Self‐constraining of low‐energy rivers explains low channel mobility and tortuous planforms

Meandering rivers are abundant on Earth, from the largest rivers to the smallest tributaries. The classical view of meandering rivers is a sinuous planform with rounded bends, which grow and migrate until they are cut‐off. However, many low‐energy meandering rivers have planforms that are much more complex than this classical view due to the heterogeneity of their alluvium, and show relatively limited channel migration. Based on a detailed palaeogeographic study of the Dommel River in The Netherlands, it is inferred that low‐energy meandering rivers may develop tortuous planforms with sharp bends, owing to self‐formed deposits that increasingly constrain the channel mobility. This mechanism is corroborated by data from 47 meandering river reaches of varied scale from around the world, which show that erosion‐resistant floodplain deposits are preserved in the river banks when the river energy is below a critical threshold. The term ‘self‐constraining’ is proposed for low‐energy rivers where an increase in bank stability over time results in progressive tortuous planforms and reduced mobility. A conceptual model, based on the dataset, shows that the increase in bank stability over time also increases the energy required to break out of the tendency to self‐constrain. Self‐constraining thereby enhances the resilience of the system to bank erosion, while an unexpected increase in bank erosion may occur if river energy exceeds the critical threshold. This study provides a novel explanation for the evolution of low‐energy river planforms and dynamics, and provides new insights on their responses to climate changes.

classical model forms the basis of both physical and numerical river meander migration models, which produce simulations of freely meandering patterns with rounded bends and continuous lateral migration (Crosato, 2009;Kleinhans, 2010;Motta et al., 2012b). However, natural meandering rivers have a wide range of planform complexities (Figure 1), and not all rivers with sinuous planforms show lateral migration (Hickin and Nanson, 1984;Güneralp and Rhoads, 2011;Kleinhans and Van den Berg, 2011;Vermeulen et al., 2014;Candel et al., 2017).
The term 'tortuosity' was introduced by Schumm (1963), and used to refer to rivers with complex planforms consisting of unusually sharp bends with variable size and abrupt, irregular changes in channel direction, lacking the typical smoothness of ideal meander curves ( Figure 1A through D). This definition of tortuosity is adopted here, and is radically different from the use of tortuosity as a synonym for sinuosity by some others (Frascati and Lanzoni, 2009). Sharp bends are commonly defined as R curv w < 2.0 (R curv = bend curvature, w = channel width), and form when outer banks are relatively erosion-resistant compared to the river stream power (Leeder and Bridges, 1975;Ferguson et al., 2003;Makaske and Weerts, 2005). Field measurements by Schumm (1963) showed that greater river tortuosity relates to larger silt-plus-clay (SC) fractions of river banks. Subsequent research indicated that large SCfractions are typically found in low-energy meandering rivers (Nanson and Croke, 1992). More recently, numerical modelling studies showed that tortuous planforms develop when heterogeneous floodplains are included in the simulations, consisting of depositional units with different resistances to erosion (Camporeale et al., 2005;Güneralp and F I G U R E 1 River planforms throughout the world, A through D showing tortuous meandering planforms, and E and F showing relatively classical meandering planforms, derived from Google Earth satellite imagery (2018) for B through F. All planforms are scaled to five predicted meander amplitudes (Carlston, 1965). Rhoads, 2011; Motta et al., 2012a;Bogoni et al., 2017). These authors stress that floodplain heterogeneity is an important control on planform complexity in (simulated) meandering rivers. Additionally, Hudson and Kesel (2000), who compared sections of different floodplain heterogeneity in the Mississippi River, found that average lateral migration rates are lowest where floodplain heterogeneity is highest. The authors explain this by greater presence of cohesive (silty and clayey) and organic-rich deposits (e.g. clay plugs), which can be 10-20 times more erosion-resistant than non-cohesive (sandy) units (Hjulstrom, 1935). Although relationships have been described in previous studies of lateral migration rates, bend curvature and floodplain sediment composition, a proper conceptual model on low-energy river planform development is still lacking. Based on earlier publications, it is hypothesized that low-energy meandering rivers in heterogeneous floodplains predominantly erode the easily erodible, non-cohesive depositional units (Turnbull et al., 1966;Hickin and Nanson, 1984), while they continuously form both easily erodible (e.g. point-bar) and relatively erosion-resistant (e.g. residual channel-fill) depositional units (Smith et al., 2009;Bogoni et al., 2017). This mechanism may explain why low-energy meandering rivers tend to have tortuous planforms with low channel mobility.
The main aims of this paper are: (a) to test the hypothesis of a relationship between inhibited lateral channel mobility, planform tortuosity and the evolution of floodplain sediment composition, and (b) to define the parameter space of river energy and bank erosion-resistance at which this conceptual model applies. Toward the first aim, the long-term evolution of the low-energy meandering Dommel River (The Netherlands) is reconstructed in detail. The second aim is addressed by analysing a large dataset of meandering rivers with data available on stream power, river energy (i.e. stream power), bed material and SC-fractions of the banks.

| Study area
The Holocene planform evolution and floodplain stratigraphy of the Dommel River (Figure 2), a low-energy meandering sand-bed river with a tortuous planform, was studied. This investigation combined coring, ground-penetrating radar (GPR) and geochronological analysis around four oxbow bend complexes. The Dommel River's source is located at the Kempen Plateau in Belgium, +77 m NAP (Dutch Ordnance Datum, ≈sea level), and drains into the much larger River Meuse at + 2 m NAP ( Figure 2). It has a length of 120 km of which 85 km is located in The Netherlands. The catchment size is ca 677 km 2 . The river has an annual average discharge of 14 m 3 /s and a mean annual flood discharge of 22.3 m 3 /s at its downstream end.
The Dommel River was a braiding river during the Pleniglacial with abundant sediment availability, and low average discharges and transport capacity (Vandenberghe and Bohncke, 1985;Vandenberghe and Van Huissteden, 1988). The cold and dry climate and absence of vegetation during the Pleniglacial resulted in large-scale deposition of coversand 0.5-2 m thick in the study area, which currently overlies all older deposits outside the valley ( Van der Hammen, 1971;Vandenberghe and Bohncke, 1985). Locally, the coversands are very fine-grained and would more properly be called loess and sandy loess, referred to as 'Brabant loam' or the Liempde Member of the Boxtel Formation (Vink, 1949;Schokker, 2003). The climate changed to warmer and wetter conditions at the Pleniglacial to Late Glacial transition, and vegetation re-established. Consequently, the sediment availability decreased and the river discharge increased resulting in a relatively large, incising meandering river (Vandenberghe and Bohncke, 1985;Vandenberghe and Van Huissteden, 1988;Vandenberghe, 1995). The result of the Late Glacial meandering phase is a well-expressed bluff along the edge of the valley ( Figure 2C through F).
This research focusses on planform and morphological development of the Dommel River during the relatively warm and wet Holocene. Historic maps show that around 1890 calibrated calendar age (CE) the river had a tortuous planform that was hardly affected by humans, except for some local modifications related to weirs and watermills (Waterschap De Dommel, 1941; Figure 1A). After 1890 CE, many river bends and bend complexes were cut-off to promote rapid drainage of the catchment (Waterschap De Dommel, 1941). Palynological data for the Dommel Valley (Janssen, 1972;Van Leeuwaarden, 1982) are available for the entire Holocene and indicate relatively small-scale human cultivation on the higher grounds around 500 BCE, while these areas were increasingly being used for agriculture after 1000 CE with the cultivation of buckwheat, rye and pine. The valley was used largely as pasture. Currently, the land use around the Dommel River is forest and agriculture (cattle and arable farming).
There is little morphological evidence of active channel migration prior to river normalization; some oxbow complexes are present, but no scroll-bar forms are observed ( Figure 2D through F). The historical map of 1837 CE shows how these bend complexes were still part of the main river ( Figure 1A). Figure 2 shows three selected research sites in the Dommel River, which were selected based on the presence of oxbow lakes. These oxbow lakes are well-preserved in the landscape and consist of sharp bend complexes, similar to Dommel River bends that are still connected to the river (Van Alphen et al., 1984).

| Ground-penetrating radar
Ground-penetrating radar was used to select suitable coring locations based on stratigraphic differences, and to support the interpretation of the lithological borehole cross-sections. The GPR measurements were conducted with a pul-seEKKO PRO 250 Hz with a SmartTow configuration. The GPR was used in different directions relative to the bend complexes ( Figure 3). In a sandy subsurface, lateral accretion surfaces and palaeochannels can usually be detected with a GPR (e.g. Figure 4). Loamy and peaty subsurfaces strongly attenuate the GPR signature (Neal, 2004), resulting in poor GPR images and no information on subsurface structure. For this study area, the electromagnetic-wave velocity was determined to be 0.052 m/ns, derived by using isolated reflector points (Van Heteren et al., 1998;Neal, 2004) in the EKKO_Project™ software, and by comparing depths of recognizable layers with the coring data.

| Coring and Lithology
Hand corings were performed along the inside and outside of the river bend complexes (Figure 3). The surface elevation of each coring site was determined using a GPS combined with the digital elevation map (DEM) (0.5 × 0.5 m grid; Van Heerd and Van't Zand, 1999). A gouge auger (Ø 3 cm) was used when the subsurface consisted of peat or water-saturated loam, an Edelman auger for unsaturated loam or sand and a Van der Staay suction corer ( Van de Meene et al., 1979) for saturated sand. In total, 130 corings were performed to a maximum depth of 5.9 m. Lithology of sediment cores was described in 10 cm thick intervals, using the USDA nomenclature (Berendsen and Stouthamer, 2001). The sediment grain size (D 50 ) of non-organic, sandy samples was visually checked in the field by comparison with a sand ruler. In addition, the plant macro-remains, any visible bedding, colour and presence of gravel were described.
The lithological data are presented in five lithological cross-sections ( Figures 5A through 10A). For each of the sections, a lithogenetic interpretation was inferred from the lithological properties, facies geometries and GPR data ( Figures 5B through 10B). In Section 3.1, maps are presented of the locations of erosion-resistant layers, defined as peaty or loamy layers with a minimum thickness of 0.5 m.

| Optically stimulated luminescence dating
Eleven samples for quartz optically stimulated luminescence (OSL) dating were taken to determine the age of erosion-resistant layers and point-bar deposits ( Figure 3). Samples were collected in a PVC tube (Ø 4 cm, 25 cm length) with a Van der Staay suction corer ( Van de Meene et al., 1979;Wallinga and Van der Staay, 1999), allowing collection of non-lightexposed sand in the middle of the tube. The OSL age was determined at the Netherlands Centre for Luminescence dating, Wageningen University. Approximately 150 g of sediment, from the light-exposed outer ends of the tubes, was used for the dose rate analysis, and the remaining sediment was prepared for equivalent dose estimation.
For dose rate estimation, samples were dried and ashed to remove water and organics and determine their weight fractions. Samples were ground and mixed with wax and moulded in a puck to ensure radon retention and provide a fixed geometry for measurement. Radionuclide concentrations were determined using high-resolution gamma-ray spectroscopy, and converted into infinite matrix dose rates  (Guérin et al., 2011). Attenuation by water and organics (Aitken, 1998) were taken into account, based on present water and organic content. Grain size attenuation was taken into account for beta dose rate estimation (Mejdahl, 1979). A contribution of cosmic dose rates was included following Prescott and Hutton (1994), and assuming immediate burial to present depth. A minor contribution from internal alpha irradiation inside the quartz grains  was also included.
For equivalent dose estimation sand-sized grains of quartz (180-212 μm) were obtained through sieving and treatment with HCl, H 2 O 2 and HF. For each sample, small aliquots (2 mm diameter, about 75 grains) were prepared on stainless-steel disks sprayed with silicon oil. Measurements were performed on a Risø TL/OSL DA20 reader (Bøtter-Jensen et al., 2003), using the single-aliquot regenerative dose (SAR) protocol (Wintle and Murray, 2006). A relatively low preheat of 200°C for 10s and 10s 'cutheat' of 180°C were used, to prevent thermal transfer effects. Earlybackground subtraction was used to maximize the contribution from the quartz fast-OSL component (Cunningham and Wallinga, 2010). Around 40 aliquots were measured per sample. The Central Age Model (Galbraith et al., 1999) was used to determine overdispersion for all samples. This model was also used to determine the palaeodose (best-estimate of the burial dose) for the sample of aeolian sediment taken from the valley side (NCL-2117118; Table 1). The overdispersion not related to heterogeneous bleaching (σ b ) was estimated to be 17 ± 7% (Cunningham et al., 2011), and used as sigma b input for the bootstrapped version of the Minimum Age Model (Galbraith et al., 1999;Cunningham and Wallinga, 2012), which was used to determine palaeodoses from scattered equivalent dose distributions for all fluvial samples. Burial ages were determined by dividing the palaeodose by the dose rate, taking all uncertainties in both into account. Following conventions, results are reported in ka relative to the year of sampling (2017 CE) with 1-sigma errors (Table 1).

| 14 C Dating
A single sample for 14 C dating was taken from a residual channel-fill using a gouge auger (Ø 6 cm; Figure 3C; sample 472). Macro-remains from terrestrial species (e.g. sedge) were selected in the laboratory using a light microscope. Samples were stored in diluted HCl (4%) at 5°C. The 14 C age was determined by Accelerator Mass Spectrometry at the Centre for Isotope Research (Groningen University). For calibration, the IntCal13 curve was used in the OxCal4.2.4 software (Bronk Ramsey, 2009;Reimer et al., 2013). Following conventions, uncalibrated radiocarbon age (BP) and CE are reported.

T A B L E 1 OSL and 14
C dating results of the Dommel River. The sample codes correspond to the codes given in Figure 3 Sample Code

| Comparison to other meandering rivers
The dataset of Kleinhans and Van den Berg (2011) was used as an analytical starting point, because similar data and selection criteria were required. The data contained in this dataset are mean annual flood discharge, bankfull discharge, median bed grainsize and valley slope. In addition, the average silt-plus-clay fraction of the river banks and tortuosity of the channel planform were determined (see below). All studied meandering rivers are alluvial rivers that have no sign of strong modification by humans, no engineering in the river, a perennial flow regime, and an effective channel-forming discharge (Q eff ) >10 m 3 /s (mean annual flood, and when not available the bankfull discharge was taken, see argumentation of choice given by Figure 3A) including the OSL sample locations.

(A) Lithological cross-section. (B)
Lithogenetic cross-section. Location of the bend complex A-1 and A-2 are indicated (see Figure 2D) From this dataset, a subset of meandering river reaches was selected for which published information on average SC-fractions of the river bank was available in the literature. Estimates on average SC-fractions of the fluvial depositional units are taken as a measure of the erosion-resistance of the floodplain units following Hjulstrom (1935), Schumm (1963) and Julian and Torres (2006), as this is the only suitable parameter that is abundantly available and was previously linked to tortuosity (Schumm, 1963). These river banks represent either depositional units of the river or the valley side. A high or low average silt-plus-clay fraction of the river banks suggests they consist of relatively erosion-resistant or easily erodible depositional units, respectively. Data were not included if SC-fractions were only qualitatively described. Where ranges of SC-fractions were reported, the middle of the range was used. Sampling methods and texture analysis varied between studies that reported average SCfractions; see cited sources in the Supplementary Data for details. Generally, multiple samples were taken of both river banks near the gauging stations, often at several depths from the exposed river bank. Samples were in most cases analysed in the laboratory using the sieving and pipette method.
Kleinhans and Van den Berg (2011) showed that the potential specific stream power (ω pot ) is a suitable measure for river energy to explain the degree of meandering. The potential specific stream power was calculated by applying the relationship presented by Kleinhans and Van den Berg (2011): where pv is the potential specific stream power (W/m 2 ), ρ the water density (kg/m 3 ), g the gravitational acceleration (m/s 2 ), and coefficient ε = 4.7 √ sm −1 for sand-bed rivers and ε = 3.0 √ sm −1 for gravel-bed rivers (Van den Berg, 1995). A large advantage of the potential specific stream power as a measure for river energy is that it relies on parameters that are independent of the actual channel planform, and hence can be used to explain the planform tortuosity of a river (Van den Berg, 1995).
There is thought to be no widely accepted metric to quantify planform tortuosity (ignoring the metric proposed that is based on channel length divided by valley length, and thus reflects sinuosity rather than tortuosity). Here a new metric is proposed, based on the fraction of bends that are 'sharp' with a R curv w < 2.0 (R curv = bend curvature, w = channel width). To estimate this metric, bend curvature of the channel centreline and average channel width of each bend were determined using satellite imagery from Google Earth for 20 consecutive meander bends in the river reaches contained in the Kleinhans and Van den Berg (2011) dataset. Including more bends in this measure would result in sharp bend measurements that are taken too far from the measurements of the other parameters.
The resulting dataset was supplemented with information from the Dommel River (this study), and the Overijsselse Vecht (recently studied by Candel et al., 2018). Finally, data for two Late-Glacial rivers were included (Dommel and Niers), based on channel patterns recognizable from DEMs or satellite imagery, and published information on average SC-fraction of the surrounding depositional units (see Supplementary Data for references). The Late-Glacial Dommel River had a bankfull discharge of a factor 12-15 higher than the current Dommel River (Vandenberghe, 2001). Valley slope was estimated using the depths of Late-Glacial deposits from DINOloket, a national geological borehole database (TNO, 2015). Data for the Late-Glacial Niers River were derived from Kasse et al. (2005). Planform tortuosity of  Late-Glacial rivers was measured from visible palaeochannels on DEMs or satellite imagery or from the valley side bluffs, divided by the estimated width of the Late-Glacial systems known from Late-Glacial oxbow channels.

| Lithogenetic units
Lithogenetic units were identified within the Holocene Dommel River valley-fill based on lithology, planform, facies architecture (GPR) and interpreted genesis. In general, the Holocene valley-fill can be distinguished from bordering Pleistocene valley side deposits and underlying Pleistocene valley-fill deposits by the presence of organic matter (OM), for example, recognizable plant remains, and dark colours (Bisschops, 1973;Berendsen and Stouthamer, 2000;Huisink, 2000).
The Pleistocene valley-fill deposits consist of very fine to medium fine sand (105-420 µm), with a light, bright colour, sometimes with small fining upward sequences several decimetres thick. Thick beds (several decimetres) of loam or OM are absent (Bisschops, 1973;Schokker and Koster, 2004), but thin gravel beds up to a decimetre thick can be found within the unit. The top of the Pleistocene valley-fill is usually found ca 4-5 m below the surface (Bisschops, 1973).
The Pleistocene valley side can clearly be distinguished from the valley-fill due to its higher surface position. The valley side consists of the sedimentological units coversand (Bisschops, 1973), which partly consists of 'Brabant loam' (Vink, 1949;Schokker, 2003), and fluvioperiglacial deposits (Bisschops, 1973). Locally, strongly consolidated, in situ peat can be found within the unit. The texture ranges from very fine sand to medium fine sand (105-420 µm), and loamy sand to clay loam. The colours are light grey, brown and yellow. Beds of OM are mostly absent, except for sporadically occurring laminae several millimetres thick.
The lithogenetic units that form the Holocene valley-fill are elaborated on here.
Overbank deposits consist of very fine sand to fine sand (median grain size 105-210 µm), peaty sand and loamy sand to clay loam. The colour of the unit is usually light grey to dark brown. The OM content is low (<1%) when not peaty. Sometimes small fractions of reworked plant remains or loam are present, which occur in layers of several millimetres to several centimetres in thickness. The unit mostly overlies the other units, but can be found within the unit in situ peat as well. The unit is usually found near a channel or channel-fill, and has a thickness of 1-2 m, but becomes thinner further away from the channel or channel-fill. The unit can be recognized by its horizontal layering in the GPR profiles when the GPR results are of sufficient quality (Figure 3).
Residual channel-fill deposits range in texture from loamy sand to clay loam, peaty sand and clayey peat. In situ peat can be present near the base of the unit. The colour of the unit is mostly dark brown, grey, green or blue. The unit is generally humic (OM content 2%-4%) or very humic (OM content 4%-8%). The unit is structureless when consisting of peat, or else consists of layers of OM, sand or loam with thicknesses of several millimetres to several centimetres. The degree of consolidation increases with depth when overlain by sediments, and the unit was difficult to core below ca 2 m depth. The unit has a relatively low width/thickness ratio, a thickness of 2.5-4 m, and is located on top of and alongside channel deposits. The unit strongly reflects the GPR signal, but the unit base can be recognized in the GPR profile as a concave structure (i.e. depression, Figure 3). When the GPR profile quality allows, the horizontal or concave layering can be recognized within the unit (e.g. Figure 4A,B).
Channel deposits were split into three different fluvial facies, in order to distinguish different types of channel deposits. Fluvial facies 1 consists of moderately well-sorted clastic sediments varying in texture from very fine sand to coarse sand (median grain size 105-600 µm). The colour of the unit is light brown to dark grey. A fining upward sequence is often present with medium fine to coarse sand at the bottom of the unit (channel lag) containing up to 15% gravel, followed by very fine sand, loamy sand or sandy loam at the top. The colour of Fluvial facies 1 is light grey or brown. Organic and loamy beds are mostly absent. The unit has a thickness of 4-5 m and reaches the present surface, although the unit is generally not recognizable from the topography. Except for its near surface location, the unit is relatively difficult to distinguish from the Pleistocene valley-fill. Gently inclined strata (1°-3°) can be visible in the GPR profile (Figures 3 and 4E,F). Fluvial facies 2 is similar to Fluvial facies 1 based on texture, geometry, extent and the presence of a fining upward textural trend. However, the colour of Fluvial facies 2 is darker, dark brown or grey, and Fluvial facies 2 contains well developed layers of fluvially reworked plant remains (e.g. wood, leaves, seeds) and organic layers with thicknesses of several centimetres up to several decimetres. Loamy beds, several centimetres thick, can be present. When located near the surface, steeply inclined strata (14°-28°) are visible in the GPR profiles (Figure 3 and 4A through D). Fluvial facies 3 consists of (peaty) sandy, clayey or silt loam, clay or clayey peat. The colour of Fluvial facies 3 is dark brown, grey, green or blue. Fluvial facies 3 is generally humic (OM content 2%-4%) to very humic (OM content 4%-8%). The fluvial facies can be structureless, or can contain layers of fluvially reworked plant remains, organic and loamy layers with thicknesses of several millimetres to several centimetres. The total thickness of Fluvial facies 3 ranges from several decimetres up to 2.5 m. Fluvial facies 3 can be found within or on top of Fluvial facies 2. Thin deposits of Fluvial facies 3 can also be present in Fluvial facies 1. Fluvial facies 3 is often found along the margins of the valley or at the upstream side of a concave bank. Overbank deposits sometimes overlie Fluvial facies 3. The unit strongly reflects the GPR signal in contrast to Fluvial facies 1 and 2, and can consequently be recognized from the GPR profiles. Different types of channel deposits can be interpreted from the described fluvial facies. Fluvial facies 1 was interpreted as point-bar deposits with a fining upward sequence. The GPR profile clearly shows lateral accretion surfaces, with a slope of approximately 1°-3°. Gently inclined strata F I G U R E 9 Cross-sections of the valley-fill (location in Figure 3E  may indicate a former river channel with a relatively large width/depth ratio (Leeder, 1973;Willis, 1989).
Fluvial facies 2 was also interpreted as point-bar deposits, with a clear fining upward sequence. The bottom and middle of the point-bar consist of thick intervals of stacked plant remains and organics, interlayered within the sandy point-bar. The presence of these thick intervals of plant remains result from the preservation of pool-infills on the river bed, or from counter-rotating flows on the convex side of a sharp river bend (Nanson, 2010;Blanckaert, 2011;Blanckaert et al., 2013). The steep inclination in the GPR profiles (14°-28°) indicates that the associated channel had a relatively low width/depth ratio (Leeder, 1973).
Fluvial facies 3 mainly represents counterpoint deposits and upper or middle point-bar deposits. Counterpoint deposits occur as thick deposits of structureless or layered fine sediments and organics along the margins of the valley or on the upstream side of concave bends, which suggests deposition from suspension (Carey, 1969;Hickin, 1979;Page and Nanson, 1982;Makaske and Weerts, 2005;Smith et al., 2009Smith et al., , 2011. Counter-rotating flows, flow separation, on the concave side of a river bend, promote the growth of these counterpoint deposits, which interfinger with point-bar deposits (Hickin, 1986;Makaske and Weerts, 2005;Smith et al., 2011). Flow separation mainly occurs in sharp river bends (Nanson, 1980;Blanckaert, 2011;Blanckaert et al., 2013). The interpretation given here matches the interpretations by Makaske and Weerts (2005) in the Hennisdijk channel-belt and Smith et al. (2011) in the meandering Peace River, who described the muddy, loamy and organic nature of these counterpoint deposits. Fluvial facies 3 can also be interpreted as middle or upper point-bar deposits, being part of the fining upward sequence of Fluvial facies 2. In this setting, Fluvial facies 3 was deposited near the downstream tail of a point-bar when flow separation occurs on the convex side of a sharp bend (Nanson, 1980;Blanckaert, 2011;Blanckaert et al., 2013), explaining the relatively organic and fine-grained nature of point-bar deposits found in the Dommel River. Point-bars can consist of substantial quantities of organics, loam and mud, which seems especially characteristic of low-energy meandering river systems (Makaske, 1998 p. 225;Makaske and Weerts, 2005;Smith et al., 2009).

| Cross-sections
The lithological and lithogenetic cross-sections are shown in Figures 5 through 10 and described below. The dating results are shown in Table 1, and also indicated in the cross sections. Figure 5 shows a cross-section of bend complexes A-1 and A-2 ( Figure 3A). On the southern side, Fluvial facies 3 is interpreted as counterpoint deposits with a depth of ca 2 m, lying on top of Fluvial facies 2. These counterpoint deposits are relatively old (7.8 ± 0.8 ka), and hence the configuration relative to the palaeochannel, which is different from the recent Dommel River channel, cannot be Figure 3E derived. Point-bar deposits on the inside of this bend complex are relatively young (0.6 ± 0.1 ka; Figure 5). Bend complex A-1 is bordered on the northern side by thick Holocene overbank deposits and in situ peat. The point-bar deposits of A-1 are older (2.3 ± 0.3 ka) than those of bend complex A-2. Figure 6 shows a cross-section of bend complex B, where the current Dommel River lies along the valley side in the southern part. The valley side deposits ( Figure 3C) consist of clay loam and very fine sands, overlying compacted in situ peat. Point-bar deposits (1.3 ± 0.3 ka) are located north of the current Dommel River, which reach channel-depth thickness (ca 4-4.5 m). The middle pointbar deposits consist of consolidated clayey and sandy peat (Fluvial facies 3). More point-bar deposits are located to the north, with peaty and loamy residual channel-fill sediments that reach as deep as the current Dommel River channel ( Figure 6B). The in situ peat dates from 9.6 ± 0.2 ka. A narrow, relatively young point-bar deposit (ca 40 m wide, 0.7 ± 0.1 ka) is located north of the bend complex, with a similar depth as the residual channel-fill deposits. The GPR cross-section shows steeply inclined strata reflecting the lateral accretion surfaces of the point-bar, and horizontal layering north of the point-bar ( Figure 4C,D). Fluvial facies 3 was interpreted here as counterpoint deposits (8.5 ± 1.2 ka), which seem to interfinger with point-bar deposits towards the north, and have a similar depth as the point-bar and residual channel deposits that are present in the cross-section. Figure 7 shows a cross-section perpendicular to the cross-section in Figure 6. A small point-bar deposit is located on the western side, reaching channel-depth thickness. Pointbar deposits are located to the east, showing gently inclined lateral accretion surfaces ( Figure 4E,F). Point-bar deposits (2.2 ± 0.3 ka) lie in between the peaty/loamy residual channel-fill and the valley side, and are similar in thickness to the current Dommel River depth (ca 4-4.5 m). The middle of these point-bar deposits are relatively organic and loamy (Fluvial facies 3). The loamy top of the valley side deposits is interpreted as the 'Brabant loam' described by Schokker (2003) and dates from 14.6 ± 1.4 ka (Kasse et al., 2016). Figure 8 shows a coring from the outer bank of bend complex B ( Figure 3C). Surrounding corings on this part of the bend complex showed a similar succession of Fluvial facies 3 overlying Fluvial facies 2. This part was interpreted as counterpoint deposits dating from 2.5 ± 0.2 ka, and shows a similar age as the point-bar deposits on the inside of the bend complex in Figure 5. Figure 3C shows the extent of the counterpoint deposits along the valley side (all green-coloured corings) and the configuration relative to the channel that formed these counterpoint deposits. Figure 9 shows counterpoint deposits along the southeastern valley side of bend complex C ( Figure 3E), dating from 2.8 ± 0.2 ka and interfingering with point-bar deposits. These counterpoint deposits are younger than the inner pointbar deposits (4.7 ± 0.4 ka), hence the younger counterpoint deposits were formed as a result of inward migration of the channel when it started to erode its older point-bar deposits. Both deposits reach a similar depth as the current Dommel River. Figure 10 shows a cross-section perpendicular to the cross-section in Figure 9. This cross-section shows that the channel is bordered by Fluvial facies 3 on the northern side, and by the valley side on the northeastern side, which are interpreted as counterpoint deposits. Relatively narrow and thick (ca 4-4.5 m) point-bar deposits are present on the inside of the bend complex, with some loamy layers present within the point-bar deposits.

| Spatial configuration
Erosion-resistant deposits are abundantly present in the valley side and floodplain of the Dommel River, on both sides of the bend complexes ( Figure 11). These erosion-resistant floodplain deposits consist of silt loam, clay loam and peaty deposits, with many reaching channel-depth thickness ( Figures 5 through 10), and are consolidated at 2-4 m below the surface, further enhancing their resistance to erosion. The sedimentology of these fine-grained erosion-resistant deposits indicates that they mainly consist of residual channel-fill deposits, middle point-bar deposits and counterpoint deposits.
Easily erodible, sandy point-bar deposits are mostly present on the inside of bends, while hardly present along the outside of the oxbow bend complexes ( Figure  11). These deposits are dated between 0.6 ± 0.1 ka and 4.7 ± 0.4 ka (Table 1). In contrast, the erosion-resistant deposits are generally older and dated between 1.3 ± 0.3 ka and 9.6 ± 0.2 ka (Table 1), reflecting the higher preservation potential of the erosion-resistant deposits (Figures 5  through 11). accretion surfaces from the old point-bars (both Fluvial facies 1 and 2) always start within 0.5 m of the surface (e.g. Figure 4).

| Morphodynamics
The configuration and age of channel deposits indicate that the Dommel River channel was largely constrained by its self-formed erosion-resistant deposits (Figure 11), and bends only migrated locally over relatively short distances where they were not restricted by erosion-resistant deposits in their outer banks. The Dommel River also shows relatively recent deposits of both easily erodible and erosion-resistant deposits (e.g. Figure 11C), but shows preferential erosion of the sandy deposits compared to the cohesive and organic deposits. Sharp secondary bends have formed within the primary bend complex forming a 'zigzagging' channel planform lying in between the erosion-resistant deposits (Figure 11), resulting in a tortuous river planform with limited channel mobility. The reference here is to secondary bends when smaller bends form within a larger, primary bend. Sharp secondary river bends formed because the river eroded its own sandy point-bar deposits due to their lower resistance to erosion compared to the fine-grained depositional units outside of the primary bend complex. Hence, the hypothesis (Section 1) can be confirmed. In Section 4, the conceptual model of this self-constraining of low-energy meandering rivers will further be developed and tested for other meandering rivers.

| Concepts of self-constraining lowenergy meandering rivers
The self-constraining process of low-energy meandering rivers as conceptualized from the Dommel River reconstructions, is illustrated in Figure 12A. The relationship between the floodplain sediment composition, tortuosity and channel mobility and how they develop over time are elaborated on in Figure 12B through D.
The river mainly erodes its sandy point-bar deposits due to their lower resistance to erosion compared to other, more cohesive depositional units ( Figure 12A). As a consequence of preservation differences, the fraction of easily erodible, non-cohesive sediments in the floodplain decreases over time ( Figure 12B) (Smith et al., 2009). Here, a self-constraining river is defined as 'a river of which the channel mobility is increasingly hampered over time by self-formed erosion-resistant banks'. This self-constraining is accompanied by increase in planform tortuosity due to the formation of sharp river bends ( Figure 12A,C), which is a phenomenon commonly found in low-energy meandering rivers that are laterally restricted by erosion-resistant deposits (Turnbull et al., 1966;Leeder and Bridges, 1975;Hickin, 1986;

Erodibility of deposits in corings (dominant lithology)
A B C | 663 CANDEL Et AL. Güneralp and Rhoads, 2011). Flow separation in sharp river bends may lead to the formation of counterpoint deposits (Leeder and Bridges, 1975;Smith et al., 2009; Figure 12A), which are generally cohesive due to incorporation of silt and organic material. Also cohesive middle point-bar deposits may form due to flow separation (Makaske and Weerts, 2005). Residual channel-fill deposits result from neck cutoffs that are promoted by preferential erosion of the sandy point bars instead of erosion of the fine-grained deposits (example of almost cut-off channel complex C, Figure 11C; Hooke, 2007). Residual channel-fills become fine-grained and organic when diversion angles to the cut-off channel are high (Constantine et al., 2010), which is especially common in rivers with tortuous planforms. Newly formed fine-grained counterpoint deposits and residual channel-fills consist of erosion-resistant deposits that reach channel-depth thickness. Thus their thickness scales with river size, and they further foster the planform tortuosity and formation of sharp bends ( Figure 12B,C). The erosion-resistance of these deposits increases even further with time as a result of consolidation. Figure 12 shows the conceptual development of a self-constraining system over time, with a decrease in the ratio of non-cohesive/cohesive banks ( Figure 12B), an increase in tortuosity ( Figure 12C), and a decrease in channel mobility ( Figure 12D). Quantifying these properties is not F I G U R E 1 2 Self-constraining of a meandering river illustrated. (A) Conceptual maps showing the potential development of floodplain deposits and channel planform of a self-constraining river, assuming that neck cut-offs and counterpoint deposits immediately form erosionresistant layers at the moment of cut-off or deposition. The tortuosity is indicated for the first and last timeframe. Conceptual graphs showing the long-term evolution of (B) bank cohesiveness, (C) planform tortuosity, and (D) average channel mobility possible with this dataset, but could be investigated using modelling experiments. Based on the conceptual model presented here, an initially exponentially increasing response is suggested due to the positive feedback between the formation of erosion-resistant deposits and increase in planform tortuosity. The average channel activity ( Figure 12D) decreases simultaneously with the relative increase of erosion-resistant deposits in the vicinity of the channel ( Figure 12B), slowing down the positive feedback loop, and eventually resulting in a low-energy meandering river with inhibited channel mobility ( Figure 12D), predominantly cohesive banks ( Figure 12B) and a tortuous planform ( Figure 12C). For simplicity, only the three main erosion-resistant deposits found in the Dommel River are shown in Figure 12A: residual channel-fill deposits, counterpoint deposits and the valley side. Other erosion-resistant deposits may be more dominant in other low-energy river systems, such as overbank deposits, fine-grained middle point-bar deposits or oblique accretion deposits (Page et al., 2003;Słowik et al., 2020), but they have the same effect on the river planform. Easily erodible deposits mainly consist of point-bar deposits for the Dommel River. Sylvester et al. (2019) showed that bends with the highest curvatures show the highest migration rates. This was confirmed by observations on the intertidal mudflat, where the highest migration rates occurred in the sharp river bends due to flow separation, but the average river channel migration was low (Kleinhans et al., 2009). Sharp bends show the highest displacement, because the remaining part of the river channel is relatively laterally stable due to the self-constraining. However, when comparing channel mobility between meandering rivers, the average channel mobility of rivers with sharp bends is expected to be generally lower than rivers with gentle, freely meandering bends (Hooke, 1980;2007;Hudson and Kesel, 2000;Smith et al., 2009;Bogoni et al., 2017), because the channel mobility of self-constraining rivers is inhibited and limited to small sections of the floodplain (Figures 11 and 12).

| Applicability to other low-energy meandering rivers
To investigate whether the concepts of self-constraining are generally applicable, the information on potential specific stream power, erosion-resistance of the river banks and planform tortuosity were combined for the 47 different-sized meandering river reaches sampled for these data ( Figure 13). As described in Section 2.6 these are all alluvial rivers with no evidence of strong modification by humans, all rivers are laterally connected with their floodplain, and are not strongly incising or aggrading (Kleinhans and Van den Berg, 2011).
The data shown in Figure 13 depict that rivers with tortuous planforms occur only when river energy is below the threshold required to erode the erosion-resistant banks (Julian and Torres, 2006). The minimum required potential specific stream power for bank erosion was derived by applying relationships from Julian and Torres (2006) and Kleinhans and Van den Berg (2011) (Equations 2 and 3): where c is the critical shear stress (Pa) to erode the SCfraction (%) in the banks, and C is the Chézy coefficient (m 0.5 s −1 ), which was taken here as the median of the values for the rivers used in this analysis (36 m 0.5 s −1 ). Rivers below the threshold will predominantly erode easily erodible banks (with below average SC-fractions), resulting in an increasing fraction of erosion-resistant deposits over time. For river energy above the threshold the river is able to erode the erosion-resistant banks, resulting in a reduction of these erosion-resistant deposits (decreasing average SC-fractions) and a lower planform tortuosity ( Figure 13). Gravel-bed rivers hardly develop tortuous planforms, because they require high river energy to mobilize the river bed material. At such energy levels they are able to erode banks irrespective of bank erodibility ( Figure 13).

| Prerequisites
Meandering rivers may become self-constraining under specific, but common, conditions. First, river energy should be insufficient to erode the cohesive depositional units, but sufficient to erode the non-cohesive material. These conditions apply to low-energy meandering rivers, especially sand-bed rivers that have a low threshold for sediment motion (ca 10 −2 W/m 2 for sand-bed rivers). This analysis demonstrates that self-constraining occurs irrespective of river size (ranging from bankfull discharges of 22 m 3 /s for the Dommel River to 1.7 × 10 4 m 3 /s for the Purus River), provided that river energy is low (Figure 13). River energy is controlled by allogenic factors like climate and land cover that change over time (Candel et al., 2018), and is therefore an allogenic control determining the occurrence of the autogenic processes of self-constraining.
Second, the river should transport a heterogeneous load of cohesive and non-cohesive material to be able to build a heterogeneous floodplain. Low-energy rivers commonly have a relatively fine-grained sediment load, and form floodplains with cohesive depositional units (Nanson and Croke, 1992). Rivers with a strictly non-cohesive sediment load will not develop selfformed erosion-resistant banks (Van Dijk et al., 2012). Channel mobility of these rivers may only become restricted by, for example, vegetation (Van Oorschot et al., 2016), soil formation (Bätz et al., 2015), bank protection measures (Hesselink et al., 2003) or peat formation (Candel et al., 2017). Finally, sufficient time is required during which the conditions fostering self-constraining of the channel prevail; thus channel belts should not frequently be abandoned due to avulsions. Such favourable conditions occur where rivers are located in a valley setting, in which valley sides may contribute to the self-constraining process when they are erosion-resistant ( Figure 12A). Strong aggradation or incision may also reset the self-constraining, because they may potentially lead to overtopping or undercutting of the erosion-resistant deposits, respectively. Therefore, aggradation and incision rates should be relatively limited, as is the case with rivers used in this dataset (Kleinhans and Van den Berg, 2011).

| Implications
Although counter-intuitive, increase of river energy (e.g. because of climate or land cover changes) in self-constraining, low-energy meandering rivers may initially accelerate the selfconstraining process and will lead to an increase in erosionresistant deposits, provided that river energy is still below the threshold ( Figure 13). If river energy exceeds the threshold, the self-constraining feedback loop is broken. It is conjectured that such rivers may then be able to erode the erosionresistant deposits and partly replace them with easily erodible, F I G U R E 1 3 Erosion-resistance of banks (proxy: average silt-plus-clay fraction of river banks) plotted against river energy (proxy: potential specific stream power, ω) for a dataset of 47 rivers (Van den Berg, 1995;Kleinhans and Van den Berg, 2011). For each of the data points, effective channel-forming discharge (Q) (Kleinhans and Van den Berg, 2011), planform tortuosity and bed texture are shown. The thick grey line represents the minimum river energy needed to erode the river banks (Woodyer et al., 1979;Page et al., 2003;Julian and Torres, 2006;Kleinhans and Van den Berg, 2011). The thick arrows indicate the hysteresis cycle of self-constraining and breaking out, in black and blue the autogenic and allogenic processes, respectively. Dashed arrows represent hypothetical arrows. The labelled rivers correspond to rivers shown in Figure 1, or reconstructed Late-Glacial (LG) systems (see methods section on reconstruction). A through D refer to rivers with sharp bends, E through H refer to rivers with classical meandering planforms: A) Dommel River ( Figure 1A non-cohesive deposits (although convincing evidence of rivers that have crossed this threshold is presently lacking). The existence of two system states would create a hysteresis cycle ( Figure 13). A striking example of the self-constraining part of this hysteresis cycle is provided by river responses in many temperate regions during interglacial-glacial cycles. Many rivers in these regions were braiding during the Pleniglacial and changed to meandering during the Late Glacial (Vandenberghe, 1995;2001). Valley slopes, bankfull discharges and thus river energy were high during the Late Glacial compared to the Holocene, due to low sea levels and high runoff from snowmelt peaks, and rivers formed their valleys within the non-cohesive river deposits that had previously been deposited by braided rivers (Mol et al., 2000). Late-Glacial rivers were commonly high-energy, laterally migrating and planform tortuosity was low (Figure 13, e.g. the Late-Glacial Dommel and Niers Rivers; Kasse et al., 2005). During the Holocene, river energy decreased, and this period provided sufficient time for rivers to develop tortuous planforms by self-constraining (Figures 12 and 13). Figure  13 indicates that these self-constraining meandering rivers can only break out of their constraints when river energy significantly increases to levels above the threshold. This may occur in a transition to a glacial period (Vandenberghe, 1995;2008), although in such cases strong incision or aggradation may take place as well (violating the conditions discussed in this paper). The hysteresis loop indicates that self-constraining, low-energy meandering rivers are highly resilient for bank erosion due to changes in river energy. This resilience may aid river management and reduce risk of infrastructure damage by channel migration, but there is always a risk of sudden unexpected and unwanted enhanced river dynamics when the threshold is crossed. Changes in the catchment land cover such as urbanization, peat extraction or deforestation may result in increased river energy by increasing peak flows (Candel et al., 2018). When the increase in river energy is sufficient, the self-constraining rivers will be replaced by actively migrating meandering rivers. Such a response in river dynamics to an increase in energy may be unexpected, and may have catastrophic consequences. A channel pattern change was recently documented for the Overijsselse Vecht River (Candel et al., 2018), showing that an increase in peak discharge changed a laterally stable river into a meandering river with lateral migration rates of 2-3 m/yr about 400 years ago.

| CONCLUSIONS
Based on a palaeogeographic reconstruction of the Dommel River (The Netherlands) it is shown here that low-energy meandering rivers may self-constrain their planform by preferential preservation of erosion-resistant deposits. This process explains the typical tortuous planform and low dynamics of low-energy rivers. The conceptual model of self-constraining is validated for a dataset of 47 meandering rivers, and from this analysis the critical threshold of river energy for self-constraining is derived. Reaches with a river energy below this critical threshold tend to have tortuous planforms and banks with a high silt-plus-clay fraction, in contrast to reaches with a river energy above this critical threshold. It is conjectured that a hysteresis cycle exists, which is controlled by the discharge regime, forced by allogenic factors such as land use and climate. Rivers self-constrain when their river energy is below the critical threshold for eroding cohesive banks, causing bank stability to increase over time, resulting in reduced channel mobility. Rivers break out of the self-constraining once the river energy crosses the critical threshold for eroding cohesive banks.