Role of discharge variability on pseudomeandering channel morphodynamics: Results from laboratory experiments

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2010jf001742, 2010 Role of discharge variability on pseudomeandering channel morphodynamics: Results from laboratory experiments F. Visconti, 1 C. Camporeale, 1 and L. Ridolfi 1 Received 27 April 2010; revised 6 October 2010; accepted 13 October 2010; published 31 December [1] Rivers experience a wide range of discharges. It is nowadays acknowledged that is not realistic to assume that the morphology of a river is influenced by only a single formative discharge. Rather, it is the full range of flows that are able to move sediments and erode banks that affect the fluvial morphology. Thus, the channel morphology emerges from the interactions between different competent discharges. A goal that has still not been completely achieved in geomorphology is the understanding of the role of discharge variability on river morphological processes. In this paper, we present the results of an experimental investigation concerning the impact of the sequencing of two competent discharges on a self forming pseudomeandering pattern. The inception of the pattern, the bar dynamics, and the bend erosion are investigated. A comparison of the experiments performed with steady and unsteady discharges has indicated the key role of the discharge variability in promoting and sustaining the pseudomeandering channel. These experimental findings shed light on some important morphological processes (bar deformation, low flow channel incision, and triggering of the bend inception) that are affected by discharge variations to a great extent, in agreement with some field studies and conceptual models. Citation: Visconti, F., C. Camporeale, and L. Ridolfi (2010), Role of discharge variability on pseudomeandering channel morphodynamics: Results from laboratory experiments, J. Geophys. Res., 115,, doi: /2010jf Introduction [2] Rivers are a key component of the environment and landscape. Through sediment erosion and deposition processes, rivers shape and modify their floodplains, and interact with several natural processes, such as the growth of riparian vegetation and fauna proliferation [Naiman et al., 2005], transport processes [Garcia, 2008], and biogeochemical cycles [Jones and Mulholland, 2000], and often have an impact on anthropogenic activities [Jansen et al., 1979]. River morphodynamics has attracted much interest in the scientific community because of its importance to river hydraulics and management [Thorne, 1997], the theoretical significance of fluvial processes [Seminara, 2010], and the beauty and the variety of river patterns [Allen, 1984]. [3] Discharge unsteadiness is a peculiarity of river flows and it influences different fluvial features, such as bed topography and bed forms [e.g., Tubino, 1991; Welford, 1994; Yen and Lee, 1995; Sear, 1995; Hall, 2004], sediment transport and sorting [e.g., Lee et al., 2004; Hassan et al., 2006; Lunt and Bridge, 2007], riparian vegetation [e.g., Tockner et al., 2000; Steiger et al., 2005; Camporeale and Ridolfi, 1 Dipartimento di Idraulica, Trasporti ed Infrastrutture Civili, Politecnico di Torino, Turin, Italy. Copyright 2010 by the American Geophysical Union /10/2010JF ; Stromberg et al., 2007], chemical dynamics [e.g., Piatek et al., 2008], and hyporheic fluxes [e.g., Boano et al., 2007]. Despite the awareness of the role of unsteady flows, most morphodynamic research and engineering applications have focused on the processes induced by steady discharges, which are assumed to be the formative or dominant discharges. In contrast, few theoretical approaches have been proposed to relate discharge variability to channel geometry. Pickup and Rieger [1979] developed a conceptual model in which the channel geometry is a function of the river flow time sequence, thus underlining that the full spectrum of discharges should be considered when the riverbed geometry discharge relation is investigated. Yu and Wolman [1987] modeled the link between channel geometry and discharge variability, demonstrating that channels narrow as a function of increasing annual flood variability. Rhoads and Miller [1991] inferred that discharge variability can lead to a modification of the exponents of the hydraulic geometry relations. Recently, Rinaldi et al. [2008] showed how bank erosion processes are very sensitive to flow sequencing. [4] In this work, we focus on the role that variable discharges have on the inception and on the development of pseudomeandering rivers. Rivers are traditionally classified as straight, braiding or meandering [e.g., Leopold and Wolman, 1957]. However, nowadays such a simplistic classification has been extended to include some intermediate patterns [e.g., Church, 1992]. The name pseudomeandering 1of18

2 Figure 1. Aerial photo of the Trebbia River (northern Italy). Flow is from left to right. The overall planform, as shown by the embankment, is slightly sinuous. A low discharge channel settles around the large alternate bars, which are surmounted during higher flows. Notice the chute channels and the absence of riparian vegetation on the bars. The star symbols indicate a typical small embayment caused by the flow diversion on the bar head during high flows (see also Figure 12). Photo courtesy of Agenzia Interregionale per il fiume Po (A.I.PO), Piacenza, Italy. has been adopted [e.g., Wolman and Brush, 1961; Hickin, 1969, 1972; Teruggi and Billi, 1997; Bartholdy and Billi, 2002] to classify single thread rivers that develop bends and alternate bars like meandering rivers, but which have low sinuosity and nonparallel banks during high flows. The banks are not parallel because the balance between erosion at the outer bank and deposition at the inner bank, which is typical of meandering rivers, does not occur in pseudomeandering rivers, where, instead, erosion outpaces deposition. [5] For example, on a pseudomeandering reach of the Cecina River (Italy), Bartholdy and Billi [2002] observed that the sediments deposited on the inner bar were about 20% of the material eroded from the outer bank. Scarce bar colonization by riparian vegetation and a cohesionless floodplain can be the causes of such an inequality between erosion and deposition rates, which is testified by the overwidening of bends (as noticed by Carson [1986]). Figure 1 shows a typical pseudomeandering reach: the slightly sinuous fluvial planform (highlighted by the embankments) and the lowflow channel that bends around large lateral bars, exhibiting the typical chute channel on their inner side, are evident. The lateral bars are exposed during low discharges and direct the flow against the banks, thus promoting the erosion of embayments in the floodplain. [6] A pseudomeandering river exhibits several features common to both meandering rivers (alternate bars, migrating bends and asymmetrical cross sections) and braiding rivers (flow diversion and tendency to create secondary channels due to the development of a chute channel between the inner side of the bar and the bank) which coexist in the same reach. Chute channels between the bars and the banks are a typical feature of pseudomeandering patterns that has been recognized both in laboratory experiments [Friedkin, 1945; Wolman and Brush, 1961; Pyrce and Ashmore, 2005] and in field studies [e.g., Lewin, 1976; Bartholdy and Billi, 2002]. [7] The widespread occurrence of pseudomeandering reaches in piedmont regions and their reproducibility in flume experiments explain the interest in this type of river morphology. Several experimental works carried out in flumes with a movable bed and erodible banks have in fact focused on pseudomeandering channels (sometimes called meandering or meandering thalweg channels). Such experiments have been performed with the aim of investigating the variables that control the channel dynamics [Friedkin, 1945], the hydraulic geometry of the channels [Ackers, 1964, 1970a, 1970c; Hickin, 1972], the channel approach to an equilibrium configuration (mainly by slope adjustment) in response to a change in sediment concentration [Eaton and Church, 2004], the presence of point dunes in subcritical and supercritical flows [Hickin, 1972], and the bed load path length [Pyrce and Ashmore, 2003, 2005]. Some researchers have experimentally demonstrated that, with the use of cohesive sediments [Jin and Schumm, 1986; Smith, 1998; Peakall et al., 2007; Kleinhans et al., 2009], suspended load [Schumm, 1972] or a vegetated floodplain [Takebayashi et al., 2006; Tal and Paola, 2007, 2010], a fully meandering pattern tends to emerge rather than a pseudomeandering one. Recently, the first self sustaining meandering river with cutoffs has successfully been reproduced in the laboratory using vegetation and suspended sediment [Braudrick et al., 2009; Howard, 2009]. Other works have reproduced the degeneration of pseudomeandering patterns in a braided system due to the formation of central bars, chute channels, and bifurcation mechanisms [Ashmore, 1982, 1991; Bertoldi and Tubino, 2005]. [8] The effects of a variable discharge on pseudomeandering inception and planform development have rarely been investigated, compared to other aspects. In the experiments of Ackers and Charlton [1970b], a hydrograph was simulated to investigate the value of the formative 2of18

3 Figure 2. Downstream view of the flume. The 3 m wide floodplain is marked by the arrow. The reference system {x,y} is also shown. discharge that allows a channel to develop the same meander wavelength under steady or unsteady flows. Differences in the spatial behavior of the flow core between high and low discharges have been pointed out by Friedkin [1945] and by Shindala and Priest [1970]. However, these seminal studies, and other works where flow unsteadiness has also been coupled with vegetation [Takebayashi et al., 2006; Braudrick et al., 2009], have not been dedicated to isolating and describing the unsteadiness driven morphodynamic processes involved in pseudomeandering and meandering dynamics. An in depth laboratory study on the self initiation, i.e., unforced growth of the river pattern, starting from an initial straight channel, of a pseudomeandering pattern under variable flow is therefore lacking. [9] In this work, we will describe and discuss a series of flume experiments that have been performed in order to investigate the role of the discharge variability on the selfinception and development of a pseudomeandering channel. We will concentrate on the morphodynamic processes of the single morphological units (such as bar growth, bed deformation, bank erosion, and bend initiation) and, through some innovative measurements, we will show how discharge variability plays a key role in affecting these processes. Even though a steady discharge is sufficient to obtain both pseudomeandering and meandering patterns [e.g., Friedkin, 1945; Braudrick et al., 2009], we will present cases in which the variability of the flow could either promote or inhibit the inception of a pseudomeandering channel. We will discuss the way by which the discharge sequencing modifies bar accretion and mobility, leading to changes in bank erosion and bend shape. Moreover, the hypothesis by Yu and Wolman [1987], that channel width decreases with increasing variability of discharge, will also be tested. Field studies reporting some examples of morphological changes of sinuous singlethread rivers due to flow unsteadiness [Lewin, 1976; Carson, 1986; Bartholdy and Billi, 2002; Rinaldi, 2003] will allow us to make useful comparisons with our experimental findings. [10] Finally, we emphasize two important aspects of our runs. First, an upstream bend is usually imposed on the channel in flume experiments on pseudomeandering and meandering patterns, to force an initial curvature that propagates downstream [Friedkin, 1945; Schumm, 1972; Eaton and Church, 2004; Peakall et al., 2007; Braudrick et al., 2009]. This kind of boundary condition yields an acceleration of the inception processes but, as pointed out by Friedkin [1945], it usually has an impact on the downstream channel geometry: a different entrance angle leads the channel to develop bends with different shapes and affects the bank erosion rate throughout the channel. For this reason, a straight entrance has been adopted here in all the runs so as not to affect and distort the channel inception and development. The second point concerns the measurement of the channel bed. In experimental works, the bed configuration is usually surveyed after the withdrawal of water. We have instead used a novel optical high precision device, which allowed us to survey the bed under the flowing water. In this way, we were able to measure the fast evolving morphological effects induced by discharge variability, thus avoiding the necessity of having to both halt the run and dip a probe into water, which would affect the local flow field and cause local erosion. This device allowed us to adopt low water depths (3 4 cm) with aspect ratios b = W/H (W is the section width and H the mean water depth) which range from a minimum of 11 at the start of the runs to a maximum of 45 at the end of the runs. These values are in agreement with the aspect ratios of many alluvial single thread rivers; e.g., see the data set collected by Rinaldi [2003] about the aspect ratios of sinuous reaches, and sinuous reaches with alternate bars, of alluvial rivers in central Italy. 2. Experimental Setup [11] The experiments were carried out in a sediment feed flume situated in the G. Bidone Hydraulics Laboratory at the Politecnico di Torino. The flume is made of concrete, is filled with sand, and is equipped with a scraper on a gantry, a sand feeder, the measurement systems, and a water supply system (see Figure 2). The flume is 18 m long, 4 m wide, and 0.6 m deep. We set the reference system {x,y} with the x axis parallel to the flume centerline and directed from upstream to downstream, while the y axis is perpendicular to the flume centerline and directed from left to right looking downstream (as indicated in Figure 2). The upstream end of the flume is connected to a water stilling tank which supplies the water discharge to the flume. Another tank collects water and sediments at the downstream end. This 3of18

4 Figure 3. Grain size distribution of the sand forming the floodplain and fed into the flume. The dots refer to the measured values. tank is equipped with a moving weir, which controls and regulates the downstream water level during the experiments, and with a siphon which removes the collected sand. The siphon is moved, by an electric motor, along the bottom of the tank in order to suck out all the deposited material. The sand is continuously weighed in a mesh by a load cell and the data are stored in a computer. Calibrated empirical corrections are implemented to obtain the correct dry/wet sand weight ratio. The flume bottom is equipped with several piezometers, which are used to initially saturate the sand and then to monitor the phreatic water table during the experiments. The sand scraper is used to shape the initial straight channel and the 3 m wide floodplain with a uniform slope (see Figure 2). The sand feeder, which supplies the upstream bed load, is a mechanical hopper with a vibrating panel that allows the sand discharge to be controlled. [12] The sand used for the experiments has a specific weight of 2650 kg/m 3, a mean grain size D 50 =0.45 mm, and is moderately sorted, having a sorting index I S = 0.5(D 84 /D 50 + D 50 /D 16 ) = The grain size distribution of the sand is shown in Figure 3. The porosity and the hydraulic conductivity are 0.4 and m/s, respectively. The water discharge is regulated by an electromagnetic valve that is controlled by a computer, which allows different hydrographs to be generated. The planimetric configuration is analyzed through a Matlab code which automatically detects the river banks from photographs taken by four cameras fixed above the flume. The resolution of the pictures allows the channel evolution, the bank erosion, and the curvature to be described with pixel precision, which corresponds to mm, depending on the experiments. Because of the lack of suspended sediment load, the bed configuration is also clearly recognizable in the photographs. [13] During the runs, the bed configuration was continuously surveyed using a novel nonintrusive device, designed by the authors, which profiles the bed under flowing water. In previous experimental studies, the bed configuration was usually measured after stopping the experiment and drying the bed [e.g., Friedkin, 1945; Bertoldi and Tubino, 2005]. This operation, if executed slowly, should not affect the bed topography or the continuation of the experiment [Bertoldi and Tubino, 2005]. However, we have observed the formation of small drainage channels as a result of water withdrawal, particularly on the stoss side of the bed forms. Even neglecting these slight modifications of the bed, a Figure 4. Photograph of the laser sonar bed measurement system. The inset shows a scheme of the laser sonar measurement system. Unlike the scheme, it should be noted that the measurements of the two instruments were taken along the same perpendicular line in order to take into account the transversal slope of the water surface. 4of18

5 Table 1. Parameters of the Performed Runs a Run W (m) S (%) b # d s Fr Q 2 (L/s) Q 1 /Q 2 T Q2 /T Q1 Q s2 (g/s) Q s1 /Q s2 l l l h h h r r * a See the text for the meaning of the symbols. The asterisk indicates that the r2 run starts with Q 1, which it is then halved after 6 h. more fundamental aspect would hamper us from following this stop and go approach. Experiments should in fact be stopped with time steps that have the same order of magnitude as the bed deformation timescale. However, when short timescale bed changes have to be captured (and this is the case for the bed evolution induced by the discharge variability investigated here) the experiments would need to be halted so frequently that the reliability of the experiment would be compromised. To avoid these problems we have implemented an optical measurement system that is able to profile the bed under flowing water. Such a device couples a high precision laser sensor to a high precision ultrasonic sensor (see Figure 4). The laser sensor is used to measure the bed elevation, while the ultrasonic sensor measures the water stage. The laser beam goes through the water and is reflected by the bed, but it is refracted at the air water interface, according to Snell s law. This refraction influences the measured distance. The use of the ultrasonic sensor allows us to obtain the distance of the laser sonar couple from the water surface and therefore to solve a system of equations that describe the path of the laser beam, in which the unknown variable is the correction that has to be applied to the error affected laser measurement in order to obtain the correct measurement (F. Visconti et al., Highprecision bed profiling under flowing water, manuscript in preparation, 2010). The corrections that must be applied were in the 1 20 mm range, depending on the water depth and velocity. Several tests have been performed to investigate the accuracy of this measurement system, by profiling some known objects in the flowing water. A vertical precision of about 1 mm has always been obtained in each trial experiment (Visconti et al., manuscript in preparation, 2010). [14] The laser and ultrasonic sensor couple was mounted onto the gantry above the flume and the sensors were moved in a two axis system by stepping motors, with a horizontal positioning accuracy of 0.1 mm (see Figure 4). This positioning system is controlled by computer and allows a channel bed area of 1 m 2 to be surveyed. Transverse channel sections, with a longitudinal spacing of 2 cm, were scanned during the experiments. This longitudinal spacing is of the same order of magnitude as the mean water depth. The transverse sections were sampled every millimeter and five measurements were taken and averaged at each point, in order to reduce noise induced by free surface fluctuations. The number of measurements along the transverse sections and the number of transverse sections were optimized so as to complete the scanning of the area (it required about 4 min) before any relevant bed evolution occurred. The bed configuration can therefore be considered steady during the measurement of a 1 m 2 area. 3. Performed Runs 3.1. Experiment Characteristics [15] We have performed several experiments pertaining to the self inception of a pseudomeandering channel, starting from a straight configuration, with a straight inlet. The experimental conditions of each run are summarized in Table 1. The values are computed with reference to the initial rectangular channel and with a uniform flow: W is the section width, S is the channel and floodplain slope, Q s is the sediment discharge, Fr is the Froude number, and b, #, and d s are the aspect ratio of the channel, the Shields stress and the relative roughness, respectively. The last three quantities are calculated as ¼ W H ; # ¼ ð s ÞgD ; d s ¼ D H ; ð1þ where t is the average bed shear stress, r and r s are the water and sediment densities, H is the water depth, D is the mean grain diameter, and g is gravity. The Froude numbers reported in Table 1 (computed with reference to the initial channel configuration) settled to values in the range during the runs, a range that is comparable to natural conditions. Correspondingly, the bulk Reynolds number (equal to 4HU/n, where U is the stream bulk velocity and n is the kinematic viscosity) had a value of about ; this provided a fully turbulent regime and hydraulically rough wall conditions during the runs. Grain Reynolds number was in the range 20 30; well within the range (15 to 70) indicative of a minimal impact of the viscous forces [Yalin, 1971], which can therefore be neglected for the aim of our study [Francis, 1973; Metivier and Meunier, 2003; Peakall et al., 2007]. [16] In order to investigate the impact of discharge sequencing, we have adopted a step hydrograph (see Figure 5), where discharge jumped at regular times between two values, Q 1 and Q 2. The discharges Q 1 and Q 2, with Q 1 > Q 2, represent two flows that are intended to be both competent (but not overbank) for the channel, since both Q 1 and Q 2 are able to move all the grain size distribution of the bed and of the floodplain. The Shields stress corresponding to Q 1 and Q 2 ranges in fact from about two to three times the sediment motion threshold; thus the equal mobility of bed material during the runs can be assumed. Consequently, our use of a moderately sorted grain size distribution should not alter significantly the overall bed load dynamics with 5of18

6 Figure 5. Typical behavior of the hydrograph used in the runs. T Q1 and T Q2 refer to the duration of the maximum (Q 1 ) and minimum (Q 2 ) discharges, respectively. respect to that observed in an alluvial river (where well sorted distributions generally occur), since no selective transport is expected. [17] Table 1 reports the characteristics of the performed runs. Two sets of parameters have been investigated: runs with the initial l refer to cases with low discharge variability, while the letter h indicates runs with high discharge variability. Three runs were performed for each set of parameters: a run with a step hydrograph characterized by T Q2 = T Q1 (see Figure 5), a run with T Q2 =2T Q1, and a run with a steady discharge equal to Q =(Q 1 + Q 2 )/2 (in the following we will indicate Q 1 and Q 2 as high and low discharge, respectively). We choose ratios Q 1 /Q 2 ranging from 1.5 to 2 in order to study the effects of significant discharge changes. These ratios are also coherent with field studies. For example, consider the work by [Bartholdy and Billi, 2002] on a pseudomeandering reach of the Cecina River (Italy). These authors identify two discharges representative for the morphology of the river: Q 1.58 = 275 m 3 /s and Q 2.33 = 419 m 3 /s (the subscript indicates the recurrence time), the ratio being Q 2.33 /Q 1.58 = 1.52, which is very close to the ratio adopted in the l runs. [18] A step hydrograph helped us to clearly isolate the flow sequencing driven processes that occur whenever a discharge increases or decreases. A continuous changing hydrograph would instead lead to a continuous but gentle channel adjustment, where the main processes induced by an unsteady flow would be less evident. We have checked this by carrying five experimental runs with sinusoidal water and sediment discharges (not shown here for the sake of space). In these runs, we observed morphological behaviors qualitatively similar to those described in section 4, but more plagued with noise. For this reason, and because a continuously changing hydrograph entails difficult experimental controls when measuring real time morphological changes, we focused on the step hydrograph. This has allowed a better visualization of the process and a clearer interpretation of the results. Apart from the advantage of being described by only two parameters, a step hydrograph can also be representative of the discharge regime in regulated rivers, whenever artificial reservoirs are present. [19] In addition to the six h and l runs, we have also performed another two experiments (indicated with the letter r) devoted to elucidating the role of discharge variability (see section 4.1). The r1 run was performed with a steady discharge equal to the Q 1 value used in the h set of parameters, while the r2 run simulated the effects of a single abrupt halving of the discharge in agreement with typical values of discharge decrease due to the presence of dams [Schmidt and Wilcock, 2008]. [20] The following experimental procedure was followed for each run. First, a straight rectangular shaped channel with width W was carved into the sand. The sand was previously wet by the piezometers, in order to achieve sufficient cohesion to maintain the rectangular shape of the channel section. The sand was then saturated using the system of piezometers, and without water flowing in the channel, so as not to disturb the bed. The run was then started with the minimum discharge value, Q 2, of the imposed hydrograph (with the exception of the r2 run) and the sand feeder was activated. The downstream weir was regulated under unsteady conditions in order to avoid backwater effects. Q 1 was designed to be slightly lower than the bankfull discharge to prevent overflow. The runs were stopped when a pseudomeandering pattern was achieved and an evolving bend overstepped the 3 m wide floodplain, or when the channel clearly showed the inhibition process (see section 4.1). The runs generally lasted about 10 h. [21] Each run was repeated twice to ensure that the results were not influenced by chance experimental factors. These repetitions always confirmed the reliability and reproducibility of the experiments: the observed processes were the same and we only observed some limited differences in the numerical values of the bank erosion velocity. These differences occurred because the sand moisture and consistency could have varied slightly from one run to another; however, these differences did not influence the experimental results. In all, 16 runs were performed. [22] A limitation of the experiments must be acknowledged: because of the use of a moderately sorted sand, the mechanism of bed armoring was partially inhibited in the present experimental conditions. However, we expect this inhibition does not weaken our findings. These findings are concerned with morphodynamical processes, essentially driven by the hydraulic characteristics of the stream at the width scale rather than at the sediment grain scale. In section 5, we will show that the crucial impact of the discharge variability is the occurrence of strong transversal components in the flow field during low flow periods, and that these components become much smaller during highdischarge periods. This fluid dynamical aspect, which plays a key role in the bed evolution, is not related to the grain scale; instead, it is strongly dependent on the transect geometry. For this reason, a slightly different sediment bed composition would not alter significantly the results of our work. [23] In addition to the aforementioned runs with sinusoidal discharge, several trial runs were carried out before the experiments described in this work were performed. The width, W, of the initial section of the straight channel and the sand discharge feeding, Q s, were investigated in these preliminary runs. Several cross section sizes were tested for each set of parameters, in order to find the best one. We observed that a channel with a starting section with a much lower W/D value than the equilibrium value presented a long lasting channel widening phase. This phase increased 6of18

7 Figure 6. Example of a measured cumulated bed load mass M s during the runs. The case refers to the l1 run. The continuous line is the linear interpolation of the measured values. Notice the increase in the bed load corresponding to the increase in the water discharge. The small jumps in the measurements are due to the movement of the siphon along the bottom of the downstream tank. the run time and, more importantly, affected the continuation of the experiment because the continuous cross section widening released a large amount of sediment along the channel, which overloaded the channel itself. Therefore, the chosen starting widths, which are reported in Table 1, are those that allowed the channel cross section to be slightly adjusted until alternate bars and bends developed. [24] Other trial experiments were focused on the calibration of the feeding sand rate, Q s. In these runs, the equilibrium sediment bed load corresponding to each discharge was measured while the channel was straight. This calibration was necessary because of the high sensitivity of freeevolution experiments to the feeding bed load; an overfed single thread channel could, for instance, achieve a multithread pattern. An example of bed load measurement is shown in Figure 6 for the l1 run, where it is possible to see the adjustment of the bed load rate caused by the change in the water discharge. We also calculated Q s using the sediment transport formulas by Meyer Peter and Müller [1948], Einstein [1950], and Ashida and Michiue [1972]. The calculated and measured sediment discharge values are reported in Table 2. These three formulations confirm the reliability of our bed load measurements. Thus, a sand discharge very similar to the measured one was fed into the flume for each water discharge value of the hydrograph (as shown in Table 1). In this way, aggradation or degradation and local scour were avoided, and no far from equilibrium external conditions were imposed. Care was also taken to introduce the fed sediment uniformly. In the trial runs, we in fact observed that a local bump in the initial reach, due to a nonuniform sand inlet, rapidly evolved into a longitudinal central bar, leading to a multithread pattern. A local lack of sediment discharge also generated a localized scour which propagated downstream and formed dunes. These dunes hindered the development of alternate bars Some General Features [25] The channel evolution during each run followed three well defined morphological phases and each phase was influenced to a great extent by the discharge variability. We introduce here some general features of each phase that were common to all runs, while, in section 4, we will describe and discuss in detail the role of flow variability in the evolution of the single phases. Figure 7 shows an example of the three phases of the channel evolution in the l3 run. [26] Phase I begins when water flows into the initial straight channel and ends when alternate migrating bars start to influence the bank erosion. At the beginning of the runs, we observed sediment moving downstream as bed load sheets [see Hein and Walker, 1977; Whiting et al., 1988] which were symmetrical to the channel axis. This behavior persisted until these sheets lost their symmetry, because of the instability of the sediment water interface, and formed diagonal shaped one or two grain diameter thick migrating structures. These structures constituted the embryonic form of the alternate bars, but were not able to direct the flow toward the banks. Simultaneously, the cross sections adjusted their width by eroding both banks throughout the channel, and the channel therefore became wider while remaining straight. The diagonal shaped structures increased in thickness due to an accumulation of sediment, which also came from cross sectional adjustment. After some time, which depended on the bed load discharge, the alternate bars became well defined and the bed showed the typical pool riffle sequence. At the same time, the thalweg increased in sinuosity, bending around the bars. The flow was alternatively deflected against the banks, but the full channel was still straight (see Figure 7a). The empirical relation between the cross sectional width of the straight channel, W, and discharge, Q, was (in the range here investigated) W = 9.76Q , with R 2 = 0.88, where W is expressed in cm and Q in L/s. In this first phase, the Froude number decreased because of the presence of friction due to the alternate bars, and because of the widening of the cross section. Table 2. Values of the Solid Discharge Obtained Through the Sediment Transport Formulas and by Direct Measurements a Run AM MPM EI Measured l max l min l mean h max h min h mean r r2 max r2 min a The formulas used are from Ashida and Michiue [1972] (AM), Meyer Peter and Müller [1948] (MPM), and Einstein [1950] (EI). The values are expressed in grams per second. The subscripts max and min refer to the maximum and minimum discharge conditions during the considered run. 7of18

8 channel between the bar and the straight bank was evident. This kind of pattern is commonly found in natural rivers (see Figure 1). As the flow velocity in the chute channel was almost zero, only a limited percentage of the discharge was conveyed. During low flows, the chute channel was occupied by still water coming from the hyporheic fluxes. Figure 7. Example of the three phases followed by the channel during its morphological evolution. Flow is from left to right. The example refers to the l3 run. The arrows indicate the typical migration direction of the bars and bends during each phase while the dashed lines indicate the bar profiles. (a) Phase I, when the channel is straight with migrating alternate bars (photograph taken at 150 min); (b) the inception of the bends in phase II (photograph taken at 360 min); (c) the large embayment induced by the fixed bars in phase III (photograph taken at 490 min). [27] In phase II, the flow impingement against the bank caused by the alternate bars was sufficient to initiate bank erosion. The locus of the bank erosion, and thus of the bend growth, was opposite the bar apex (see Figure 7b). As the bars were still migrating in this phase, the bank erosion regions moved downstream with a similar velocity to that of the bar migration. This second phase was relatively short: when the bend curvature and W/D value increased, the bars stopped migrating. [28] In phase III, the accretion of the nonmigrating bar by sediment deposition was observed and the bends increased in size and curvature (see Figure 7c). The sediment came from the upstream bend erosion and moved through the thalweg to deposit on the downstream bar. The bed load deposition was mainly concentrated on the bar head and on the bar apex, with the consequent downstream lateral accretion of the bar. As a consequence, both the width of the channel and the deviation angle of the stream against the bank increased [Pyrce and Ashmore, 2005]. In this third phase, the formation of large embayments and a chute 4. Results [29] We here describe the experimental findings concerning the role of the discharge variability on the three evolution phases of the pseudomeandering channel introduced in section 3.2. For the sake of clarity, the results are described in three separate subsections, but it should be emphasized that all the presented phenomena interact with and influence each other. The following three subsections describe the role of flow variability on: the inception of the channel pattern (section 4.1), bar dynamics (section 4.2), and bank erosion (section 4.3) Pseudomeandering Pattern Inception [30] An inspection of the experiments has pointed out how discharge variability plays a key role in promoting or, sometimes, in preventing the formation of a pseudomeandering configuration. Runs with a variable flow (l1, h1, and h2) exhibit an acceleration in the formation of alternate bends compared to those with a steady flow (l3 and h3). In other words, discharge variability induces the channel to develop bends with a similar amplitude and sinuosity to the ones observable in the steady discharge case, but in less time. This is due to a phenomenon that we call triggering, which happens in phase II during each transition from high to low discharge. [31] Let us consider the scheme shown in Figure 8. Figure 8a shows the channel at the beginning of phase II during a high discharge. The high flow has a great formative effect on the bed, promoting the formation of large alternate bars with a deep sinuous thalweg. As depicted by the arrows in Figure 8a, the high discharge is only weakly influenced by flowing over the alternate bars, and the core of its flow is only slightly sinuous. As a consequence, the limited impact angle of the core of the discharge against the bank is not able to promote high rates of localized bank erosion. Instead, as shown in Figure 8b, when the discharge decreases from Q 1 to Q 2, the impact angle of the flow core increases and can trigger bend inception. The greater impact angle is due to the flow of the low discharge on the bed features (e.g., the height of the bars and the pool riffle spacing) that have been inherited from the Q 1 period and which are oversized for Q 2. Consequently, most of the low flow is channeled along the sinuous thalweg and only a limited part surmounts the bars. Therefore, the low discharge presents a higher sinuosity and higher impingement against the banks than the quasi bankfull discharge. Other studies [e.g., Friedkin, 1945] have pointed out these different high and low flow paths, but they did not investigate its effects on bank erosion or bend inception. Figures 8c (high discharge) and 8d (low discharge) show the effect of bend inception in the l1 run derived from the decrease in the discharge. [32] A comparison of the variable flow runs with runs performed with the steady discharge, Q, clearly indicates 8of18

9 Figure 8. (a and b) Scheme of the triggering process and (c and d) its experimental evidence in the l1 run. Flow is from top to bottom. Planimetries show the channel during high discharge (Figures 8a and 8c) and low discharge (Figures 8b and 8d). The photo in Figure 8c was taken at 230 min, and the photo in Figure 8d was taken at 260 min, 20 min after the change from Q 1 to Q 2. The dashed lines indicate the bar profiles while the arrows show the direction of the flow core. It is possible to observe that when the highdischarge flows (Figures 8a and 8c), it has a limited impact angle on the bank; instead, when the discharge decreases (Figures 8b and 8d), the flow core presents a higher curvature on the bars and is able to start localized bank erosion (marked as bumps in Figure 8b and easily detectable in Figure 8d). that the variable flow accelerated the bend inception process and that the low flow triggered bank erosion. The times of the transition between phase I and phase II (i.e., the inception of bends) are reported in Table 3. It is evident how the discharge variability reduced the duration of phase I. Moreover, the longer the duration of Q 2, the faster the channel reached phase II. To demonstrate that the dynamical effect of the variable discharge regime is to develop bends at a faster rate than the steady flow (whatever the value of the steady discharge), the r1 run was carried out with a steady discharge equal to Q 1, instead of Q. A comparison of the r1 run with the h1 and h2 runs (performed with a flow varying from Q 1 to Q 2 ) once again emphasized the acceleration in bend inception of the variable flow runs. In fact, when comparing the time at which the first bends emerged between the steady versus the variable flow runs, we found that the steady runs were delayed by some 50% when compared to the runs with variable flows. [33] We have also performed the r2 run, where an abrupt halving of the discharge has been simulated, with the aim of confirming the existence of the triggering process. After 6 h of steady discharge, the channel was still substantially Table 3. Time of the Transition Between Phase I and Phase II a Run Development Time of First Bends (min) l1 260 l2 l3 340 h1 270 h2 250 h3 380 r1 370 r2 390 a TransitionoccurredduringtheQ 2 period in the runs with a variable flow. The acceleration of the process in such runs should be noted. The l2 run did not show any bends because of the inhibition process. 9of18

10 channel curvature induced the alternate bars to stabilize during the low flow period. During the following highdischarge period, the bars were remobilized and moved downstream faster than during the low discharge. Rapidly migrating bars were unable to produce high rates of localized bank erosion [see also Bertoldi and Tubino, 2005]. In our runs, the high discharges always tended to slightly widen the channel rather than increase the amplitude of the small bends. When the high discharge period ended and the low discharge was again introduced into the flume, the alternate bar configuration was out of phase with the planimetry: the bars were adjacent to the previously incepted bends (indicated with circles in Figure 9b) instead of being on the opposite channel side. Therefore, the low discharge flowing on this bed configuration triggered the growth of bends at points opposite and a little downstream (as shown by the boxes in Figure 9b) the already incepted bends. The result was a river planimetry with a series of bulb like shapes with a central bar which deflected the flow onto both banks. The central bars promoted channel widening and a multithread pattern [see Leopold and Wolman, 1957], which also persisted for the following high low discharge cycles. [35] As shown in Figure 9, the inhibition process requires that the downstream shift of bars during the high discharge period, T Q1, is similar to the spacing L of the pre Q 1 alternate bank erosion, as indicated in the following relation v bar T Q1 ffi L; ð2þ Figure 9. Sketch of the inhibition process. Flow is from top to bottom. (a and b) The bar pattern during two lowdischarge steps separated by one Q 1 period (not shown). The circles and boxes mark the bends incepted during the pre Q 1 period (Figure 9a) and the post Q 1 one (Figure 9b), respectively. The dotted lines indicate the bar profiles, and the arrows show the direction of the core of the flow. The intermediate high discharge phase moved the bars downstream by a similar distance to the spacing of the initial alternate bank erosion L (see the downstream movement of the bars marked with A and B). (c) The planimetry of the l2 run during the inhibition process. straight with large migrating bars (phase I). After the halving of the discharge, 30 min of low discharge was sufficient to develop a series of well defined bends. Thus, the discharge decrease strongly accelerated the transition of the channel from phase I to phase II. [34] Although most of the runs with the variable discharge exhibited a triggering process, we observed that the l2 run showed different dynamics and did not reach a pseudomeandering pattern. This run did not exhibit transition between the second and the third phase: the channel rapidly degenerated into a multithread pattern. This was the main consequence of what we call the inhibition process. Figure 9 describes this phenomenon. Like the triggering process, bank erosion and bend growth started during the lowdischarge step (the bend inception points are marked with circles in Figures 9b and 9c) and alternate bars (formed during the high discharge step) with a constant longitudinal spacing, L, were visible (see Figure 9a). The increase in where v bar is the mean downstream migration rate of the bars. In run l2 we measured v bar = 2.2 cm/min and L = 140 cm. As T Q1 = 60 min, equation (2) is satisfied. [36] We observed that the discharge variability dampened the intrinsic tendency of pseudomeandering experiments to braid, except for the run with the inhibition process. The degeneration of the laboratory experiments (with a steady discharge) to a braided pattern is well known [e.g., Ashmore, 1982]. The transition from pseudomeandering to braiding evolves through typical braiding mechanisms, namely chute cutoff, central bar inception, flow diversion on the bar, and bar dissection [Ashmore, 1991]. It has also been acknowledged that an increase in chute channel sizes allows the alternate bars to separate from the bank and to become central bars, thus leading to a multithread pattern [e.g., Ashmore, 1982, 1985]. Such mechanisms were not present in our runs during the low discharge periods and were highly minimized in the high discharge periods. The low flows did not increase the chute channel size (sometimes not flowing in it) and did not present flow diversion on the bars, which was partially exposed. [37] In short, the main effect of the relatively low discharge was to increase the asymmetry of the cross section via thalweg incision and bank erosion. Therefore, the next high discharge flowed highly skewed on the outer bank and the chute channel widening induced by Q 1 was minimized compared to the steady discharge experiments Bar Dynamics [38] The different paths followed by low and high flows in the channel (see Figure 8) affect the bar dynamics in different ways. As previously noted for the triggering process, high discharges induce a predominant longitudinal compo- 10 of 18

11 nent of the flow while low discharges induce a remarkable transversal component with respect to the channel. This entails a different orientation of bed shear stresses on the bar. The experimental bed profiles and the aerial photographs show that the main effect of high flows was the modification, by accretion and downstream translation, of the entire bar structure. Instead, low flows, even when submerging the bar, were not able to transport sediment to the bank attached side of the bar; the downstream bar movement was therefore bounded on the lateral side of the bar, near the thalweg channel. [39] Let us consider Figure 10, which highlights the bar dynamics related to discharge changes in the h1 run (the dynamics here reported have been observed in all the runs with variable discharges). The x and y axes represent the longitudinal and transversal coordinates of the 1 m 2 surveyed area. The origin of such axes is an arbitrary point on the noneroded floodplain. The z axis is the elevation of the bed above an arbitrary datum. Figure 10b shows the bar tail during the Q 2 period. The bar appears close to the right bank. The bar is still being formed, thus the visible bank erosion on the left is low. Figures 10c and 10d show the accretion of the bar as the discharge increases to Q 1. A deep thalweg channel is evident near the left bank and the chute channel emerges between the right bank and the bar. The thalweg channel occupies about half of the river bed during the flow of Q 1. Figures 10e and 10f report the bar modifications induced by the halved discharge, Q 2. The instantaneous response of the bar is the widening of its area by lateral accretion, thus reducing the thalweg channel width (see Figure 10e), and the increasing of the bends incision (i.e., the triggering process). The bed profiling and the aerial photographs (not shown for the sake of space) clearly show that, immediately after the transition from Q 1 to Q 2, the inner side of the bars and the bar tails were not points of erosion or deposition (because of the shifting of the Q 2 flow core on the outer side), and therefore they did not move downstream or become deformed. Thus, all the bar modifications were instead concentrated on the bar head and on the bar apex. [40] After a sufficiently long period of minimum discharge, Q 2, we detected the deposition of a secondary bar a little downstream from the tail of the bar originated by the previous Q 1 (see Figure 10f). These two bars were attached in the middle and detached in the downstream sections by a narrow and slightly incised channel. Therefore, apart from the lateral accretion of the main bar, the settling of a secondary bar adjacent to the previously formed one is the cause of the narrowing of the thalweg channel during the Q 2 period. The secondary bar settling enhances the transversal component of the low flow, which in turn is the cause of the lateral accretion of the bar, since deposition of the sediment occurs not on the bar tail but laterally. There is therefore a strong feedback between the secondary bar growth and the transverse component of the flow induced by Q 2. The presence of secondary bars also enhances the triggering process through the deviation of the flow toward the bends. As can be observed on the downstream portion of Figure 10f, the secondary bar induces the left bank to develop a high curvature, due to the increase in the impact angle of the flow against the bank. A subsequent high discharge tends to unite the two bars in a single sedimentary structure. A similar impact of the different discharge values on the bar morphodynamics of a pseudomeandering reach was also pointed out by Lewin [1976]. [41] The bed profiling was also used to calculate the deposited and eroded volumes on the channel bed and on the floodplain due to the discharge changes, as shown in Figure 11. Figure 11 is obtained by subtracting each bed elevation shown in Figures 10b 10f from the previous one (e.g., Figure 10f minus Figure 10e). As the surveyed area is fixed, with respect to the flume, the calculated differences are due both to bar accretion and to the downstream bar movement. However, the migration rate of the bar is low, especially during the low discharge period, and the plots in Figure 11 can therefore be considered to be attributable mainly to altimetric processes rather than to longitudinal displacement. The sediment deposition processes that form the secondary bar during the low discharge are shown in Figures 11c and 11d. It can be observed that the low discharge, Q 2, inhibits deposition or erosion processes on the bank attached side of the bar. Moreover, there is no erosion in the chute channel. During the low flow, a large depositional area is present where the formation of the secondary bar can be observed (see Figure 11d), while the eroded areas correspond to bank erosion. It follows that the secondary bar does not originate from the deposition of sediments coming from the already formed bar (which is not eroded), but from sedimentation of materials from upstream. [42] We have been able to detect the source of the material that composes the secondary bar in both the bed load derived from the upstream bank erosion and in the bed material coming from a bar head incision process. This process emerged immediately after the discharge decrease, when the low discharge did not submerge the entire bar, but incised a channel on the bar head surface. The incision was caused by knickpoint migration which began in the boundary area between the riffle and the less elevated region downstream (as shown in Figure 12 by the upstream migrating water wave train). The reduced discharge presented a local acceleration in this area, where such discharge flowed above the knickpoint between the riffle and the less elevated thalweg. Instead, Q 1 induced a higher water level and the flow field was less affected by the presence of the step; consequently, no erosion was observable on the step. An animation of the wave train of the knickpoint migration is shown in Animation 1. This animation is a collection of the photographs taken every 30 s immediately after the discharge halving (at t = 360 min) in the h2 run. Figure 12 shows how such an incision induced self confinement of the low discharge in this incised low flow channel and modification of the pool riffle morphology. In other words, the incision process of the bar head allowed the pools to be directly connected by a channel incised through the riffle. The self confinement of Q 2 in the incised channel inhibited the low discharge from flowing over the bar and a consequent flow diversion was avoided. In addition, the topographic lowering of the low flow channel under the chute channel bed meant that Q 2 rarely flowed in the chute (see the inset in Figure 12b, where the R and S markers show the bar and the incised channel, respectively). Thus, the chute channel was rarely active during low flows and it was mainly occupied by still water derived from hyporheic fluxes. 11 of 18

12 Figure 10. Bar evolution in the h1 run obtained through the use of the laser sonar measurement system. Flow is along the x axis orientation. (a) The discharge values during the measurements versus the bed surveying times; the letters refer to the corresponding frames. (b) The bar tail that reaches the surveyed area during the minimum discharge. (c and d) Images correspond to the bar accretion during the high stage of the hydrograph; (e and f) images refer to the secondary bar deposition process during the falling stage of the hydrograph. The highly increased bank erosion in this step is related to the triggering process. The color bar represents the elevation (in millimeters) above an arbitrary datum. 12 of 18

13 Figure 11. (a d) Bed elevation change, Dh, between the bed configurations shown in Figure 10. Positive (negative) values correspond to deposited (eroded) sediment. The unit of measurement of Dh is millimeters. Flow is along the x axis orientation. For example, Figure 11a shows the difference between the bed elevation displayed in Figures 10c and 10b. The subscripts with Dh refer to Figures 10b 10f Bank Erosion [43] A high precision Matlab routine has been developed in order to detect the bankline evolution and to calculate the bank erosion rate from the aerial photographs. In our runs, bank erosion always developed as a continuous process without exhibiting episodic slump blocks, because of the uniformity of the bank material. The main differences in the bank erosion induced by steady or variable flows are shown in Figure 13, which reports the longitudinal distributions of the bank erosion rates of a channel bend during different time intervals in phase III of the l3 run (steady discharge) and of the l1 run (variable discharge). The bank erosion rate is evaluated by measuring the normal displacement of each bankline point from the different shots of the banks. The normal component of the bank erosion rate, V n, is obtained by dividing the normal displacement by the temporal delay between the photographs (see the inset in Figure 13c). The distributions of V n along a fixed reference that coincides with the centerline of the initial straight channel (axis x) are then plotted. During bend evolution, the steady discharge induces erosion distributions with similar shapes (see Figure 13a). The peaks maintain their values and are only shifted slightly downstream. Thus, the bend evolves preserving its shape and with a slight increase in the downstream skewness. [44] The V n distribution observed during flow sequencing is qualitatively different. The bank erosion distributions during the Q 2 and the Q 1 periods and immediately after the discharge changes (dashed lines) are compared in Figure 13b. It is immediately clear how the discharge variability induces the distributions to be shifted downstream. During the increase in the discharge, the instantaneous response of the bank is a transitory widening of the erosion region and a doubling of the erosion rate peak (see distribution 2 in Figure 13b), which settles at a lower value during the Q 1 period (distribution 3). In a similar way to the rising stage, the falling stage of the hydrograph also presented a transition (distribution 4) between the erosion rate of the high and low discharges. The subsequent low discharge (distribution 5) exhibited a 13 of 18

14 Figure 12. Shown are two bends in the h1 run after 7 h, during the Q 2 step. Flow is from left to right. Notice the incision of the low flow channel in the riffle and the bar, as marked by the dashed line. This incision developed through a knickpoint migration mechanism, as schematically shown by the water wave train. The star symbol marks the limited bank erosion caused by the flow diversion on the bar head when the bar head incision process has not occurred yet. A comparison of this photograph with a natural pseudomeandering river (see Figure 1) highlights the reproducibility of the pattern in flume. The inset is an enlargement of the channel area incised by Q 2 (marked by the box in the figure). The dashed line emphasizes the boundary line between the bar (indicated by marker R) and the incised channel (indicated by marker S). The elevation of the upstream section of the chute channel bed (shown by the black and white triangular marker) is about 1.5 cm above the incised channel bed; thus, Q 2 did not flow in the chute channel. Animation 1. Animation of the bar head incision process. For scaling a meter is on the floodplain. Animation available in the HTML. 14 of 18

15 Figure 13. Typical distribution of the bank erosion rate, V n, in a bend for (a) a steady (run l3) and (b) an unsteady (run l1) flow along the flume centerline (x axis). The legend in Figures 13a and 13b indicates the time intervals in which the erosion rates have been evaluated. Notice the downstream shifting of the peaks induced by the variable discharge. (c and d) Photographs of the bend (marked with the arrow) at the end of the analysis. The dashed lines indicate the bankline configurations in the previous analysis period (i.e., at 490 min in Figure 13c and at 380 min in Figure 13d). The inset in Figure 13c schematically shows the vector V n between an old (dashed line) and a new bank line (solid line). similar erosion rate distribution to the previous one (distribution 1), but shifted downstream by about 1m. [45] Such behavior can be explained in light of the aforementioned bar dynamics (see section 4.2). In phase III of the runs with a steady discharge, the alternate bars are fixed, thus inducing bank erosion in the same bank region. During phase III of the runs with a variable discharge, the bars which were fixed during the Q 2 period are instead remobilized by the high discharge, thus shifting the bank erosion downstream during the Q 1 period. Moreover, the deposition of the secondary bar during the low discharge period deviated the bank impact point induced by the core of the flow of Q 2 downstream to that of Q 1. These variable flow driven processes are the reasons for the overall downstream shifting of the distributions. [46] The variable discharge introduces a dynamical component to the bar behavior which in turn has an impact on the spatial distribution of the bank erosion. Comparing Figure 13c with Figure 13d, it can be observed that the bankline shapes induced by the variable flow evolve through a more complex path than the ones generated by a steady discharge. The main difference is that the variable flow induces the inner bank of a bend not to be straight. In fact, the inner bank was always straight in runs with a steady discharge, while it exhibited a convex shape in runs with an unsteady discharge: compare, for instance, the straight inner banks in Figures 7c and 13c with the more sinuous inner banklines in Figures 12 and 13d. 5. Discussion [47] Our experimental results indicate that variable flows promote and sustain a pseudomeandering configuration, and prevent it from shifting toward a multithread configuration. As already noticed in field studies [e.g., Rinaldi et al., 2008],we have detected that low formative (i.e., able to move sediments) discharges play a key role in the morphodynamics of pseudomeandering channels. The low discharges acting on a bed configuration, which can even be originated by only sporadic bankfull discharge periods, promote two morphological modifications which have the purpose of sustaining the pseudomeandering channel: the cut of a sinuous preferential channel by thalweg incision and the bar head incision (see Figure 12). The more such incisions are developed, the more braiding mechanisms are prevented from emerging, even during high discharge periods. In addition, the altimetric and planimetric asymmetry enhanced by low discharges (e.g., by the deposition of the secondary bar) allows the core of high 15 of 18