_REF] Bourdat | Débordements des cours d'eau en présence de remblais routiers dans les lits majeurs[END_REF][START_REF] Peltier | Physical and numerical modelling of overbank flow with a groyne on the floodplain[END_REF], 2009).

This type of flow commonly occurs in the fields, but has been rarely studied. Among the few studies dealing with overbank flows with an obstacle on the floodplain [START_REF] Proust | Ecoulements non-uniformes en lits composés : effets de variations de largeur du lit majeur[END_REF][START_REF] Peltier | Physical and numerical modelling of overbank flow with a groyne on the floodplain[END_REF], the results indicated that 2D-H numerical modelling has some difficulties in capturing the recirculating flows and that the physics of the mixing layers in the channel is still not well understood. Additional detailed measurements of the turbulence characteristics and of boundary shear stress are required, along with some theoretical developments. The understanding of overbank flows in compound channel with a transversal obstacle blocking off the floodplain is indeed paramount for flood modellers. The accurate estimation of the characteristics of the one hundred year return period flood, for instance, is necessary for designing unsinkable motorway and railway embankments [START_REF] Lefort | Mécanisme de l'écoulement à surface libre. In De la goutte de pluie jusqu'à la mer : traité d'hydraulique environnementale[END_REF].

Moreover, as part of the establishment of flood hazard prevention plans, flooded area in the vicinity of embankments must be determined with minimal uncertainties.

The present study then aims at assessing the effects on the hydraulic parameters of the superposition of two types of flows: (i) a rapidly varied flow in the vicinity of a thin embankment and (ii) a compound 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 compound channel

The present experiments were conducted in an experimental flume located at the Laboratoire de Mécanique des Fluides et d'Acoustique (LMFA, Lyon, France). The flume has a length, L, of 8 m and a total width, B, of 1.2 m. This flume is straight with an asymmetrical crosssection and has a longitudinal bed-slope, S ox , of 0.18 %. The main channel cross-section is rectangular (Figure 1) and is 0.4 m wide. The bank-full height, b, is of 5.1 cm and the floodplain is 0.8 m wide. The floodplain and the main channel are PVC made and their surface state is smooth.

Following the recommendations of [START_REF] Bousmar | Upstream discharge distribution in compound channel flumes[END_REF], separated inlet tanks for the main channel and the floodplain were installed (see schematic top view in Figure 1). They are used to distribute the required discharges 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 canalised by a succession of grids and the free surface oscillations are attenuated by a float. The outlet consists of two independent adjustable tailgates, one for each sub-section. The separated tailgates enable a better adjustment of the downstream boundary conditions by reducing the backwater effects and the lateral mass exchange between the sub-sections at the far end of the flume.

In the present paper, we use a Cartesian coordinate system in which x, y and z are the longitudinal, lateral and vertical directions, respectively (as presented in Figure 1). x = 0 immediately downstream from the inlet tanks and y = 0 at the lateral bank of the floodplain.

z is taken along a plan following the mean slope of the flume and obtained by the root mean square method. The origin of the plan is taken in the main channel.

Measurements devices

Water depth and level

The water depths and the water levels were measured using an ultrasonic probe (Baumer Electric, UNDK 20I 6912 S35A). The uncertainty of the probe was estimated to ±0.42 mm for a recording time greater than 20 s.

Mean and instantaneous velocity

A micro-propeller (Nixon, Streamflo Velocity Meter 403) was coupled to a vane and an encoding angle device for simultaneously measuring the flow direction and the mean velocities. The recording time was set to between 60 s and 90 sdepending on the lateral position in the flumeto ensure an accurate estimation of the mean and standard deviation of the velocity. With such recording time, the uncertainties were estimated to 1.5 % of the mean velocity.

Measurements of instantaneous velocities were performed using a 2D side-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 dB in order to have weak influences of the noise [START_REF] Mclelland | A new method for evaluating errors in highfrequency ADV measurements[END_REF]. The recording time was set at least to 3 min to ensure an accurate estimation of the mean and standard deviation of the signal.

The uncertainties for the estimated Reynolds stresses from the instantaneous velocities were minimised. The measured velocity signals were despiked using the method of [START_REF] Goring | Despiking acoustic doppler velocimeter data[END_REF] and the probe misalignment was estimated and corrected using the methods presented in [START_REF] Peltier | Physical modelling of overbank flows with a groyne set on the floodplain[END_REF].

Boundary shear stress

The boundary shear stress was measured with a Preston tube (outer diameter of 2.72 mm) using the calibration law specified by [START_REF] Patel | Calibration of the Preston tube and limitations on its use in pressure gradients[END_REF]. For each experiment, the Preston tube was aligned with respect to the longitudinal direction and the uncertainty was within 6 % of the measured boundary shear stress [START_REF] Preston | The determination of turbulent skin frictions by means of pitot tubes[END_REF]. In case of large lateral velocities, a correction coefficient was applied to the pressure measurements for taking into account the fact that the Preston is no longer aligned with the main flow direction. The correction coefficient was worked out by measuring the resulting pressure when the Preston tube was turned by a known angle in a uniform flow.

Measurement grid

The measuring devices were mounted on a movable carriage moving on a metal frame in the vicinity of the flume. This metal frame is independent of the flume and has the same longitudinal mean slope as the flume. The carriage was programmable and was moved through a DC motor with an accuracy of ±0.2 mm in both x-and y-directions.

Along the y-axis, the grid-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) and 2.5 or 5 cm from y = 0.85 m to y = 1.15 m. The grid-step along the x-axis

was not regular and depends on the measuring device used. The water depth and the mean velocity were measured at every 0.5 m from x = 1.5 m to x = 3.5 m (the embankment is placed at x e = 2.5 m) and then at every 1 m until the end of the flume. The instantaneous velocity and the boundary shear stress were measured 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 and two downstream from the embankment at x = 4.5 m and 6.5 m. Along the z-axis, the velocity was measured at least at 2 vertical positions on the floodplain for the shallowest case and at 6 vertical positions for the deepest case.

Flow conditions

The total discharge and the length of the embankment were chosen in order to examine a large range of flow conditions, with in particular a large mass exchange between sub-sections.

In these experiments, the mass exchange was generated by a transverse embankment set on 1), with the boundary conditions used for the reference flows, i.e. the same upstream discharge distributions and height of the tailgates.

To analyse the flow conditions, we first consider the longitudinal lengths of the recirculation zones that develop upstream ( u x L ) and downstream ( d x L ) from the embankment (see the fifth and sixth columns in Table 1). u with an embankment (not shown in Table 1). This generates a constricted cross-section in the flow. Regarding the normalised length /

d x d
L , it decreases with increasing d/B f or decreasing Q t , therefore emphasising the role of the bed-generated turbulence in the development of the recirculation zone [START_REF] Chu | Friction and confinement effects on a shallow recirculating flow[END_REF][START_REF] Rivière | Recirculating flow behind groynes for compound channel geometries[END_REF][START_REF] Peltier | Physical modelling of overbank flows with a groyne set on the floodplain[END_REF]. Considering the Reynolds number in the sub-sections, R i = 4R i U i /ν (ν the kinematic viscosity, U i and R i respectively the mean velocity and the hydraulic radius in a subsection), the values in the main channel are one order of magnitude greater than those on the floodplain (see seventh and eight columns in Table 1). However, the Reynolds numbers in both sub-sections are sufficiently high to neglect viscosity effect in the computation of the stresses. Finally the minimal and the maximal relative flow depths (last column in Table 1) indicate very weak longitudinal variations in the flow depth for the reference flows, while significant variations are observed for the flowcases with an embankment: for such flow conditions, the depth on the floodplain can be twice higher than that measured without an embankment.

Author-produced version of the article published in Journal of Hydraulic Research (2013), 51,4, p. 446-458 The original publication is available at http://www.tandfonline.com/, DOI: 10.1080/00221686.2013.796499

In the following sections, the flow-cases are referenced in the form Q/d, where Q is the total discharge and d the embankment length. Reference cases have d = 0.0 (see in Table 1).

A rapidly varied flow

In this section, we show how the embankment set on the floodplain generates a rapidly varied flow on the floodplain and in a lesser extent in the main channel.

Water depth and level

The left plots in Figure 2 show the longitudinal variations in the floodplain water depth, H f .

Putting aside the most downstream position and the three first meters for flow-case 17.3/0.0, a constant flow depth (to the uncertainty) is observed in the flume for the reference flows. The increase in depth at the end of the flume is due to a slight backwater effect caused by the difference in level between the bottom of the flume and the bottom of the tailgates. Regarding the decrease in depth at the inlets (particularly marked for 17.3/0.0), it is due to the grids in the reservoir that induce a strong head loss and a plunging flow at the channel entrance. For the embankment-cases, the embankment induces strong variations in the water depth and the distortions (relative to the reference flows) are felt until the end of the flume. On the floodplain near the embankment the longitudinal mean slope of the free surface, S wx , is one order of magnitude greater than the longitudinal mean slope of the bed (S ox = 0.18 %) and the steepness of this slope increases with both the embankment length (S wx ൎ 1.5 % for 24.7/0.3 and S wx ൎ 3 % for 24.7/0.5) and the total discharge (S wx ൎ 1 % for 17.3/0.3 and S wx ൎ 4 % for 36.2/0.3). It is interesting to see that the water depth at the end of the flume is equivalent to the uniform one for most flows with an embankment. This seems to indicate that, in our short flume, the recirculation is hardly affected by any backwater effects coming from the downstream condition, though a uniform lateral velocity profile is not recovered.

The lateral distribution 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 and 36.2/0.3. The lateral mean slope of the free surface, S wy , can be of the same order of magnitude as S ox in the zone of large lateral velocities. This slope increases with both the embankment length (S wy ൎ 0.25 % for 24.7/0.3 and S wy ൎ 1 % for 24.7/0.5) and the total discharge (S wy ൎ 0.

Depth-averaged velocity

Figure 3 shows the 2D fields of the longitudinal and lateral depth-averaged velocities (U d , V d ).

The embankment and the resulting recirculation zones (Table 1) are responsible for large variations in the flow section, therefore leading to significant lateral depth-averaged velocities This width is also modified by the embankment, as shown in section 4.

Froude number

A typical distribution of the local Froude number, F =

2 2 / d d U V gh +
(h the local water depth), is presented in Figure 4 (flow-case 24.7/0.3). Because of the large velocities (see in

Figure 3) and the relatively low water depths on the floodplain (see H f in Figure 2), Froude numbers higher than 0.5 are found for all flow-cases with the embankment. Moreover, the flow becomes supercritical from the contraction until at least the half of the downstream recirculation zone. This supercritical zone expands with both the total discharge and the embankment length. The transition from the supercritical to the subcritical regime is operated through a normal undulated jump consistent with the maximal Froude number smaller than 1.7 [START_REF] Graf | Hydraulique fluviale: écoulement et phénomènes de transport dans les canaux à géométrie simple[END_REF]. By contrast, the flow in the main channel is always subcritical.

Lateral mass exchange

100 / ref ref f f f Q Q Q × - .
The exchange of mass between the sub-sections occurs until the end of the flume for each case and the longitudinal variation in the floodplain discharge increases with the embankment length, but decreases with the total discharge. The minimal floodplain discharge is reached near the contracted cross-section: the floodplain can here lose up to 65 % of its discharge (flow-case 24.7/0.5).

To get a deeper insight into the lateral mass exchange, the Figure 5(b) shows the longitudinal variations in the normalised intensity of the lateral mass exchange per unit length:

d f n f Q q Q = - (1)
defined at the junction between the sub-sections (a mass exchange from the floodplain towards the main channel corresponds 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 compound channel, it does not exceed 0.2 for the most extreme case [START_REF] Proust | Effect of different inlet flow conditions on turbulence in a straight compound open channel[END_REF][START_REF] Proust | Turbulent non-uniform flows in straight compound open-channels[END_REF]: the initial objective of working with larger mass exchanges is then achieved. The strongest exchanges are observed in the cross-sections near the embankment and 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 discharge has little effect on the variations of q n .

Time-averaged local velocity

The time-averaged longitudinal velocity, u , is displayed in Figure 6 for the flow-case 24.7/0.0 at x = 5.5 m (where the reference flow is almost established; Peltier 2011) and 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) and x = 4.5 m (downstream from the embankment). Notice that missing data in some of the contour plots in Figure 6, is due to the metrological considerations: intrusive device and low water depths in some cross-sections. Regarding the flow-case 24.7/0.0, the inflection of the isovels in the main channel clearly emphasises the presence of secondary currents of Prandtl's second kind [START_REF] Tominaga | Turbulent structure in compound open channel flow[END_REF]. These secondary current cells are due to the presence of the two vertical solid boundaries in the main channel. By contrast, the presence of secondary 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 floodplain towards the main channel (flow-case 24.7/0.5 at x = 2 m and x = 2.5 m in Figure 6), some slow water enters the upward part of the main channel until the centreline (above the bank-full level) and also the downwards part of the main channel near the floodplain edge, which destroy the secondary 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 towards the floodplain (flow-case 24.7/0.5 at x = 4.5 m in Figure 6), the flow in the main channel and on the floodplain is homogenised by the mass exchange and only boundary layers at the walls can be observed. Once the reattachment point of the downstream recirculation zone is reached and q n is close to zero, the flow in both sub-section starts establishing a typical compound channel flow.

Interaction between a rapidly varied flow and a compound channel flow

In this section, we discuss how the parameters usually studied in compound channel flows are affected by the lateral mass exchange induced by the embankment on the floodplain. Figure 7 then shows b τ for the flow-cases with the embankment 24.7/0.3, 24.7/0.5 and 36.2/0.3. The boundary shear stress on the floodplain at x = 2 m (upstream from the embankment and q n > 0) decreases compared to those measured for reference flows, because of the rise in the water depth and of the flow deceleration. This decrease is even larger when the embankment length is longer or the discharge is higher. By contrast, in the embankment cross-section, at x = 2.5 m, the boundary shear stress rapidly increases, as the flow here is plunging and is strongly accelerated close to the bottom. Downstream from the embankment where q n < 0, the boundary shear stresses measured at x = 4.5 m and x = 6.5 m out of the downstream recirculation zone can be 375 % greater than those measured on the floodplain under uniform flow conditions. These changes are due to the strong flow acceleration and the very shallow flow related to the supercritical flow regime (Figure 4). It can be noticed that the distribution of boundary shear stress on the floodplain does not coincide with the referenceflow one as long as the downstream recirculation zone has not reattached (see flow-cases 36.2/0.0 and 36.2/0.3 at x = 6.5 m in Figure 7).

Boundary shear stress

Mixing layer between the sub-sections

U 1 and U 2 are the mean longitudinal velocities worked out with the depth-averaged velocities located in the outside of the mixing layer in the main channel and in the floodplain respectively. We can define the lateral location y α (x) for 0 < α < 1 such that the longitudinal depth-averaged velocity, U d , writes:

( ) 2 1 2 , ( ) ( ) d U x y x U U U α α = + - (2)
The width of the mixing layer, δ(x), can be defined as follows [START_REF] Van Prooijen | Momentum exchange in straight uniform compound channel flow[END_REF]:

( ) 0.75 0.25 ( ) 2 ( ) ( ) x y x y x δ = - (3)
and the centre of the mixing layer, y c , is defined as being equal to y 0.5 .

The Figure 8(a) shows the longitudinal variations in the mixing layer width, δ(x), for the embankment-cases, compared to the width, ( ) ref x δ , of the reference flows. As long as the recirculation zone is present in the measurement cross-section (from

u e x x x L ≈ - until d e x x x L ≈ + ), δ(x) is smaller than ( ) ref x δ , because the velocity difference, U m -U f (see in
Figure 3), is smaller than that for the reference flows (not shown here); e.g. the flow contraction induces an increase in the floodplain velocity higher than the increase in the main channel velocity. Upstream and downstream 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), does not always follow the geometrical forcing created by the floodplain edge. On the one hand, y c (x) is shifted in the main channel when the normalised intensity of the lateral mass exchange per unit length q n > 0 and the shift is proportional to q n . On the other hand, it seems to remain on the floodplain edge for q n < 0 as observed by [START_REF] Proust | Turbulent non-uniform flows in straight compound open-channels[END_REF] in a straight compound channel with a similar value of q n . The shape of the mixing layers that develop in the flow-cases 24.7/0.0, 24.7/0.3 and 24.7/0.5 are displayed in Figure 8(c). The part of the mixing layer on the floodplain is highly impacted by the lateral mass exchange and for the most extreme cases (see flow-case 24.7/0.5), the mixing layer can even disappear where q n is maximum.

Reynolds shear stress

The Figure 9(a) shows the lateral distribution of the depth-averaged Reynolds shear stress, T xy , for the three reference-cases at the downstream position x = 5.5 m, where the flows were established in term of water depth and longitudinal depth-averaged velocity. The lateral extent of the high shear region between the channel sub-sections is close to δ ref (x) (not shown here) and as observed in the literature for vertical banks, the maximum of T xy is located at the subsections' junction. The magnitude of the maximum of T xy is inversely proportional to the relative flow depth H r and is proportional to the velocity difference between the sub-sections U m -U f : max(T xy ) = 1.28 Pa and 0.57 Pa, U m -U f = 0.33 m s -1 and 0.17 m.s -1 , and H r = 0.2 and 0.4 for cases 17.3/0.0 and 36.2/0.0 respectively. These results confirm the relationship between T xy and H r under uniform flow conditions with a constant floodplain width [START_REF] Shiono | Turbulent open channel flows with variable depth across the channel[END_REF].

Author-produced version of the article published in Journal of Hydraulic Research (2013), 51,4, p. 446-458 The original publication is available at http://www.tandfonline.com/, DOI: 10.1080/00221686.2013.796499

The lateral distribution of the depth-averaged Reynolds shear stress, T xy , is strongly correlated to the lateral gradient of the depth-averaged longitudinal velocity, / The lateral extent of the high shear region also coincides with the one of δ(x). When q n > 0 (Figure 10(a)), the lateral extent reduces with an increase in the embankment length or in the total discharge. By contrast, when q n < 0, the variations in the lateral extent are not so 3). This is due to the presence of the velocity dip in the distribution of U d near the sub-sections junction, as demonstrated by [START_REF] Nezu | Coherent horizontal vortices in compound open channel flows[END_REF]. This behaviour is observed from the contraction to at least the half of the downstream recirculation (i.e. while both mixing layers can interact). Finally, the very large peak of Reynolds stress at the sub- sections' junction at x = 4.5 m for case 24.7/0.5, which is related to an almost discontinuity of velocity, highlights an extremely high turbulent diffusion that can lead to bank erosion.

Conclusion

The 375 % greater than those of the reference flows. The mixing layer developing at the interface between the sub-sections is also highly affected by the embankment, the recirculation zones and the lateral mass exchange. As long as a recirculation zone is present in the measurement cross-section, the mixing layer width remains smaller than the reference flows one and the turbulent exchange (i.e. depth-averaged Reynolds shear stress) is strongly affected. The magnitude of the peak of depth-averaged Reynolds 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 besides not always located at the junction: it is shifted in the main channel when mass is transferred from the floodplain towards the main channel and remains at the sub-sections' junction in the opposite direction. Nevertheless, the Boussinesq hypothesis can still be used in first approach for describing the evolution of the high shear region.

Thanks to the present data-set (depth, velocity, boundary shear stress, Reynolds stress), further work could be devoted to numerically model such rapidly varied compound channel flows in 1D and 2D-H [START_REF] Linde | Errors in 2-D modelling using a 0th order turbulence closure for compound channel flows[END_REF]).

• Concerning 1D modelling, the description of the turbulent exchange at the interface between the sub-sections is paramount for calculating the discharge distribution between sub-sections. The present results are of interest to modellers for improving its modelling, since for now only the shear at the interface between the sub-sections is considered (apparent shear stress, mixing length model…), and assumed to be maximum [START_REF] Nicollet | Ecoulements permanents à surface libre en lit composés[END_REF]Uan 1979, Proust et al. 2009).

• Concerning 2D modelling, we showed that the Boussinesq hypothesis is still valid for flows with embankment, which is interesting for low-cost modelling in an operational point of view. We also highlighted the behaviour of the secondary currents in the presence of an embankment, which could be used to correct the shallow water equations by adding terms taking into account the dispersion on the vertical of the horizontal velocities [START_REF] Peltier | Physical modelling of overbank flows with a groyne set on the floodplain[END_REF].

Lagouy for their technical support. The authors also thank the anonymous reviewers for their advices.

Notation

xL

  is close to d for the upstream recirculation zone and the lateral extent L y (x) is never larger than d. By contrast, d x L increases with the total discharge and the embankment length, and the lateral extent L y (x) of the downstream recirculation zone can reach 1.1 × d between x = 2.75 m and x = 3.25 m for the six flow-cases

  Figure 3): upstream from the contraction, the lateral velocities are positive and the flow converges from the floodplain towards the main channel; downstream, the flow diverges from the main channel towards the floodplain. The comparison of the distribution of the longitudinal depth-averaged velocity with the reference flow emphasises that as long as a recirculation zone is present in the measurement cross-section the velocity difference, U m -U f , decreases while the maximum of the velocity gradient within the mixing layer, / d U y ∂ ∂ , increases. Indeed / d U y ∂ ∂ also depends on the width of the mixing layer that develops between the channel sub-sections.

Figure 5

 5 Figure 5(a) shows the longitudinal variation in the floodplain discharge compared to that for the reference flows,

Figure 7

 7 Figure 7 first shows typical distributions of boundary shear stress, b τ , measured under uniform flow conditions with no embankment on the floodplain (at x = 4.5 m). The boundary shear stress on the floodplain is always smaller than that in the main channel and it increases with the total discharge. The changes in b τ are smaller in the main channel, since the changes in the velocity are smaller in the main channel than in the floodplain.

  constant turbulent eddy viscosity, ν t , equal to 0.3 × 10 -3 m²s -1 in order to respect the dimension 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 and 36.2/0.3 are displayed in Figure10at various locations along the channel. Similarly to the reference flows (Figure9(a)), the position of the maximum of T xy coincides with y c (x) (see in Figure8(b)). By contrast, the magnitudes of the maximum of T xy can be 3 or 5 times greater or smaller than those measured for the reference flows. It can be noticed that a secondary maximum is also observed on the floodplain downstream from the embankment (see at x = 4.5 m for 24.7/0.5 in Figure10(c)) and exists as long as the downstream recirculation has not reattached. This secondary maximum is due to the mixing layer that develops between the recirculation zone and the main flow.

  clear (see at x = 4.5 m in Figure10(c)), because the second mixing layer that develops between the downstream recirculation zone and the main flow constrains the floodplain flow and prevents the mixing layer between the sub-sections from spreading too far on the floodplain.All the modifications undergone by the turbulent exchange within the mixing layer are due to the changes imposed by the lateral mass exchange to the distribution of the longitudinal velocity in the flume. The right plots in Figure10show the lateral distribution of the depth-averaged longitudinal velocity, U d , in the same cross-sections as those for T xy . As shown in Figure10(a-b: upstream and in the embankment cross-section), the lateral extent of the high shear region is proportional to the velocity gradient, / the maximum of T xy is proportional to U m -U f . When considering the stations downstream from the embankment (see at x = 4.5 m in Figure10(c)), the lateral extents of the high shear region can be smaller than that measured upstream from the embankment although /

  present paper investigates experiments in a compound open-channel with a transverse embankment on the floodplain. The embankment creates a rapidly varied flow on the floodplain, which subsequently interacts with the flow in the main channel. Each varied flow is compared to the reference flow obtained under uniform flow conditions in the same flume.The embankment and the recirculation zones that develop upstream and downstream are responsible for a strong lateral mass exchange, which induces significant changes in the water depth and the velocity distribution across the compound channel, when compared to the reference flows. The mean slopes of the free surface (lateral and longitudinal) can be one order greater than the mean bed-slope and the lateral depth-averaged velocity near the embankment can reach 50 % of the longitudinal depth-averaged velocity. Moreover, because of the low water depth and the high velocity on the floodplain downstream from the embankment, a supercritical flow occurs until at least the half length of the downstream recirculation zone.These changes have also great impacts on the parameters more specific to compound channel flows. It confirms the implication for flood risk assessment and geomorphology mentioned in the introduction. While the increase in water depth can reach about 50% in the floodplain upstream the embankment, the 3D flow at the tip of the embankment and the acceleration in the supercritical zone downstream, induce boundary shear stresses up to

b

  Figure is not to scale).

Figure 2 (

 2 Figure is not to scale).

Figure 3

 3 Figure 3 2D depth-averaged velocity fields for flow cases (a) 17.3/0.3, (b) 24.7/0.3, (c) 24.7/0.5 and (d) 36.2/0.3 (presented in Table 1). The coloured surfaces represent the velocity intensity. The separation line between the recirculation zones and the main flow is identified by the bold black line. Uncertainty: δU d /U d = ±1.5 % and δV d /V d = ±1.5 %.

Figure 4

 4 Figure4Froude number distribution for flow-case 24.7/0.3 (presented in Table1). The black dashed line corresponds to F = 1.

Figure 6

 6 Figure 6 Cross-flow distribution of time-averaged longitudinal velocity, u , for flow-cases 24.7/0.0 and 24.7/0.5. Uncertainty: δ / u u = 1.5 %.

Figure 7

 7 Figure7Lateral distribution of boundary shear stress, τ b , measured under uniform flow conditions for flow-cases 17.3/0.0, 24.7/0.0 and 36.2/0.0 and with an embankment for flowcases 24.7/0.3, 24.7/0.5 and 36.2/0.3 (Table1). Uncertainty: δτ b /τ b = ±6 %.

Figure 8

 8 Figure 8 (a) Longitudinal variations in the width, δ(x), of the mixing layer developing between the sub-sections for the flow-cases with an embankment compared to the width, δ ref (x), of the corresponding reference flows. (b) Position of the centre, y c (x), of the mixing layer. (c) y c (x) and outer boundaries, y 25 (x) and y 75 (x), of the mixing layer for the flow-cases 24.7/0.0, 24.7/0.3 and 24.7/0.5. Uncertainty: δδ(x) = ± 2.5 cm, δy α (x) = ±1 cm.

Figure 9

 9 Figure 9 (a) Lateral distribution of depth-averaged Reynolds shear stress, T xy , measured at x = 5.5 m for the reference flow-cases. (b-d) T xy compared to / d U y ∂ ∂ .

Figure 10

 10 Figure 10 Lateral distributions of the depth-averaged Reynolds shear stress and depthaveraged longitudinal velocities for the flow-cases 24.7/0.3, 24.7/0.5 and 36.2/0.3 at three downstream distances.

  -produced version of the article published in Journal of HydraulicResearch (2013), 51,4, p. 446-458 The original publication is available at http://www.tandfonline.com/, DOI: 10.1080/00221686.2013.796499

	2 % for 17.3/0.3 and S wy ൎ 0.8 %
	for 36.2/0.3). A transverse flow is observed 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 undulated hydraulic jump at this station makes locally rise the water level (see subsection 3.3).

Author

  Author-produced version of the article published in Journal of HydraulicResearch (2013), 51,4, p. 446-458 The original publication is available at http://www.tandfonline.com/, DOI: 10.1080/00221686.2013.796499

  Author-produced version of the article published in Journal of HydraulicResearch (2013), 51,4, p. 446-458 The original publication is available at http://www.tandfonline.com/, DOI: 10.1080/00221686.2013.796499

  Author-produced version of the article published in Journal of HydraulicResearch (2013), 51,4, p. 446-458 The original publication is available at http://www.tandfonline.com/, DOI: 10.1080/00221686.2013.796499

  The lengths of the recirculation zones were assessed by Large Scale Particle Imaging Velocimetry

	Table 1
	embankment
	17.3/0.0
	24.7/0.0
	36.2/0.0
	17.3/0.3
	17.3/0.5
	24.7/0.3
	24.7/0.5
	36.2/0.2
	36.2/0.3

(Hauet et al.

Acknowledgements

The research was funded by IRSTEA and by the Rhône-Alpes region (SRESR -EXPLORA'DOC 2008 Bourse Cluster 6). The authors are grateful to F. Thollet and M.


Jacques Jayez

Valeria Mongelli

Anne Reboul

Jean-Baptiste Van Der Henst

Weak and strong triggers

Keywords: Experimental Perspectives on Presuppositions, Studies in Theoretical Psycholinguistics Series, Springer

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Presupposition triggers are often felt to presuppose more or less 'strongly'. For instance, whereas (1b) strongly gives rise to the inference that Paul has missed the point, (1a) does not. Verbs like discover, realize or know are generally considered Jacques Jayez ENS de Lyon and L2C2, CNRS, Lyon, France -e-mail: jjayez@isc.cnrs.fr

Valeria Mongelli

Institut du Cerveau et de la Moelle Épinière Research Center, Institut National de la Santé et de la Recherche Médicale, U975 Paris, France -e-mail: valeria.mongelli@ens.fr Anne Reboul L2C2, CNRS, Lyon, France -e-mail: reboul@isc.cnrs.fr Jean-Baptiste van der Henst L2C2, CNRS, Lyon, France -e-mail: vanderhenst@isc.cnrs.fr to be 'weaker' than regret, in that they do not (always) give rise to an intuition of entailment.

(1) a. If Paul realizes he has missed the point, he will probably reformulate his objection. b. If Paul regrets he has missed the point, he will probably reformulate his objection.

This kind of observation, originating with [START_REF] Karttunen | Some observations on factivity[END_REF], suggests that presupposition triggers might differ in their presuppositional strength. Parallel observations for adverbials like too or again or clefts, as opposed to aspectual verbs like stop, might be taken to reinforce this impression.

(2) a. If Paul missed the point again, this proves that he does not really understand the subject.

Paul has missed the point before b. Maybe Paul is quitting smoking or something. That would explain why he is so edgy.

Paul smokes

More recently, [START_REF] Abusch | Lexical alternatives as a source of pragmatic presuppositions[END_REF]2010) has argued for a distinction between hard and soft triggers on the basis of a simple test. The presupposition of soft triggers like win can be accommodated in the antecedent of a conditional although their truth is explicitly suspended, whereas that of hard triggers like too cannot.

(3) a. I don't know if Paul participated in the race, but, if he won, he must be very proud. b. I don't know if Paul participated in the race, but if Mary participated ?? too they probably had a drink together just after.

In this paper we examine the distinction between weak (aka soft) and strong (aka hard) triggers from an experimental point of view. In section 1.2 we examine the major recent works relevant to the weak/soft distinction. In section 1.3, we present two experiments in French and discuss the results in section 1.4. Although we do not reject the weak/strong distinction altogether, our findings lead us to adopt a more nuanced view. In view of the experimental results, the most plausible conclusion is that the distinction is not purely lexical but results from the combination of a number of independent factors.

Weak and strong triggers

It is a truism that the literature on presuppositions is potentially confusing. The interesting question is why. Why should presuppositions be more difficult to describe and categorize than other semantic or pragmatic phenomena? It seems that the main reason is an unresolved tension between two types of evidence.

On the one hand, there are the so-called projection tests. Putting a trigger in the scope of certain operators preserves the presupposition, although the very same operators cancel or suspend the main content. Negation, interrogation, if -clauses and modal verbs are well-known cases, see [START_REF] Beaver | Presupposition[END_REF][START_REF] Chierchia | Meaning and Grammar: An Introduction to Semantics[END_REF][START_REF] Geurts | Presuppositions and Pronouns[END_REF] for different surveys. For instance, (4) suspends the truth of the main content (the event of Paul forgetting to lock his car) but keeps the presupposition that Paul has a car alive. In such cases, the presupposition is said to project.2 (4) Maybe Paul forgot to lock his car.

On the other hand, it has been observed repeatedly that projection is not a stable property. From browsing through the literature, one might get the impression that non-projection concerns only a small subset of carefully chosen examples. However, it is not difficult to find less well-known cases. In (5a), where 'F' marks new information, it is possible that no one guessed the secret word, although only A normally presupposes that A. In (5b), it is possible that Paul arrived just before running out of power and had time to load his battery, thus preventing any breakdown.

(5) a. If only [Wilma] F guessed the secret word, she has won A C100. [START_REF] Geurts | Interpreting focus[END_REF], example 33b) b. Paul arrived just before his car broke down.

So there is a potential conflict between two sets of observations. A straightforward way out would be to assume that (i) the projection behavior of presuppositions is only a default property and (ii) context can obviate projection more or less easily. Under that perspective, non-projection in a given context would be a matter of plausibility and, when sentences are given in isolation, the final perception would depend on the possibility of abducing reasonable contexts for precluding projection. In essence, this is Stalnaker's project. Stalnaker notes that "the constraints imposed by a statement on what is presupposed seem to be a matter of degree, and this is hard to explain on the semantic account." (Stalnaker, 1974, p. 54). By 'semantic account' Stalnaker means any theory that attributes projection to a lexical item or linguistic construction, irrespective of contextual cues. He favors instead a pragmatic account, in which context and inference play a central role.

For instance, Stalnaker would explain the difference between (6a) and (6b) as follows. If the speaker presupposes that she has missed the point, she necessarily realizes that she did so. So, by contraposition, if she does not realize she has missed the point, she cannot presuppose that she did, hence the lack of projection with (6a). In contrast, in (6b), the speaker can perfectly well presuppose that she missed the point and consider the possibility of regretting that later. However, a simple pragmatic strategy does not work as smoothly in each and every case.

First, Stalnaker's analysis does not seem to extend to (1) very easily. The speaker of (1a) can presuppose that Paul missed the point without any contradiction (see [START_REF] Beaver | Have you noticed that your belly button lint colour is related to the colour of your clothing?[END_REF]). Yet, projection is not automatic. Second, when the presupposition does not project, it has to be accommodated in the local context of the trigger. For instance, in a pattern like If p, q, where p presupposes some p ′ , if it happens that the truth of p ′ can be questioned, we have to reconstruct an interpretation corresponding to If p ′ & p, q, where p ′ is accommodated in the local context, that is, the antecedent of the conditional. If we observe a variation in accommodation, the pragmatic strategy predicts that it is due either to a difference in contexts or to a difference in the possibility of abducing a favorable context. But consider (3) again.

(3) a. I don't know if Paul participated in the race, but, if he won, he must be very proud. b. I don't know if Paul participated in the race, but if Mary participated ?? too they probably had a drink together just after.

We do not need any extra context to tell us that, in both cases, we have to accommodate the proposition that Paul participated in the race. Should we argue that this proposition is more accessible, salient, plausible, etc., in the presence of win than in the presence of too? This is not unreasonable, given that win entails or implies very strongly participating, whereas Mary participated too does not entail that Paul participated. So, we might say that, in a sense, participating is more strongly associated with winning than x did y with z did y too. However, two new problems come up. First, one might argue that someone did y is strongly associated with z did y too.3 Yet, substituting someone for Paul in (3b) does not produce a more felicitous text, see (7).

(7) I don't know if someone participated, but, if Mary participated ?? too . . . Second, [START_REF] Abusch | Lexical alternatives as a source of pragmatic presuppositions[END_REF]2010) claims that clefts are strong triggers. Clefts have the property that their main content entails their presupposition. For instance, It's Paul who solved the problem asserts that Paul solved the problem (main content) and presupposes that someone did (presupposition), an obvious consequence of the main content. If Abusch is right about the status of clefts, we have a case where an entailed presupposition cannot be suspended, in contrast to participate with respect to win.

Third, the location of verbs like regret in the landscape of triggers is not clear. The experimental results reported in (Cummins et al. , 2013;Cummins & Amaral, 2014) 4 suggest that regret patterns with weak triggers, which apparently clashes with other taxonomies [START_REF] Abbott | Where are some of the presuppositions gone[END_REF][START_REF] Abusch | Presupposition triggering from alternatives[END_REF].

In view of the variation exhibited by the literature, we decided to investigate the difference between French weak and strong triggers in an experimental perspective, starting with basic experiments based on native speakers intuitions about French sentences. With respect to the introspective observations reported in the present section, there are three main differences: (i) We adopted Abusch's basic frame in order to keep the standard of comparison constant, (ii) we used only contextualized sentences in order to reduce as far as possible the effect of context abduction by the subjects, (iii) we systematically compared targets and controls, that is, sentences with and without suspension of the presupposition or sentences with and without the trigger. We did not compare triggers directly, for instance regret and clefts, because this amounted to comparing very different sentences. We focused on three French elements that are considered as very close to their English counterparts, aussi corresponding to too, regretter corresponding to regret, qui-clefts corresponding to subject clefts. In the rest of the paper we refer to these elements using their English counterparts for simplicity.

Experimental findings

Experiment 1: Too (aussi)

The first experiment is based on an introspective difference illustrated in (8) vs. (9), which are English translations of the original French stimuli (see Appendix). It seems that (9b) is much better that (8b). The intuitive status of (8a) and (9a) is less clear.

(8) Context: Paul has been invited to a party. He is on very bad terms with Mary and they would prefer not to come across each other. Paul thinks that Mary might have been invited too.

a. I don't know whether Paul will go to the party but, if Mary goes , it will be embarrassing. b. I don't know whether Paul will go to the party but, if Mary goes too, it will be embarrassing.

(9) Context: Paul has been invited to a party. He is on very bad terms with Mary and they would prefer not to come across each other. Paul thinks that Mary might have been invited too.

a. I don't know whether Paul will go to the party because, if Mary goes, it will be embarrassing. b. I don't know whether Paul will go to the party because, if Mary goes too, it will be embarrassing.

The goal of the experiment was to take into account the possible effect of discourse structure on the strong trigger too. We used a contrast between mais (but) and parce que (because), in order to have two very different discourse structures, contrast/opposition and explanation/justification. Moreover, we compared texts with and without the trigger too in order to take into account the possibility that accommodating the proposition corresponding to the presupposition could be partly independent from the presence of too. If, for instance, the discourse structure is in itself a sufficient cue to help subjects accommodate, the effect of too in inducing an accommodation should be at best marginal.

The difference between but/because control stimuli where the presupposition was not suspended and target versions with the suspension in effect had already been tested in [START_REF] Jayez | How hard are hard triggers?[END_REF]. But targets were significantly worse than their control. Because targets were not significantly different. We focus here on the comparison between but and because structures, as illustrated in examples ( 8) and ( 9).

Description of the experiment

Participants 82 subjects were recruited. 5 were taken out because they were not native speakers or were bilingual. The remaining subject (77) were undergraduate students and native speakers of French between 18 and 51 (mean 23.5).

Material and design

We used 5 basic sentences in 5 contexts (see Appendix). Each final sentence had the form: I don't know whether p because/but, if p ′ too/ø, q. where p ′ too, but not p ′ alone, presupposes p and ødenotes the null string, alternating with too. So, there were 2 × 2 conditions: because/but × with too vs. without too. We also had 8 fillers, common to all the participants.

Subjects were divided into 4 groups in a between-subject design shown in table 1.1.

because but Group 1 (19) with too: 1-3 without too : 4-5 Group 2 (19 ) without too: 1-3 with too : 4-5 Group 3 (18) without too: 4-5 with too: 1-3 Group 4 (21) with too: 4-5 without too: 1-3

Table 1.1 Design of experiment 1

Each subject saw 5 experimental stimuli and the 8 common fillers. No subject saw the but and because versions of the same text or the with and without too version of the same text. Procedure The stimuli were pseudo-randomized and presented on a sheet. The participants were instructed to follow strictly the order of presentation and not to modify a previous answer. They had no time limit or speed indication. The task consisted in reading the context and the sentence and evaluating its comprehensibility on a seven point scale (1-7), where 1 was the worst and 7 the best mark.

Results and analysis

The basic results are shown in table 1 Since the response is ordinal, we analyzed the data with a standard Mann-Whitney test for independent samples.5 table 1.3 reports the p-values. The last column indicates under which null hypothesis the p-value was estimated. We considered that it was a priori more likely to have high scores for a because sentence with too than with the same sentence without too, because the adverb was supposed to help derive the correct inference that the simultaneous presence of Paul and Mary may lead to tensions. We made a similar assumption for but. For the but/because contrast, we assumed that the because-versions were likely to get higher scores than the but-versions.

The results, shown in table 1.3, show that the because and with too levels improve the scores, a fact which can be visualized through density plots (figure 1.1). The pvalues suggest that:

1. Because-sentences are better with too (line 1). 2. But-sentences are better with too (line 2).

3. With too, because-sentences are better than but-sentences (line 3). 4. Without too, because-sentences are better than but-sentences (line 4). The fact that but sentences with too are better than without too (line 2 of table 1.3) is not surprising. In the but version without too, the conclusion of the if sentence bears no clear relation to its antecedent. For instance, in (8a), the dominant interpretation is that if Mary goes to the party, it will be embarrassing, no matter whether Paul goes to the party or not, which clashes with the context.

The main conclusion one can draw from these results is that there is no absolute or even strong prohibition of accommodation with too in the antecedent of a conditional. Clearly, the context can help subjects accommodate the missing presupposition, up to the point where the difference with a control where the presupposition is not suspended is no longer discernible [START_REF] Jayez | How hard are hard triggers?[END_REF]. The processing of accommodation remains, however, unclear. We don't know at which point in the reading sequence subjects accommodate the missing presupposition and it is possible that the accommodation schedule is different across subjects or categories of subjects.

Given that there is no difference between the with/without too versions for because, it is tempting to assume that, at the moment too is read, the missing presupposition has already been made salient. We return to this point in section 1.4.

Experiment 2: Regret and clefts

Regret-sentences and clefts are considered to be strong triggers by Abusch. Regret is mentioned as a full factive by Karttunen, in contrast with semi-factives such as discover. We tested regret-sentences and clefts along the same lines as too. Subjects had to evaluate contextualized sentences like the following ones.

(10) Context: Véronique is wondering whether she will change her current car for a bigger one.

a. I think that Véronique bought a bigger model. If she regrets it later, it will be difficult to change again.

[control] b. I wonder whether Véronique bought a bigger model, but, if she regrets it later, it will be difficult to change again. [target] (11) Context: An employee cannot log in on his computer.

a. I think that someone changed the password. If it was my colleague, I just have to wait to ask him.

[control] b. I don't know whether someone changed the password but, if it was my colleague, I just have to wait to ask him. [target] 1.3.2.1 Description of the experiment Participants 40 undergraduate students were recruited. 7 were taken out because they were not native speakers of French or were bilingual. The 33 remaining subjects ranged over 18-26 years with a mean of 21. They had neither participated in the first experiment nor heard about it.

Material and design 6 regret-sentences and 6 clefts were created together with 8 fillers. Each subject saw 3 regret items and 3 clefts, one control and two targets or one target and two controls for each category (regret/cleft). No subject saw a target and its control. The design was between-subject in the sense that no two subjects evaluated exactly the same set of stimuli. Procedure Subjects had to read 14 stimuli (6 experimental items and 8 fillers) and to evaluate the stimuli as in the first experiment.

Results and analysis

The net results are shown in table 1.5. Unlike in the case of too, it is not advisable to run non-parametric comparisons directly because the groups of subjects that would be compared are not independent. The first lines of the design matrix illustrate the problem.

Subject Group Type1 Cat1 Type2 Cat2 Type3 Cat3 Type4 Cat4 Type5 Cat5 Type6 Cat6 1 1 1 regret1 C regret2 T regret3 T cleft1 C cleft2 T cleft3 T 2 2 1 regret1 C regret2 T regret4 T cleft1 C cleft2 T cleft4 T 3 3 1 regret1 C regret2 T regret5 T cleft1 C cleft2 T cleft5 T 4 4 1 regret1 C regret2 T regret6 T cleft1 C cleft2 T cleft6 T 5 5 1 regret1 C regret3 T regret4 T cleft1 C cleft3 T cleft4 T 6 6 1 regret1 C regret3 T regret5 T cleft1 C cleft3 T cleft5 T
Suppose we want to study the contrast between controls and targets for regret. We have then to gather the results for controls and targets and run a non-parametric test. However, the experiment is such that subjects evaluate controls and targets. For instance subject 1 sees two targets-stimuli number 2 and 3-for regret, and one control-stimulus number 1-for regret, subject 2 sees stimuli number 2 and 4 as targets for regret and stimulus number 1 as control for regret, etc. We might consider a paired non-parametric test, typically a Wilcoxon test for paired samples. Unfortunately, this solution is far from optimal because it requires that we have enough data points to calculate two means-for controls and targets-for each subject and subjects see only three stimuli in the regret (or cleft) category.

A better option is to divide the set of subjects into two complementary sets and to compare the scores of controls for one of the sets with the scores of targets for the other. By doing this, we get more data points. E.g., we have 32 observations for regret-target and 16 observations for regret-control for the first sixteen subjects. Of course, we have to repeat the non-parametric comparison many times to make it independent from any particular choice of subsets. We randomly divided the 33 subjects of the experiment into two groups of 16 and 17 subjects and compared their scores over 10000 such samplings. The end result is a distribution of contrasts between controls and targets for 10000 independent samples of 16 and 17 subjects. As can be expected from the net results in table 1.5, the non-parametric comparisons revealed no difference between targets and controls, see table 1.6. The distribution of p-values after sampling suggests that, overall, clefts are easier to interpret than regret, see figure 1.2. The question arises whether clefts and regret-sentences are significantly different. Since the stimuli for the two categories are themselves extremely different, in order to avoid self-adjustment effects on the subjects, it is difficult to answer in a really convincing way. Two points are worth noting, however. First, comparing clefts and regret-sentences aggregating the target and control conditions suggests that there is a difference. The p-value mean is practically zero with a 10000-sample test and the distribution of the p-values is Gaussian around the mean, which excludes a possible effect of extreme values. Second, comparing clefts and regret-sentences under each condition (control/target) with a 10000 sample test suggests the existence of a difference. The p-value is 0.08 for controls and 0.04 for targets, which is compatible with a global difference between clefts and regret and a slightly larger difference under the target condition.

It must be borne in mind that the stimuli for clefts and regret-sentences are different. In the absence of a comparison based on similar stimuli, there are at least two (mutually compatible) hypotheses: (i) clefts are easier to process because of their presuppositional profile, (ii) clefts are easier to process because the stimuli used in the experiment were more natural, simple, etc. If (i) was the main factor, we would expect to see the difference between clefts and regret-sentences decrease in the control condition. Figure (1.3) does not suggest that there is any difference. Moreover, if we assimilate the ordinal response to a continuous one, it is useful to note that a linear model with scores as the response variable failed to detect any interaction between control and target conditions. 7 More convincingly, two binarizations of the response produced a similar result. We divided the scores into TRUE (FALSE) according to whether they were superior to 4 (≤ 4) (binarization 1) or whether they were superior (≤) to 5 (binarization 2). A logistic regression model was fitted on the two binarizations with glm. The results are shown in table 1.7. The results obtained by using lmer with subjects as random effect with respect to the intercept are practically identical. R pattern : glm(Score∼Condition*trigger,family="binomial",data=D) binarization 1 binarization 2 interaction: 0.59 interaction: 0.78 Table 1.7 Logistic regression for condition and trigger Summarizing, the hypothesis that the difference between regret-sentences and clefts is due to the presuppositional profile of the two triggers is at best dubious. The alternative hypothesis that the difference is due to other factors is more plausible. Moreover, the two triggers give rise to accommodation in suitable contexts. 7 The lm function in R with scores as dependent variable and interaction between condition and stimulus type as independent object provides a p.value of 0.87 for the interaction. A linear model calculated by lmer, with subjects as random effect with respect to the intercept, gave a low t-value of -0.187. So, the two models are consistent.

Discussion

General discussion

The goal of the present work was to assess the robustness of the lexical weak/strong distinction based on Abusch's suspension test. The experimental results show that the distinction is not as robust as one may wish, since what is taken to be a characteristic of strong triggers, namely their resistance to accommodation under Abusch's configuration seems to evaporate in the presence of particular contexts. As noted by a reviewer, we did not compare directly strong and weak triggers, so we cannot conclude that the distinction is illusory, since there is always the possibility that some 'weak' triggers behave as strong triggers are predicted to behave. Our conclusion is, accordingly, more modest. We claim that there is at the moment no clear empirical evidence supporting the existence of a separate class of lexically or conventionally strong triggers and that it is not clear that triggers in general encode directly the strength/persistence/likelihood of projection. In contrast, it is possible that lexical information and context interact in certain ways that may produce the illusion of a purely lexical distinction. This makes room for various distinctions between triggers, including prototypical weak and strong profiles.

The present results support a more precise claim in line with [START_REF] Jayez | Orthogonality and presuppositions. A Bayesian perspective[END_REF]. There are in fact three categories of triggers. With triggers like discover or clefts, the presupposition and the main content are not independent of each other. The main content of clefts entails their presupposition: It's Mary who solved the problem ⇒ Mary solved the problem (main content) ⇒ someone solved the problem. The situation is the same for win: winning ⇒ participating. Concerning discover and similar terms, the main content makes the presupposition more probable. It has been noted by [START_REF] Simons | Observations on embedding verbs, evidentiality, and presuppositions[END_REF] that verbs like discover or realize imply accessing some evidence that the presupposition is true. In this respect, the examples used by Karttunen and others are similar to examples like (12). In (12), we observe exactly the same behavior as with discover and its mates, namely: (i) in positive assertions (12a), the conveyed information strongly implies that Paul missed the point and it is not possible to cancel the latter proposition (12b) and (ii) in suspension environments, there is no longer an implication (12c). With a negation, we have a choice between two interpretations: either we deny the existence of a proof, which amounts to suspending the presupposition in the case of discover or we deny that Paul is aware of the truth, which amounts to preserving the presupposition.

(12) a. Paul has a proof/conclusive evidence that he missed the point.

b. Paul has a proof/conclusive evidence that he missed the point but ?? he didn't miss it. c. If Paul has a proof/conclusive evidence that he missed the point, . . . When the main content entails the presupposition or makes it much probable, the very mention of the trigger is sufficient to activate the presupposition, which predicts that the Abusch suspension test will not cause an impression of anomaly, a prediction which was borne out by the results about clefts. It is also expected that triggers for which the main content does not entail the presupposition or make it significantly more probable could be harder to process in general. This is compatible with the fact that regret had overall a lower score than clefts in our experiment, although, at this stage, it is impossible to exclude a confound with other factors, for instance the semantic content of the stimuli.

Verbs like regret or stop can be parceled together. The main content is independent from the presupposition. The differences between the triggers come from the relative degree of difficulty they present when a plausible context has to be constructed. For example, one might feel that it is impossible to find a situation similar to that of (2b) for regret, but it is only a matter of degree in context abduction, as shown by ( 13), where no presupposition emerges and the interpretation is that of a vague speculation, in the manner of (2b).

(13) I don't know what is wrong with the guy. Maybe he regrets having the job he has, or the wife he has, or whatever. Lastly, there is a class of triggers like too or again that carry only the presupposition, as noted by [START_REF] Abbott | Where are some of the presuppositions gone[END_REF]. [START_REF] Jayez | Orthogonality and presuppositions. A Bayesian perspective[END_REF] argues that what we observe with such triggers is a side-effect of a very general discourse constraint, studied in [START_REF] Ducrot | Dire et ne pas dire[END_REF][START_REF] Jayez | Projective meaning and attachment[END_REF][START_REF] Simons | What projects and why[END_REF]. Non-main content information, including presupposition and implicatures is in general not involved in the normal, that is, non-metalinguistic, flow of discourse. For instance, non-main content information is not 'seen' by discourse markers and cannot be used naturally to answer a question. Operators like negation, if, question, etc., contradict or suspend the main content. They tend to ignore the non-main content and this what has been called 'projection'. Projection is stronger when the part of the message that carries the main content is distinct from the part that carries the non-main content. This is clearly the case with conventional implicatures, wich are, in general, separate from the main content [START_REF] Gutzmann | Expressives and beyond. An introduction to varieties of use-conditional meaning[END_REF][START_REF] Potts | The Logic of Conventional Implicatures[END_REF]. For instance, expressives like the stupid N do not allow for suspension (14). Examples like (14) exhibit the same mechanism as Karttunen's example (6a). Since expressives are endorsed by the speaker, it is impossible for the same speaker to suspend in the ignorance sentence what he endorses in the rest of the discourse.

(14) I don't know whether Paul is stupid, but, if ?? the stupid Paul . . . Should we then expect that strong triggers behave basically like expressives or similar conventional implicature triggers? There are two sides to the answer. Since the suspension operators target primarily those parts of the message that convey main content information, they tend to ignore other parts, including pure presupposition triggers. This accounts for the fact that we have an impression of automatic ('strong') projection. However, because they are anaphoric, 8 triggers like too or again, are open to accommodation processes whenever the context provides enough 'independent' cues to make this accommodation plausible, where 'independent' means 'independent from the presence of the trigger itself'. Let us return to the too experiment to gain an intuitive understanding of how that would be possible.

When presented with the segment I don't know whether Paul will go the party because -, one can expect to find a reason why the speaker is ignorant about Paul's decision or why Paul might not go to the party. Concerning the latter interpretation, it is unlikely that one finds a reason why Paul might go to the party, as evidenced by the contrast in (15).

(15) a. I don't know whether Paul will go to the party because he does not like parties. b. ?? I don't know whether Paul will go to the party because he likes parties.

As to the reason why Paul might no go to the party, there are two possibilities. First, Paul might run into some unexpected objective obstacle. For instance, he has missed his train or is sick, etc. Second, Paul might plan not to go although he has the possibility to go. In the first case, there is an independent cause that prevents Paul from going. In the second case, Paul has a reason not to go. Summarizing, we have the following possibilities (figure 1.4). At S 1 + S 2 , the CAUSE OF IGNORANCE interpretation becomes unlikely, since there is no clear relationship between Mary possibly going to the party and the speaker's state of ignorance. So, the CAUSE and REASON interpretations (Paul might hesitate because . . . ) are both better candidates. Given that the explicit part of the antecedent in the conditional is the hypothetical proposition that Mary goes to the party, we have two possibilities. Either the conclusion of the antecedent (the situation will be embarrassing) plays a role in allowing subjects to accommodate the missing hypothetical presupposition (Paul goes to the party), or this accommodation is already set at the moment the explicit antecedent (Mary goes to the party) has been processed. Both strategies are a priori possible and it is also possible that different subjects apply different strategies. The evaluation experiment does not allow one to tease apart the different processing scenarios. However, it is clear that subjects develop a sort of counterfactual reasoning, which amounts to inferring a reason for Paul for not going to the party from the consequence of two simultaneous events of Paul going and Mary going. How is that possible? Is it a property of the specific sentences we used in the experiment or something more general? Providing a reason for a non-action-here, not going to the party-involves in general a counterfactual reasoning about the possible negative consequences of the suspended action. Suppose for instance that Paul deliberately refrained from signing a document in order to block a project. Paul's non-action does not make much sense if we do not assume that signing the document would have increased the probability that the project is accepted, that is, if we do not take into consideration the effect of the contrary proposition. In the case of ( 8) and ( 9), the context makes it clear that one of Paul's goals is to avoid Mary as far as possible. Therefore, one can expect that, for some subjects at least, a counterfactual reasoning is on its way at S 1 + S 2 or S 1 + S 2 + S 3 . So, although it is not possible to be more specific on processing issues (see [START_REF] Jayez | How hard are hard triggers?[END_REF] for perspectives on this point), it is very likely that subjects engage at some point in a counterfactual reasoning which helps them abduce the missing presupposition.

Comparison to other work

Recent work by Cummins and colleagues (Cummins et al. , 2013;Cummins & Amaral, 2014) suggest a partly different picture than the findings reported above. [START_REF] Jayez | Orthogonality and presuppositions. A Bayesian perspective[END_REF] discusses (Cummins et al. , 2013) at some length and the remarks made there extend to (Cummins & Amaral, 2014) to a large extent. The main goal of these two papers is to investigate experimentally the difference posited by [START_REF] Zeevat | Presupposition and accommodation in update semantics[END_REF] between resolution and lexical presupposition triggers. Resolution triggers behave like anaphors. They look for a referent already introduced in the context or in the discourse. Lexical triggers refer to a concept whose applicability conditions correspond in part to the presupposition. For instance, the presence of too-a resolution trigger-invites one to find a suitable antecedent (an individual or an event), whereas stop refers to a transition between two states. The main intuition of Cummins and colleagues is that the negation of the presupposition does not affect a sentence containing a resolution trigger and a lexical trigger in the same way. For resolution triggers, the presupposition is not easily accommodated because it remains 'ambiguous', in Cummins and Amaral's 2014 terminology. In contrast, lexical triggers provide more information as to the identity of the presupposition, which makes it more recoverable. Excluding a presupposition with a lexical trigger will affect (negatively) the asserted content, whereas, with a resolution trigger, the relation to the asserted content will remain weak. Accordingly, Cummins and colleagues predict that there are differences in acceptability between the sentence types illustrated in ( 16) and ( 17). B's answer in ( 16) amounts to endorsing the asserted content and refuting the presupposition, whereas C's answer amounts to refuting both. ( 17) has a similar structure, with a resolution trigger. Since negating the presupposition has more effect with lexical triggers than with resolution triggers, it is expected that C's answer in (16) will be perceved as better than in (17).

(16) A -Did Mary stop smoking? B -Yes, although she never smoked before. C -No, because she never smoked before.

(17) A -Did Mary watch the movie again? B -Yes, although she never watched it before. C -No, because she never watched it before. This is indeed what Cummins and colleagues observe on a set of English triggers (Cummins et al. , 2013) and their Spanish counterparts (Cummins & Amaral, 2014). By and large, their observations and those reported in the present paper are consonant. For instance, in both approaches, regret is classified as lexical/weak. It seems that there are three main differences. The first is empirical. Since the experimental settings and the triggers under consideration are different, it is difficult to compare the observations.

The second one has to do with the pre-classification of triggers. the reason why again and still would be different remains unclear. Intuitively it seems that the presupposition can be very easily accommodated in both cases.9 For instance, in (17), we accommodate immediately the proposition that Mary has watched the movie before. One might argue that this presupposition is too vague and that we need to know when Mary watched the movie (before). But, this would be asking for too much, since a sentence like I know Mary watched the movie before and watched it again yesterday is perfectly natural, although the temporal antecedent of again is very vague.The results provided by Cummins & Amaral (2014) are of two types. There are means on a 5 point Likert scale and there are differences between ratings for Yes, although and No, because patterns. The differences are significant for lamentar (regret), seguir (continue), dejar de (stop) and todavía (still), whereas they are not for otra vez (again) and tambíen (too). However, when we focus on the Yes, although pattern, we see that (i) todavía gets practically the same score than otra vez and tambíen and that lamentar and dejar de do not pattern with seguir and todavía. In our opinion, this calls for clarification and makes it perhaps difficult to interpret what is going on.

The third difference is a variant of the second. In the Abusch pattern, the content to be accommodated is in general transparent. For instance, in a sentence like ? I don't know whether Mary hit the target before, but if she hit it again, she is really gifted, it is rather obvious that the proposition to accommodate in the antecedent of the conditional is 'Mary hit the target before'. In this respect, it does not seem possible to explain the difficulties of accommodation with strong triggers in terms of ambiguity or vagueness. The problem is rather with the possibility of the accommodation process itself, given its interaction with discourse coherence.

Conclusion

In this paper, we have shown that context plays a crucial role in the perception of the 'projection strength' of triggers, and that, as a result, projection strength can hardly be interpreted as an intrinsic lexical property of the various triggers mentioned in the literature. This is clear with allegedly strong triggers like regret or clefts. The situation of too is more complex since it is most probably a consequence of several properties, including the fact that it does not carry any main content information, as noted by Abbott, and the facilitation of accommodation under a counterfactual interpretation. Obviously, much work remains to be done, in particular extending the behavioral experiments to other triggers (e.g. factives), exploring the time course of accommodation, and extending the experimental coverage to other languages, as done in (Cummins & Amaral, 2014) for Spanish.

  (6) a. If I realize I have missed the point, I will probably reformulate my objection. I have missed the point. b. If I regret I have missed the point, I will probably reformulate my objection. I have missed the point.

Fig. 1 . 1

 11 Fig. 1.1 Density plots for because and but

Fig

  Fig. 1.2 p-value distribution

Fig. 1 . 3

 13 Fig. 1.3 Density plot by trigger under control and target conditions

  Fig. 1.4 Possible families of interpretations after because

  .2. Net results for the aussi experiment

	Sentence.Type Nb.Obs Nb.Subjects Mean Variance
	1 bec.with.too 99	40	6.25 3.33
	2 but.wo.too	100	40	5.08 3.85
	3 bec.wo.too	93	37	5.73 4.24
	4 but.with.too 92	37	5.68 3.62
	Table 1.2

Table 1 . 3

 13 Contrasts for the aussi experiment

	Contrast	p-value null hypothesis
	1 because with/without too 0.055 without-score ≥ with-score
	2 but with/without too	0.021 without-score ≥ with-score
	3 because/but with too	0.016 but ≥ because
	4 because/but without too 0.0086 but ≥ because

  Net results for the regret/cleft experiment

	Sentence.Type Nb.Obs Nb.Subjects Mean Variance
	2 regret.target	52	33 4.87	3.45
	3 cleft.target	52	33 5.92	2.23
	4 cleft.control	47	33 6.11	2.05
	5 regret.control	47	33 5.13	4.03
	Table 1.5

Table 1 .

 1 6 reports the means and the proportions of p-values for various intervals. All the tests assumed that controls are better than targets as the null hypothesis.6

	Sentence.Type Mean ≤ 0.01 0.01 ≤ 0.05 0.05 ≤ 0.1 0.1 ≤ 0.5
	1 regret	0.326 0.041	0.10	0.10	0.50
	2 cleft	0.388 0.015	0.065	0.076	0.51

Table 1 .

 1 6 Distribution of contrasts between controls and targets by trigger

Although we are not fond of this terminology, which is heavily syntax-oriented, we will stick to it because it is established usage.

This is the standard hypothesis on the semantics of too, see van der Sandt & Geurts (2001) on too.

The results were controlled with the npar.t.test function from the R package nparcomp (Konietschke, 2012), in order to ensure that there was no parasitic effect of difference of variance in the comparisons.

Weak and strong triggers

The tests were carried out using the npar.t.test function of the nparcomp package with the method parameter set to t.app. The Mann-Whitney test is not reliable due the presence of ex-aequo.

This remark does not commit us to the view that every presupposition is anaphoric.1 Weak and strong triggers

Too is a different case, see[START_REF] Jayez | Orthogonality and presuppositions. A Bayesian perspective[END_REF].

Appendix

Experimental items with too for experiment 1

The context is in boldface because Paul et Marie se sont disputés et ne tiennent pas à se retrouver ensemble. Paul est invité à une soirée, où il pense qu'il est possible que Marie ait été invitée. Je ne sais pas si Paul ira à la soirée parce que, si Marie y va aussi, ce sera très embarrassant.

Julien veut offrir un tee shirt à son neveu pour son anniversaire, mais il a peur que quelqu'un ait eu la même idée. Je ne sais pas si Julien offrira un tee shirt parce que, si quelqu'un en offre un aussi, ça sera décevant pour son neveu.

Nadine envisage de faire couper le sapin de son jardin, mais il ne resterait plus que celui de son voisin.

Je ne sais pas si Nadine fera couper son arbre, parce que, si son voisin fait aussi couper le sien, il y aura trop de soleil l'été.

La Chine et la Russie veulent éviter une opération militaire contre la Syrie. Il faut que les deux pays donnent leur accord pour que l'intervention ait lieu mais aucun des deux n'est trop sûr du choix que ferait l'autre en cas de crise vraiment grave. Je ne sais pas si la Chine acceptera une intervention proposée par l'ONU, parce que, si la Russie l'accepte aussi, une opération sera lancée contre la Syrie.

Après la tempête de la veille, Louise est inquiète pour son petit bateau et descend au port avec son chien. Le bateau a l'air plein d'eau et Louise aimerait bien le vider. Le bateau supporterait certainement que Louise ou son chien montent, mais pas les deux. Je ne sais pas si Louise va monter dans le bateau parce que, si le chien monte aussi, le bateau risque de chavirer.

For but, the stimuli are the same, except that mais replaces parce que. The contexts are strictly identical. For instance, the first stimulus becomes: Je ne sais pas si Paul ira à la soirée mais, si Marie y va aussi, ce sera très embarrassant.

Experimental items for experiment 2

The context is in boldface regret Paul hésite à resigner dans son club parce que ça ne se passe pas très bien avec son président. Je crois que Paul a resigné dans son club. S'il le regrette plus tard, il ne pourra s'en prendre qu'à lui-même. [control] Je ne sais pas si Paul a resigné dans son club mais, s'il le regrette plus tard, il ne pourra s'en prendre qu'à lui-même. [target] Véronique se demande si elle va acheter une voiture plus grosse que celle qu'elle a. Je crois que Véronique a acheté un modèle plus gros. Si elle le regrette ensuite, ce sera difficile de changer de nouveau. [control] J'ignore si Véronique a acheté un modèle plus gros mais, si elle le regrette ensuite, ce sera difficile de changer de nouveau. [target] Céline se demande si elle va signer la pétition pour défendre une collègue de bureau. Je suis sûr que Céline a signé la pétition. Si elle le regrette après coup, ce sera trop tard. [control] Je ne sais pas si Céline a signé la pétition mais, si elle le regrette après coup, ce sera trop tard. [target] Lucien ne sait pas s'il va voter pour le maire en place ou pour sa concurrente. Je pense que Lucien a voté pour le maire actuel. S'il le regrette par la suite, il ne pourra plus rien y faire. [control] Je ne sais pas si Lucien a voté pour le maire actuel mais, s'il le regrette par la suite, il ne pourra plus rien y faire. [target] Ariane s'interroge sur l'utilité de faire couper la haie de son jardin. Je suis certain qu'Ariane a fait couper la haie. Si elle le regrette dans quelque temps, elle ne pourra pas revenir en arrière. [control] J'ignore si Ariane a fait couper la haie mais, si elle le regrette dans quelque temps, elle ne pourra pas revenir en arrière. [target] Nathan ignore s'il va remplacer son gros ordinateur par un portable. Je pense que Nathan a acheté un portable. S'il le regrette, ce sera trop tard et il devra garder son portable. [control] Je ne sais pas si Nathan a acheté un portable mais, s'il le regrette, ce sera trop tard et il devra garder son portable. [target] clefts

Jules est très vaniteux et ne peut s'empêcher de se vanter dès qu'il réussit quelque chose.

Je pense que quelqu'un a trouvé la solution du problème. Si c'est Jules, on n'a pas fini d'en entendre parler.

[control]

Je ne sais pas si quelqu'un a trouvé la solution du problème mais si c'est Jules, on n'a pas fini d'en entendre parler. [target] Une société craint d'avoir été espionnée par ses concurrents. Marie est particulièrement compétente sur les nouveaux projets secrets. Je suis sûr que quelqu'un nous a trahi. Si c'est Marie, nos concurrents seront très bien informés.

[control]