2.1. Experimental Arrangement
 All experiments were conducted in the Lyon LMFA laboratory (Laboratoire de Mécanique des Fluides et d'Acoustique). The experimental arrangement was presented by Recking et al. [2008a] and consisted of an 8-m-long tilting flume (slope varying from 0 to 10%). The flume width was adapted to each run (between 0.05 and 0.15 m) in order to satisfy the two following conditions: (1) avoiding divagations and (2) keeping a width-to-depth ratio W/H higher than 3.5 to ensure a fairly two-dimensional flow [Song et al., 1995]. Since the purpose of this experiment was to investigate fluctuations associated with transport mechanisms, it was very important to ensure constant feeding (both for fluids and solids). The water discharge was supplied from a constant head reservoir and controlled by an electromagnetic flowmeter. A customized sediment feeding system was specifically developed using a feeding tank and a conveyor belt, the velocity of which allowed us to control the sediment discharge. The stability of the conveyor belt was controlled during all experiments by recording the belt velocity using a special tachometer device. This feeding system was tested with several mixtures of uniform materials. All measurements indicated that no sorting effects occurred inside the tank, with the average solid discharge for each class remaining constant [Recking, 2006].
 Different sediment mixtures were obtained by mixing uniform materials of a median diameter of 2.3 mm, 4.9 mm, and 9 mm (the D84/D16 ratio was, respectively, 1.15, 1.22, and 1.25 for each material; the grain size distribution curves are presented by Recking et al. [2008a]). Bimodal mixtures were preferentially used to facilitate observations and to be representative of natural gravel bed sediments [Kuhnle, 1996; Parker, 1991; Van den Berg, 1995]. Sediments were mixed by hand to avoid segregation, and mixtures collected at the flume outlet were stored, tested by sieving and readjusted to the initial distribution if necessary.
 There was no recirculation of either solids or liquids. This choice was imposed by the study's objectives: understanding the bed response immediately downstream of a cross section for a given constant feed in sediment mixture and water, considering that, in the short-term and short distance, rivers can be compared to feed systems with a given initial slope.
 Local bed slopes and mean bed slope (difference between the bed height at the flume entrance and the bed height at the flume outlet divided by the total flume length) were measured every 10–20 min along the flume sidewall using eight staff gauges placed 1 m apart, starting at the channel outlet. Since flows were two-dimensional in all our runs, it was easy to define a reference bed level corresponding to nonmoving grains (fixed bed) and valid for the flume cross section. However, in some runs (essentially for the 15-cm-wide flume) we averaged two readings obtained from both sides of the flume. We considered only the long-term bed changes because there were no large bed forms (such as dunes) capable of changing the bed topography in our experiments. When antidune waves were present, we averaged several measurements so as to consider the mean bed level at the flume control section. We estimate that the error made on the fixed bed level reading was no more than 5 mm. But in many experiments including the 2.3-mm sediment, bed load transport developed above a bed consisting of the 2.3-mm material with very few asperities, resulting in greater precision. In addition, the measurements were repeated many times for all control sections, also reducing the error. Consequently, the error in slope calculation (when considering the entire flume length) was estimated to be within 3% for the 8-m-long flume experiments (used in the following analysis). This error could attain 5% in the 2-m-long flume used to extend long flume observations to a wider range of flow conditions and sediment mixtures. The energy slope was not measured. However, in most runs the flow was supercritical and the bed slope fluctuation was slow enough to maintain a free water surface that was always in phase with the bed. The bed slope therefore approximated the energy slope well.
 Sediment feeding rates were measured from the feeding system calibration, and outlet transport rates were obtained from dried and weighed samples collected in a basket at the flume outlet during bed load sheet passage. Sampling lasted between 1 and 3 min and three to four samples were collected for a given run. For run 7, we measured continuous outlet solid discharge with a customized video system [Frey et al., 2003a]. At the outlet of the flume, the mixture of sand, gravel and water was forced to flow on a tilting transparent ramp placed above an illuminated waterproof box. A video camera was placed above the plate and operated in backlighted mode. Software with specific libraries was developed to grab and save series of several images. These images were then processed with an algorithm (WIMA software [Ducottet, 1994]) using specific image analysis methods, the main steps being (1) segmentation based on gradient operators and hysteresis thresholding, (2) object separation based on an erosion algorithm, and (3) object measurement, i.e., area and diameters after determining principal axes. Finally, from a series of 2-D images as input, the algorithm calculated the three principal dimensions of each particle using an ellipsoid-shaped model. This system was used to measure total and fractional solid discharge every 0.05 s over an integration period of 3 s.
 The bed surface and subsurface grain size distribution were estimated in different ways. Since we used essentially bimodal mixtures, on many occasions of interest (transport above a paved bed and transport over a smooth bed after pavement destruction), it was possible to estimate the bed surface grain size visually. Direct sampling was also carried out by incorporating a customized short plastic pipe into the bed [Recking, 2006]. The bed surface sediment was first removed over a thickness of approximately one grain diameter when the subsurface was sampled.
2.2. Flow Conditions
 The flow conditions are presented in Table 1 (Run Number–T columns). All experiments were conducted with constant ingoing flow and sediment discharge. For each run, measurements were made only after attaining a dynamic equilibrium condition, i.e., near equality of the feed and trap rates for each fraction of the sediment mixture, and a near constant time-averaged bed slope. The procedure to match flow and sediment transport so as to obtain dynamic equilibrium for a given flow and flume slope consisted of calculating an equilibrium transport rate using equations (1) and (4) defined below, considering the mean diameter of the sediment mixture. Setting this calculated feed value at the flume entrance, the run was maintained until the slope attained a constant average slope. In these constrained flume experiments, and considering mass conservation, the constant average slope was necessarily associated with an equilibrium average transport rate for a feeding rate that was maintained constant. This was confirmed with image analyses in run 7.
Table 1. Experimental Conditions and Main Resultsa
|Run Number||Mixture Composition||W (m)||L (m)||Q (l/s)||Qs (g/s)||S (%)||H (mm)||Fr||θ/θc||T (h)||dS (%)||Qs Maximum (g/s)|
|2.3 (%)||4.9 (%)||9 (%)||2.3||4.9||9|
 Long experiments were conducted to obtain dynamic equilibrium (eight runs lasted between 4 and 64 h). Shorter experiments (12 runs lasting less than 4 h) were also conducted with a reduced flume length (2–4 m) and by varying either the sediment mixture or the flow discharge. The principal objectives for these shorter experiments were to extend the long experimental observations to a wider range of flow conditions and sediment mixtures, and only long-duration experiments conducted in long flumes were used for a detailed analysis. Long runs (64 h for run 6) had to be stopped and started again many times. The procedure always involved acting as slowly as possible (flow and sediment feed rate shutting off/starting up) in order not to disturb the bed material size. In the following, every run designated by its slope corresponds to the dynamical equilibrium average slope resulting from the imposed feeding rates and sediment mixture. The feeding rates were changed for every run in order to test equilibrium slopes between 1 and 9%. Maximum and minimum values of the Shields number, θ = τ/[g(ρs − ρ)D] where τ = ρgRS is the bed shear stress, R is the hydraulic radius, ρs is the sediment density and ρ is the water density, in Table 1 were calculated considering variations of the bed surface grain diameter observed during the run and the maximum and minimum slopes averaged over the entire flume length (S ± dS).
2.3. Friction and Bed Load Transport Equations
 The friction (equation (1)) and bed load transport (equation (4)) equations based on previous uniform sediment experiments [Recking et al., 2008b] are reviewed here. These equations were used to analyze the nonuniform results
where U is the vertically averaged flow velocity,
where αRL is a roughness layer coefficient taking into account deviation from the logarithmic profile at small relative depth flows (with an increasing influence of the roughness layer) and αBR is a bed load roughness coefficient taking into account additional flow resistance due to bed load. The bed load equation (valid for low flow conditions with θ < 2.5θc) is
where ϕ = qsv/[g(s − 1)D3]0.5 is the Einstein dimensionless parameter [Einstein, 1950] and qsv [m3/s/m] is the volumetric unit solid discharge. Equation (5) yields greater values of dimensionless critical shear stress for increasing values of slope, as explained by the effects of changing flow hydraulics with increasing slope and decreasing relative depth [Lamb et al., 2008; Recking, 2009].