Controls on the Leeside Angle of Dunes in Shallow Unidirectional Flows

Dunes are ubiquitous features in alluvial channels, serve as major agents of sediment transport and contribute significantly to flow resistance. Research in the past decade has illustrated the complexity of dune geometry and widespread occurrence of dunes that have a low leeside angle. However, there is a debate concerning the occurrence of such dunes and their formative processes. This paper seeks to further our understanding of low‐angle dunes by utilizing data from a robust set of shallow flow laboratory experiments detailing equilibrium bedform morphology across a range of sediment transport conditions. Analysis of bedform morphology demonstrates that dunes with low‐angle leesides are generated in shallow laboratory flows and are not restricted to deep rivers. Of the possible processes that have been proposed to explain the formation of low‐angle dunes, this finding unequivocally shows that liquefied leeside avalanches, which rely on deep flows for their generation, are not a controlling mechanism. In addition, dunes formed under suspension‐dominated conditions possess lower leeside angles compared with those formed under bedload‐dominated conditions. However, where bedload transport dominates and sediment suspension is likely of lesser importance, low‐angle dunes are still present, and preliminary analysis shows that bedform superimposition can result in lowering of the dune leeside angle. Low and intermediate angle dunes formed under these various conditions also have a lower potential for large‐scale, permanent, leeside flow separation compared with angle‐of‐repose dunes, confirming the need to account for these differences in predictions of flow resistance associated with dune form roughness.


Introduction
Dunes are the most prevalent alluvial bedform and their morphology is determined by the flow and sediment conditions in which they form, and the feedback of dune morphology upon flow and sediment transport (Allen, 1968a(Allen, , 1968b(Allen, , 1968c;;Bennett & Best, 1995;Best, 1993Best, , 2005a;;Mclean et al., 1994;Yalin, 1964).Dunes exert a major influence on flow and sediment suspension through the generation of macroturbulence in the region of the dune crest and leeside (Bennett & Best, 1995;Best, 1993Best, , 2005b;;Hardy et al., 2021;Jackson, 1976;Jopling & Forbes, 1979;Mclean et al., 1994;Nelson et al., 1993).Through dune migration and changes in shape and size, dunes are major movers of sediment (Engelund & Fredsøe, 1976;Naqshband, Ribberink, Hurther, & Hulscher, 2014;Ten Brinke et al., 1999), with their translation and amalgamation leading to the development of larger barforms that can influence river planform change (Best, 2005a;Carling, 1996;Dinehart, 1992;Hickin, 1974).Most bedload transport is captured within individual dunes through leeside deposition, whereas the suspended load flux is largely advected downstream (Naqshband, Ribberink, Hurther, & Hulscher, 2014).Several scales of bedforms may co-exist superimposed on another bedform for long periods of time, especially when primary dunes are in disequilibrium for prolonged times (Leary & Ganti, 2020).When superimposition occurs, both scales of bedforms may contribute to the rate of sediment transport in equal magnitudes, with the smaller superimposed bedforms sometimes exceeding the volume of transport related to the primary dunes (Lee et al., 2022;Zomer et al., 2021).In addition, dune migration and leeside deposition determine the nature of crossstratification preserved in the sedimentary record and are key to paleoenvironmental interpretations (Allen & Collinson, 1974;Almeida et al., 2016;Best & Fielding, 2019;Paola & Borgman, 1991).Therefore, quantifying the links between flow, sediment transport, and dune morphodynamics is vital to understanding modern and ancient sedimentary environments.
Much of our understanding concerning the formation and morphodynamics of dunes has relied on physical experiments conducted using shallow laboratory flows (Best, 2005a;Bridge & Best, 1988;Guy et al., 1966;Southard & Boguchwal, 1990;van den Berg and Van Gelder, 1993;Yalin, 1964), where the principal mode of transport was bedload.In these cases, quantification of dune morphology has often occurred through sidewall visual observations or single centerline bed profiles.Although such experiments have yielded much progress in our understanding, they have not covered the full range of conditions that may characterize natural channels.For example, when physical experiments are undertaken to observe the formation of bedforms in fine sands, it becomes difficult to make morphologic observations via sidewall imaging or use acoustic techniques, as fine sand in suspension may hinder visibility or signal backscatter.However, recent research using lightweight sediment as bed material (Naqshband & Hoitink, 2020;Nashqband et al., 2021) has investigated conditions more akin to highsuspension conditions in natural rivers and illustrated the need to rethink bedform phase stability diagrams to account for sediment suspension under lower Froude number conditions than traditionally assumed.
Research has also shown that dunes in large rivers possess low-angle leesides, a finding that is different to that reported from many shallow flow experiments and rivers (Almeida et al., 2016;Best, 2005a;Best & Kostaschuk, 2002;Bradley & Venditti, 2017;Cisneros et al., 2020;Galeazzi et al., 2018;Guy et al., 1966;Kostaschuk, 2000;Kostaschuk & Venditti, 2019;Kostaschuk & Villard, 1996;Roden, 1998).Low-angle dunes, with leesides less than 10°, do not possess a zone of permanent flow separation (Best & Kostaschuk, 2002;Kwoll et al., 2016;Lefebvre & Cisneros, 2023;Motamedi et al., 2013), and in deep flows often possess a height with respect to flow depth that is less than dunes in shallower flows (Cisneros et al., 2020).Additionally, Reynoldsaveraged models indicate that intermediate dunes, with a small zone of intermittent flow separation, form at leeside angle greater than 10°and their intermittent flow separation zone grows until 17° (Lefebvre & Cisneros, 2023).Finally at 17°, high angle dunes with permanent flow separation zones form and the spatial extent of this zone depends on leeside shape (Lefebvre & Cisneros, 2023) until becoming a fully developed zone of permanent flow separation at 24°producing angle-of-repose dunes (Lefebvre & Winter 2016).These differences in the spatial and temporal occurrence of flow separation over the lee side result in lower magnitude turbulence and a weaker shear layer associated with lower angle leesides (low and intermediate dunes) compared with high angle and angle-of-repose dunes (Best, 2005a;Best & Kostaschuk, 2002;Kwoll et al., 2016).Kwoll et al. (2016) found that leeside angles of 10°and 20°experience bed shear stresses 8% and 33% greater than a flat bed, whereas dunes with leeside angles of 30°resulted in shear stresses 90% greater than those over a flat bed.In addition, lowangle dunes are associated with increases in suspended sediment flux due to suspension events occurring along both the stoss and lee sides (Bradley et al., 2013).Superimposed bedforms have been observed to climb over the stoss and lee sides of low-angle dunes when the lee side is less than 11° (Zomer et al., 2021) and the occurrence of this amalgamation leads to the production of turbulent coherent structures that result in sediment resuspension (Bennett & Best, 1996;Frias & Abad, 2013).Debate also exists as to the influence of different scales of form roughness upon hydraulic resistance in a river, with flow resistance produced by very low-angle (less than 5°) bedforms being found to be minimal compared to the influence of both superimposed bedforms and the undulating longitudinal gradient of an alluvial channel (de Lange et al., 2021).
Several mechanisms have been proposed to explain the formation of low-angle dunes (Figure 1) in both shallow and deep flows (Best et al., 2020), including: (i) The influence of sediment suspension in modulating turbulence or increasing the bypassing of sediment over the dune leeside slope (Figure 1a; Baas & Best, 2002, 2008;Baas et al., 2016;Bradley & Venditti, 2017;Hendershot et al., 2016;Naqshband et al., 2016).Significant concentrations of suspended sediment have been hypothesized to cause a dampening of turbulence associated with the leeside flow separation zone, thereby decreasing leeside scour in the trough region, and enhance the bypass of sediment over the dune leeside that will increase sediment deposition in the dune leeside and trough.Both of these mechanisms will produce lower leeside angles.(ii) Bedform superimposition, whereby dune interactions modify the flow structure in the crestal region of the downstream bedform due to the leeside separation zone and associated free shear layer of the upstream bedform, thus causing crestal/leeside erosion and lessening the dune leeside angle (Figures 1b, Allen, 1978;Allen & Collinson, 1974;Reesink & Bridge, 2009;Reesink et al., 2018).In steady flows, Reesink and Bridge (2009) describe the influence and interactions between a smaller, superimposed bedform (height, H S ) and the large bedform that it is climbing over (height, H L ).Specifically, Reesink and Bridge (2009) describe how these two bedform scales interact during the migration of the smaller bedform, when the reattachment point of its flow separation zone becomes coincident with the crest of the larger dune.If H S is sufficiently large (>25%) relative to H L , Reesink and Bridge (2009) argue that erosion occurs at the brink point of the large dune (Reesink & Bridge, 2009).However, when a relatively small dune (H S /H L < 0.25) passes over the large dune, the large dune leeside is only partially reduced in angle and this erosion surface does not reach the base of the large dune, with the base of the leeside slope of the larger dune thus remaining at the angle-ofrepose (Reesink & Bridge, 2009).Reactivation surfaces are thus formed by the passage of superimposed bedforms over a larger dune, with these surfaces being lower angle with passage of a relatively high (H S / H L > 0.25) compared to a relatively small (H S /H L < 0.25) superimposed bedform (Reesink & Bridge, 2009).(iii) The influence of three-dimensional dune crestlines in constricting/expanding flow, which controls leeside flow patterns and sediment routing (Figures 1c, Allen, 1968c;Hardy et al., 2021;Lawless & Robert, 2001;Parsons et al., 2005;Venditti, 2007).Three-dimensional dune crestlines may lead to the development of 3D flow structures that influence lateral flow, resulting in complex sediment routing during the constriction and expansion of flow (Allen, 1968c;Hardy et al., 2021;Lawless & Robert, 2001;Parsons et al., 2005;Venditti, 2007).The orientation and location of dune slip faces also determine the occurrence of flow separation and downstream extent of its associated turbulent wake, which results in variations in bed shear stress when morphologic variations in crest location and slip face exist along a three-dimensional dune (Lefebvre, 2019;Venditti, 2007).Hardy et al. (2021) show an increase in flow velocity over 2D crestlines compared to 3D crestlines that is related to a reduction in the separation zone on the dune leeside, but flow over threedimensional crestlines exhibits more turbulent vortices that generate higher shear stresses compared to 2D crestlines.From these variations, it follows that variations in bedform three-dimensionality may influence form roughness and bed shear stress and lead to differences in the predicted sediment transport (Kostaschuk & Villard, 1996;Kwoll et al., 2016;Lefebvre & Winter 2016;Smith & McLean, 1977;Venditti, 2007).Although it remains unclear whether changes in flow and sediment transport that occur from 3D to 2D dunes are related to changes in leeside angle, such variations in the topology of flow separation zones could influence the generation of low angle dunes.Thus, evaluating the relationship between crestal sinuosity and leeside morphology may be invaluable for understanding the formation of low-angle dunes.(iv) The presence of liquefied avalanches produced as a result of excess pore pressures in grain flows present on dune leesides in deep flows, which travel further into the lee trough and lower the leeside angle (Figures 1d, Kostaschuk & Venditti, 2019).However, several problems arise in this model being able to produce liquefied avalanches (Best et al., 2020).First, liquefied avalanches may occur at any flow depth as long as there is a pressure differential to create an excess of pore pressure (Benjamin & Yeh, 2016;Best et al., 2020).This excess pore pressure may be produced in several ways, for example, through the result of grain rearrangement and rapid shear (Iverson & LaHusen, 1989) or turbulence fluctuations in the dune leeside (Abe, 2019;Motamedi et al., 2013), which is prevalent in all environments where flow and sediment transport occurs over a non-uniform and mobile bed (Allen, 1968a(Allen, , 1968b)).The assertion that low-angle dunes are only found in deep flows due to this liquefaction process also suggests that high-angle dunes cannot be formed under the same conditions; however, in deep rivers, while the majority of dunes are lowangle, high-angle dunes do exist with leesides up to 30°, albeit at low abundance (Cisneros et al., 2020;Roden, 1998).Additionally, over a range of dune sizes, low-and high-angle dunes exist (Best et al., 2020).
The liquefied avalanche mechanism is also based on a conceptual model with a simple-shaped leeside (Kostaschuk & Venditti, 2019), yet Cisneros et al. (2020) have shown that leesides often have complex leeside shapes with high and shallow sloping segments.Consequently, it is improbable that a liquefied flow would be able to traverse over a leeside with various high and low sloping segments without halting or becoming discontinuous (Best et al., 2020).Following the hypothesis of Kostaschuk and Venditti (2019), the leeside liquefaction process should be absent in shallow flows, resulting in low-angle dunes also being absent.
It is also unclear whether shallow flow experiments and shallow rivers exhibit the flow and sediment transport conditions required to promote the formation of low-angle dunes.In large rivers, low Froude numbers, high transport rates, and highly variable flow and sediment transport rates are common (Best & Kostaschuk, 2002;Julien & Klaassen, 1995;Kostaschuk, 2000;Kostaschuk & Venditti, 2019;Kostaschuk & Villard, 1996;Roden, 1998;Shugar et al., 2010).In shallow flume experiments, the Froude number is often much larger compared to deep rivers (Naqshband & Hoitink, 2020), whereas sediment mobility often represents conditions of bedload or mixed load transport (Bradley & Venditti, 2017;Naqshband, Ribberink, & Hulscher, 2014).In such laboratory experiments, high Froude numbers result in observations of dunes near the transition to upper-stage plane bed conditions; however, the physical mechanisms that link dune morphology to Froude number are poorly understood (Naqshband & Hoitink, 2020).The inability to correctly scale the Froude number in shallow flow experiments thus leads to a knowledge gap in investigating and understanding dune stability regimes under shallow laboratory flows.As a result, our ability to predict bedform regimes has been dominated using laboratory observations of high-angle dunes (Kostaschuk & Villard, 1996;Naqshband & Hoitink, 2020;Naqshband, Ribberink, & Hulscher, 2014).The formation of low-angle dunes in shallow flow experiments under properly scaled low Froude numbers and sediment transport parameters (Naqshband, Ribberink, & Hulscher, 2014;Naqshband & Hoitink, 2020) suggests that the reason low-angle dunes are absent in the laboratory is not that they do not exist but that: (a) they are difficult to produce under similar conditions, and (b) that it is difficult to measure and create their formative conditions in a laboratory setting.
Recent work has created dunes at low Froude numbers in shallow flow laboratory flows by using low-density sediment, with low-angle dunes being successfully formed under suspension numbers (the ratio of bed shear stress to grain settling velocity, u*/w s ) similar to large rivers (c.0.4 to >3; Naqshband & Hoitink, 2020, their Figure 3).In this case, an increase in leeside angle is seen for increasing suspension numbers less than c. 1, but when the suspension number equals and exceeds unity, the dune leeside angle decreases with increasing suspension number at a rate similar to data from deep flows (Naqshband & Hoitink, 2020).In these experiments, the growth of dune height, wavelength, and leeside slip face angle also adjusted at similar timescales (Naqshband et al., 2021).Specifically, before the leeside angle reaches the onset of flow separation (10°; Lefebvre & Cisneros, 2023), sediment largely bypasses the dune crest and flow reattachment point.When the leeside angle increases, associated with more permanent flow separation scour in the bedform trough intensifies, resulting in dune growth as more sediment is delivered to the crest and deposited in the leeside region of flow recirculation (Naqshband et al., 2021).Naqshband et al. (2021) also confirmed, through a liquefaction model, that low-angle dune slip faces were maintained without liquefied avalanches.
Recently, an extensive and robust set of experiments were conducted across a range of transport conditions from dune growth through to dune equilibrium and that illustrated a transport scaling relationship between dune height and dune wavelength (Bradley andVenditti, 2019a, 2019b).These experiments focused on five transport conditions ranging from the threshold of sediment transport through to suspended sediment transport dominated conditions, and across three flow depths (0.15, 0.20, 0.25 m; see Bradley & Venditti, 2019a), offering a unique insight into the development and equilibrium morphology of dunes across different transport stages.Bradley andVenditti (2019a, 2019b) found that dunes become flatter and longer with increasing suspended load, and suggested that sediment suspension is a major control determining the morphology of dunes in these shallow flow experiments.These recent studies detailing the formation of low-angle (Naqshband & Hoitink, 2020) and flattened (Bradley & Venditti, 2019a) dunes in laboratory flows thus suggest that suspended sediment transport is likely an important control on the formation of low-angle dunes in both deep and shallow flows, as also highlighted in earlier work on the dune-upper stage plane bed transition (Bridge & Best, 1988).However, a detailed quantification of leeside angle, and its change with transport stage, has not been conducted on the data sets of Bradley and Venditti (2019a), but is pivotal to discussions of changing dune morphology.
The present paper thus aims to examine the nature of dune leeside character by analyzing the data sets from Bradley and Venditti (2019a) to address three research questions: (a) Do low-angle dunes form in shallow flow laboratory experiments?(b) What is the relative prevalence of different angle dunes across transport stages, and do these conditions provide insight into the possible controls on low-angle dune formation, and (c) What is the relative importance of sediment suspension and bedform superimposition on the formation of low-angle dunes?

Data Detailing Equilibrium Morphology of Dunes
The data used herein comprise c. 600 maps detailing the equilibrium morphology of dunes across various flow depths and transport stages reported by Bradley and Venditti (2019a).These data comprise xyz grids and are available through a data archive (Bradley, 2018) that accompanies the papers by Bradley andVenditti (2019a, 2019b).The laboratory flume used by Bradley andVenditti (2019a, 2019b) was 15 m long, 1 m wide, and 0.6 m deep, recirculated both water and sediment and possessed an adjustable slope (slope range = 0.5%-2%).The experiments used a well-sorted medium sand (D 50 = 550 μm, Bradley & Venditti, 2019a).The transport stages studied ranged from the threshold of sediment transport through bedload-dominated to suspended load dominated transport, and with initial flow depths of 0.15, 0.20, and 0.25 m.Each transport condition was investigated at each of the three flow depths.In each run, a constant steady flow was imposed over an initially flat bed, and dunes began to develop.Each run continued through bedform growth until morphological equilibrium had been reached, defined as when the bedforms were not systematically increasing or decreasing in size, and flow was then sustained for 10 hr at the desired discharge (Bradley & Venditti, 2019a).The initial flume slope for each run was set so that it matched the water level slope over an initially flat bed.For each run under each flow depth, sediment transport conditions were varied by increasing the pump discharge in five steps from the initiation of motion (threshold) to washout of dunes: threshold (THLD), bedload (BDLD), lower-mix (LMIX), upper-mix (UMIX), and suspended load (SPSN), which coincide with increasing sediment transport in suspension.In each run, a fullbed morphological scan was taken every 10 min, over 10 hr of run time, using the Swath Mapping System detailed in Venditti et al. (2016).The original maps were gridded with an x-axis (downstream) spacing of 1.29 cm and a yaxis (cross-stream) spacing of 3.05 cm.For the analysis conducted herein (see below), equal x and y spacing is required and thus the y-axis was interpolated from the original spacing of 3.05 to 1.29 cm.In the experiments, only the THLD and BDLD conditions were scanned under 0.25 m flow depth because the higher discharges required to reach high transport conditions were above the capacity of the pump.Herein, the runs will be referred to by their flow depth-transport condition pair, such that, for example, the threshold (THLD) run at 15 cm flow depth is referred to as THLD 15.
The entirety of bed scan data (every 10 min over 10 hr for each condition) acquired after equilibrium was reached were analyzed using the Bedform Analysis Method for Bathymetric Information (BAMBI, see details in Cisneros et al., 2020) to compile extensive measurements detailing the morphology of dunes.In brief, BAMBI uses aspect maps of the bathymetry to define crest and trough locations as the transition between downstream facing lee sides and upstream facing stoss sides.This operation occurs across the entire gridded map by slicing the map into profile lines with a length equal to the downstream axis of the map in the flow direction and width equal to one grid cell.Measurements occur along each profile line for each dune that is defined by having an upstream trough point, a length of stoss defined cells, a crest point, a length of lee defined cells, and a downstream trough point.Morphologic measurements include dune height, mean leeside angle, maximum leeside angle, dune wavelength, flow depth at the dune crest (local flow depth), and the relative height of the location of the steepest slope on the leeside for each dune measured.The maximum leeside angle is referred to herein as the steep slope (following similar nomenclature in Lefebvre and Cisneros (2023) when referring to the morphological element commonly known as the "slipface," so as to not infer the type of sediment transport on the dune leeside).The mean leeside angle is herein referred to as "leeside angle."Morphologic measurements were reported for the primary dunes and secondary superimposed bedforms.In the figures presented herein, the average of the morphologic measurements for each bed scan are reported, such that each experimental case has a total number of datapoints that correspond to the total number of scans per experiment (53-59 scans/points).Additional data, reported by Bradley and Venditti (2019a), include transport stage (τ * /τ * c ) where τ*and τ * c are bed shear stress and critical bed shear stress respectively, shear velocity (u * ), particle fall velocity (w s ), and Froude number (Fr), for each scan in each experiment.For more information regarding the acquisition of this additional data, see Bradley and Venditti (2019a).
To assess the leeside angle over three-dimensional crestlines, the leeside slope was also measured manually over different types of dune crestline planform shapes, including straight, lobe and saddle shaped crestlines (see Figure 1 for definitions).Measurements were taken along profile lines that were defined along the apex of the dunes, and values of leeside angle were measured.Manual quantification was required to explicitly measure the apex of the dune because, depending on the crestline length and map resolution, the BAMBI measurements were not always centered at the apex.This manual measurement was consistent with the BAMBI method, except for the use of a looking angle within BAMBI to determine cell slope changes from stoss to leesides.For manual measurements, the crest was defined as the point where the slope along the profile changed from upstream to downstream facing, whilst the trough was defined as the point where the slope changed from downstream to upstream facing.The main difference in measurement technique is that the manual method was performed along a single profile, and did not take into account the cells around the area within one cell in the downstream and spanwise directions (a 3 × 3 grid) from each point along the profile.In this case, only one measurement was used for each dune along the apex of the crestline, which is different to the BAMBI method that outputs dune measurements across the entire width of a dune.For this reason, the measurement values may not be directly comparable to BAMBI measurements, but deploying this method allows the measurements to be compared for threedimensional crestlines.

Results
Data are presented herein detailing the relationship between dune leeside angle for each bed scan and a range of parameters, including relative dune height, flow depth, transport stage, suspension number and Froude number (Section 3.1).The analysis shows the range of dune leeside angles across each experimental condition from threshold to suspension dominated flows and each flow depth (Section 3.2).In the diagrammatic presentation of results in Sections 3.1 and 3.2, each point represents the average of the morphological measurements reported for a bed scan, whilst the bold outline points represent the average value from all of the bed scans for each case.To ensure clarity, the mean leeside angle reported in BAMBI is referred to as the leeside angle whilst the average, maximum, and minimum values are referred to as such.For the threshold conditions at 0.15 m flow depth, the response of the dune leeside angle during bedform superimposition is explored (Section 3.3) and the leeside angle over three different dune crestline types-straight, lobe and saddle-is examined (Section 3.4).Finally, the potential for flow separation over all dunes is examined in order to quantify the percentage of dunes that potentially experience no flow separation, intermittent, permanent and developing, or permanent and fully developed flow separation.

Leeside Angle
The relationship between local flow depth and leeside angle for all experiments, ranging from THLD to SPSN transport stages and flow depths from 0.15 to 0.25 m (Figure 2a), shows that dunes were formed at all flow depths, with leeside angles ranging from 10°to 30°.In general, a trend is present where minimum leeside angle increases with increasing flow depth for the 15 and 20 cm flow depths (Figure 2a and Table 2) for each condition, similar to observations regarding flow depth and dune height that have been reported from large rivers (Cisneros et al., 2020).For experiments at 25 cm flow depth, where only the THLD and BDLD conditions were investigated, the minimum leeside angle increases to c. 15°, with the maximum leeside angle remaining at c. 28°.However, in all transport cases, the average leeside angles are at, or below, 24°(Figure 2 bold outline symbols).
The relationship between leeside angle and relative dune height (Figure 2b) also reveals that for the same relative dune height, the leeside angle is lower at greater transport stages, specifically for the UMIX and SPSN experiments.Relative dune height is often lowest for the THLD case, whereas BDLD and LMIX are characterized by relatively higher dunes, with UMIX and SPSN dunes being lower and possessing relative dune heights between these extremes.
The relationships between leeside angle and suspension number (u*/w s , Figure 2c), transport stage (τ * / τ * c , Figure 2d), and Froude number (Fr, Figure 2e) show broadly that from the THLD condition to the BDLD condition, dune leeside angle increases and then decreases through to the SPSN condition.A polynomial regression was fitted to the average values of each transport and flow depth condition pair to assess the inflection point at which the leeside angle changes from increasing to decreasing for all transport and flow depth cases.The transition to decreasing leeside angle occurs below a suspension number of unity, highlighted by the bold line (Figure 2c), and specifically the inflection point of this curve is at 0.76 with a THLD and BDLD case falling on either side of the inflection point.For the same flow depth conditions, the leeside angle decreases between the BDLD and LMIX cases.Within the same transport conditions, for example, THLD, UMIX, and SPSN, the average leeside angles are lower in the 15 cm than the 20 cm flow depth experiments (Figure 2c).
With increasing transport stage for the same flow depth (Figure 2d), the average leeside angles increase (from THLD to BDLD) and then decrease (from BDLD to SPSN).Similar to the relationship with suspension number, for THLD, UMIX, and SPSN, the average leeside angle is lower for the 15 cm flow depth than at 20 cm.The inflection point for the τ * /τ * c regression fit line is 10.6, with the polynomial regression line possessing a peak between the THLD and BDLD cases (Figure 2d).
Leeside angle also increases and decreases with increasing Froude number (Figure 2e), with the decrease for the same flow depth occurring between the BDLD and LMIX conditions.The inflection point of the regression fit for Fr = 0.44 occurs within the range of the bedload cases.For the THLD, BDLD, LMIX, and UMIX experiments, the Froude number is always greater at shallower flow depths.This is most obvious in the UMIX condition, where the average Froude numbers for the 15 and 20 cm flow depths are 0.76 and 0.62, respectively (Figure 2e), but the leeside angle only differs by c. 2°.For the SPSN condition, both the 15 and 20 cm flow depths possess similar average Froude numbers (0.84 and 0.85, respectively) and leeside angles (leeside angle changes from c. 18°to 20°, respectively).In the SPSN case, however, the average leeside values are at, or just above, Fr = 0.84 (Figure 2e) and these dunes are likely at, or near, the transitional regime from dunes to upper-stage plane bed (Bridge & Best, 1988;Best & Bridge, 1992;van den Berg and Van Gelder, 1993).Importantly, the decrease in leeside angle that occurs at Fr = 0.44 indicates that suspension likely plays a significant role in decreasing leeside angle at Fr < 0.84, also providing additional support for the contentions of Naqshband and Hoitink (2020).
To assess the statistical significance of differences in dune leeside angles for different transport stage-flow depth experimental conditions, t-tests were performed comparing each experimental condition with the other 11 cases.A t-test was chosen because of the unequal sample size and variance in each case.Table 1 shows a matrix representation of the t-test statistic, with an alpha value of 0.05, whilst Table S1 in Supporting Information S1 displays a matrix representation of the t-critical values, which changed slightly for each test based on the degrees of freedom and thus sample size.
Two key points are apparent from tests of the statistical significance of differences between the experimental conditions.First, most sample populations are statistically different when compared to a reference population, including each sample compared to the THLD15, BDLD15, BDLD20, UMIX20, SPSN15, and SPSN20 cases.Of the samples that are statistically similar to the reference population, BDLD25 and SPSN15 stand out as examples that are statistically similar to a different transport condition (e.g., BDLD25 is similar to the THLD25 case).Less surprisingly, statistically similar cases also exist between the same transport condition; for example, LMIX20 is similar to LMIX15.Of all these comparisons, the most notable are that the THLD 15, BDLD15, BDLD20, UMIX20, and SPSN20 cases show no statistical similarity to any other case, including those that are either similar in transport or flow depth.Second, the lower-mix, upper-mix and suspension cases are not statistically similar to any of the bedload or threshold cases, as shown by the lack of red values reported in the bounded areas of the t-test matrix (Table 1).Overall, across different transport conditions for the same flow depth, the inflection point of the polynomial fit occurs between the THLD and BDLD cases for suspension number and transport stage, and between BDLD and LMIX for Froude Number.Comparing the same flow depth conditions, an increase in the leeside angle consistently occurs from the THLD to BDLD cases, followed by a decrease from the BDLD through to SPSN cases.These findings are consistent with previous literature that shows particles can be entrained into suspension at suspension numbers as low as 0.4 (Nino et al., 2003), suggesting that the lowering of leeside angle may begin shortly after the onset of particle entrainment into suspension and not suspension dominance.Thus, the consistent decrease in leeside angle occurs as transport begins to be characterized by an increasing suspended sediment flux.

Distributions of Leeside Angle
The distributions of leeside angles from all scans reveal differences across experimental conditions, especially between upper and lower transport conditions (Figures 3a-3l).A kernel distribution was fitted to the distribution, which allows a better fit compared to parametric models (e.g., gamma, Gaussian), especially when there is more than one peak (Naqshband & Hoitink, 2020).Additionally, the steep slope is plotted on Figure 3a-3l for all dunes in each scan and represented as a black outlined histogram.The leeside angle and steep slope angles of dunes in a range of large rivers (Cisneros et al., 2020) are also presented in Figure 3m.
For the experimental leeside angles, average values of the distributions range from >20.8°in the low transport cases (THLD, BDLD, and LMIX) and <20.6°in the high transport cases (UMIX and SPSN, Figures 3a-3l).Peaks of these distributions also lie above 20°for the low transport cases and below 20°for the high transport cases.Some distributions have two peaks, such as BDLD20 that has peaks at 23°and 27°.The standard deviation of all distributions is consistently between 1.5 and 2.5 for the low transport cases, whereas the high transport cases possess standard deviations greater than 2.9, with the higher transport cases having distributions with a wider spread (Table 2).The skewness for all cases is low and has a maximum range of 0.62 from zero, but the skewness is negative for all THLD and BDLD cases and positive for LMIX, UMIX, and SPSN cases (Table 2).Thus, the tails of the distributions are skewed to lower leeside angles for THLD and BDLD cases and to higher leeside angles for LMIX, UMIX, and SPSN cases.The kurtosis of all distributions ranges up to ±1 from 3, and there is no trend with increasing transport stage (Table 2).Thus, the tails of the distributions range from slightly heavy or light compared to a normal distribution for all cases.
The average values of the steep slope for all experimental cases are shifted by c. 10°higher compared to the leeside angles in all experimental cases.The average angles of steep slopes for all cases range between 29.5°and 35.8°(TableS2 in Supporting Information S1).From low transport cases to high transport cases, the standard  S1 in Supporting Information S1).The value of alpha is 0.05.The values represented in red show that the two populations compared, as shown through the x and y axis of the matrix, failed to reject the null hypothesis and the sample population is not statistically different than the reference population.The values presented in black thus reject the null hypothesis and these sample populations are statistically different than the reference population.Rows represent cases as a sample and columns represent cases as a reference population.deviation of steep slopes increases from values <2 in the threshold experiments to >c. 5 in suspension load cases (Table S2 in Supporting Information S1).The distributions thus adopt a wider spread as the transport stage increases.Additionally, skewness is low across all cases with values ranging up to ±0.72 (Table S2 in Supporting Information S1).Generally, the low transport cases have a more negative skewness, whereas the high transport cases have positive skewness.Apart from the THLD 15 case, the kurtosis of all low transport conditions from  2 for descriptive statistics of leeside angle distributions and Table S2 in Supporting Information S1 for descriptive statistics of steep slope distributions.THLD through LMIX is greater than 3, whereas the higher transport cases possess kurtosis values less than 3 (Table S2 in Supporting Information S1).Thus, the low transport cases possess heavier tails compared to a normal distribution, whereas the high transport cases have lighter tails.
Data from large rivers (Figure 3m; as reported in Cisneros et al., 2020) have an average leeside angle of 12.1°and an average steep slope of 17.8°(Table 2 and Table S2 in Supporting Information S1).The distribution of leeside angles from these large rivers is widely distributed with a standard deviation of 5.89 with heavier tails (shown by a kurtosis of 4.71) and a tail skewed toward higher values, with a positive skewness of 1.48 (Table 2).The histogram of steep slopes for large rivers is also widely distributed (Figure 3m), shown by a standard deviation of 7.78, with a light tail (kurtosis of 1.54) and a less positive skewness with a value of 0.95 (Table S2 in Supporting Information S1).
Overall, from low to high transport stages, these distributions confirm the trend that dune leeside angles change from dominantly high (peaks >20°) to low (peaks <20°), and the distributions of leeside angles vary from having discrete high peaks to being peaks that are broader and flatter.With increasing transport stage, the leeside angle decreases, and the standard deviation and skewness of the leeside angle distribution increase (Figure 3).Across all transport cases, steep slopes are high angle, peaking around 30°regardless of the average leeside angle.Finally, the leeside angles shift toward lower values with positive skewness for large rivers, showing a similar distribution to the high transport cases in the experiments, whereas the distribution of steep slopes is dissimilar to any of the experimental cases, possessing lower average values that are more widely distributed compared to the experimental cases.

Response of Leeside Angle to Bedform Superimposition
During dynamic equilibrium conditions, as superimposed bedforms climb up and over the stoss side and crestal platform of a larger dune, the leeside angle of the downstream bedform may sometimes lower (Figure 4), similar to the sequence proposed by Reesink and Bridge (2009).This is illustrated herein for one example from the THLD 15 case where the temporal change in leeside angle for one large dune is reported together with the leeside angle of the superimposed bedforms when they are present (Figure 4a).In this figure, the bedform height and leeside angles are presented only for the dune and superimposed bedforms highlighted in yellow (Figure 4c).When there is more than one superimposed bedform on the stoss side of the large dune, the largest height is reported as H S .When a superimposed bedform is present, the ratio of the superimposed bedform height (H S ) to the large dune height (H L ) is also plotted (Figure 4b).Here, the profile corresponds to 160-250 min after equilibrium has been  reached, with each successive profile being at a time increment of 10 min (Figure 4c).The four shaded 3D maps (Figure 4d) show the area around the single line profile at t = 160, 210, 230, and 250 min (±five resolution cells in the y-direction from the profile line taken from the center of the map).The areas shaded yellow (Figures 4c and  4d) highlight the large dune discussed herein.
At t = 160 min (Figures 4c and 4d(i)), the dune leeside angle is 24.3°and, over time, three superimposed bedforms begin to develop (t = 190 min, Figures 4c and 4d(ii)).These superimposed bedforms migrate over the stoss and crest of the larger dune, and at 200 min H S /H L = 0.23 and the dune leeside of the larger dune begins to lower.The leeside angle of the superimposed bedform declines to 17°at t = 190 min and reaches a minimum of 6°at t = 200 min.From t = 190-220 min (gray shaded area, Figures 4a and 4b), the leeside angle of the larger dune thus lowers from 26.3°to 10.4°(Figure 4a), at the same time as superimposed bedforms form on the stoss side of the large dune (t = 190 min), migrate along the stoss, and eventually move onto the dune leeside (t = 210 min).During this sequence, H S /H L decreases from 0.23 to 0.12 (from t = 190-220 min).The purple outlined map (Figures 4c and 4d(ii)) corresponds to one profile before the large dune reaches its lowest angle (dune leeside angle = 15.7°at210 min) and after superimposed bedforms climb over the larger dune crest and onto the dune leeside.At 220 min, the last superimposed bedforms arrive at the large dune crest and the large dune leeside angle reaches its lowest value in this sequence of 10.4°.The leeside angle of the superimposed bedform at this time (t = 220 min, Figure 4a) is 19°.By 230 min, the superimposed bedform has migrated over the crest and dune leeside, and the leeside angle of the larger dune begins to increase again.From t = 230-250 min, when no bedform superimposition is evident, the leeside angle of the large dune increases from 19.0°to 23.9°.The orange shaded map (Figures 4c and 4d(iii)) shows a higher angle large dune at 230 min.Finally, at 250 min, superimposed bedforms begin to form on the stoss side of the large dune once again, and the corresponding 3D map (red shaded box, Figures 4c and 4d(iv)) shows developing superimposed bedforms with H S /H L = 0.255 and leeside angle = 30°.In summary, this example illustrates that bedform superimposition influences the leeside angle as superimposed bedforms migrate over a dune.Specifically, it suggests that when a superimposed bedform of sufficient height migrates over a dune crest, turbulence generated along the shear layer of the flow separation zone in the lee of the superimposed bedform causes erosion of the large dune crest, and thus lowering of the leeside angle (Reesink & Bridge, 2009).In the example presented herein, where H S /H L is near 0.25, the superimposed bedform leeside angle is likely great enough (c.15°) to possess a zone of flow separation, and its migration causes the large dune leeside angle to decrease by c. 16°over a period of 30 min.As superimposed bedforms migrate over the large dune crest and amalgamate with the large dune, the large dune leeside angle increases back to 19°over a 10-min time period.The leeside angle continues to increase when superimposed bedforms are present if H S /H L is low (c.0.12), although the superimposed bedform leeside angle is 19°, supporting the results of Reesink and Bridge (2009) that detail amalgamation of a superimposed bedform with the main dune, crestal/leeside erosion and the lowering of the dune leeside angle.Such increases in dune leeside angle have also been reported on the rising stage of flood hydrographs (Bradley & Venditti, 2021;Roden, 1998) and suggest that relative dune height, related to time-varying flows, may be critical in influencing dune leeside angle.Bedform superimposition may thus contribute to the formation of lower dune leeside angles under low sediment transport conditions.

Leeside Angle and the Three-Dimensionality of Dune Crestlines
To assess any difference in leeside angle between three-dimensional dune crestlines, manual measurements of leeside angle across lobe, straight, and saddle planform segments of dune crestlines (Figure 5 inset), as defined by Allen (1968c), were made for scans from the THLD 15, BDLD 15, and SPSN 15 experiments (Figure 5).In this plot, the number of leesides measured ranges from 2 to 54, and the slope from the crest to dune trough was averaged to yield a mean leeside slope.The mean leeside angles of the straight, lobe, and saddle crestlines vary slightly in the THLD case, from 13.8°to 12.0°.In the BDLD case, leeside angles range from 29.9°to 27.4°, but in the SPSN case the range was more significant, from 18.7°to 9.3°(Figure 5).
Maps of the leeside angles measured by BAMBI, color coded by leeside angle, show the range of angles present in a scanned map for all cases (Figures S1 and S2 in Supporting Information S1).In the threshold cases, lobes, saddles and straight crestlines are present and leeside angles range across the dune crestline, with segments transitioning between low angle (<10°) and intermediate and high angle (10°-24°) and angle-of-repose (>24°).
For the straight-crested dunes in the threshold, bedload and lower-mix cases, leeside angles vary from <10°to >24°, with more segments of 10°-24°(Figures S1a-S1c in Supporting Information S1).Across all flow depths, saddle crestlines have distinct segments of <10°and between 10 and 24°(see Figures S1d and S1e in Supporting Information S1) and in other cases possess higher values between 10 and 24°and greater than 24°and lower angles along the crestline nearest to the sidewall (Figures S1f and S1g in Supporting Information S1).Lobe crestlines have greater leeside angles (>24°) across the entire dune (Figures S1h-S1j in Supporting Information S1).
In the upper transport cases, lobes and saddles become less common, and the crestlines are more often straight crested.Here, the leeside angles are less variable, as shown by similar colors, across straight crestlines (Figure S2a-S2e in Supporting Information S1).Leeside angle also differs across the lobes and saddles, with lower values along the crestline nearest to the sidewall, and higher values at dune crestline apices (Figures S2f and S2g in Supporting Information S1).Overall, decreasing three dimensionality appears more prevalent with increasing transport stage, as reflected by the difficulty in detecting three-dimensional crestlines in the upper transport conditions, but this trend is difficult to quantify given the current data.Specifically, the ability to quantify the relationship between leeside angle values measured by BAMBI to the three dimensionality of the crestlines is not possible, and this creates a difficulty in investigating any possible trend.However, Figure 5 shows little difference between leeside values across the apices of different three-dimensional dune crestlines for each transport case.Specifically, for all crestline types and transport stages, except lobes in the SPSN case, the median values of leeside angle are within the first and third quartiles of the other crestline types, and the first and third quartile values of each case lie within the minimum and maximum values for the other cases.Thus, whilst position on a three-dimensional dune may have some influence on leeside angle, with the saddle and lobe segments being lower-angle than straight-crested segments, the changes in leeside angle due to three-dimensionality are less marked than those shown previously in relation to either transport stage or bedform superimposition.However, future research with appropriate data sets is needed to quantify the variability in leeside angle across threedimensional dune crestlines.

Discussion: Processes Controlling the Formation of Low and Intermediate Dunes in Shallow Flows
The extensive laboratory data set examined herein demonstrates unequivocally that low and intermediate dunes form in shallow flows (0.15-0.25 m flow depth) across a range of transport stages from the threshold of sediment transport through to suspended load dominated transport.The percentages of dunes that experience no flow separation, intermittent, permanent, developing, and fully developed permanent flow separation are presented in Table S3 in Supporting Information S1, as derived from finding the percentages of dunes in each category for each scan, and calculating the average value of each experimental condition using the scan averages.In shallow flows with low to high sediment transport rates, up to 4% and 7% of dunes, respectively, on average, have leeside angles <10°.Intermediate dunes (10°-17°) make up to 27% and 44%, respectively.High angle dunes (17°-24°) reach up to 44% and 50%.Finally, angle-of-repose dunes represent up to 54% and 44% of dunes from low and high transport stages, respectively.These results demonstrate that low and intermediate angle dunes are present (from 4% to 44%) in shallow laboratory flows, and thus that the role of liquefied leeside avalanches as a major control in the formation of low-angle dunes, which has been proposed to be related to flow depth (Kostaschuk & Venditti, 2019), cannot be operative.In addition, limited analysis of bedform three-dimensionality reveals only a small influence on leeside angle.It is thus more likely that the causative mechanisms promoting the growth of lower-angle dune leesides (low and intermediate) relate to sediment transport stage and bedform morphodynamics and kinematics, and specifically the importance of sediment suspension and bedform superimposition (Figure 6).

The Formative Processes of Low-Angle and Intermediate Dunes
Suspension-dominated transport is likely to influence the formation of low and intermediate angle dunes in two ways.First, sediment suspension acts to modulate turbulence associated with the shear layer bounding the flow separation zone in the dune leeside (Baas & Best, 2008;Baas et al., 2009;Bridge & Best, 1988;Kostaschuk & Villard, 1996, 1999), with a dampening of turbulence leading to greater sedimentation on the leeface and decreased trough scour.High suspended load concentrations have also been hypothesized to lead to more sediment bypassing the dune crest than in bedload-dominated conditions, thereby promoting increased sediment deposition in the dune leeside (Kostaschuk & Villard, 1996, 1999).Recent work in the Huang He River, China (Ma et al., 2017) shows the overwhelming influence of suspension-dominated transport in very-fine sediments (130-190 μm).Ma et al. (2017) suggest that reformulation of the Engelund-Hansen sediment transport prediction (Engelund & Hansen, 1967) is required to better predict total load (bedload and suspended load) transport in finegrained rivers, and that transport in such channels has been underpredicted by an order of magnitude.Most salient to the present work is that a transition exists between sediment transport modes, from when suspension and bedload coexist to when suspension dominates.In the latter case, sediment flux is much greater than predicted for a range of fine sediment grain sizes, and this transition may be linked to differences in dune morphology, namely the "flatness" of the dunes (Bradley & Venditti, 2019a;Bridge & Best, 1988;Ma et al., 2017;Naqshband & Hoitink, 2020) that are a result of the influence of conditions with large concentrations of suspended sediment (Figure 6, Ma et al., 2017).The present analysis illustrates how this transition may also reflect the influence of sediment suspension on the dune leeside angle when the transport stage increases (Figure 6).
Examination of the relationships between leeside angle, suspension number, transport stage, and Froude number under equilibrium flow conditions reveals a range of leeside angles from 10°to 32°(Figure 2).From transport threshold through to suspension-dominated conditions, leeside angles increase and then decrease with increasing suspension number, transport stage and Froude number (Figures 2c-2e).Specifically, a transition occurs near a suspension number (u * /w s ) of ∼0.75, transport stage (τ/τ * c ) ∼10 and Froude number (Fr) ∼0.4,where the average leeside angle begins to decrease above these values.The transition from slightly increasing to decreasing leeside angle occurs consistently at the onset of suspended sediment transport.In these experiments, this onset occurs between the bedload (BDLD) and lower-mix (LMIX) conditions when suspended load flux increases from 0 to 70.8 g s 1 m 1 but bedload flux only exhibits a slight increase from 14.8 to 21.3 g s 1 m 1 .This is similar to previous field and experimental observations that have documented a decrease in dune leeside angle and dune height at higher transport stages (Bradley & Venditti, 2019a;Ma et al., 2017;Naqshband & Hoitink, 2020).Specifically, these data exhibit a similar behavior with increasing leeside angle at low suspension numbers until suspension transport increases, and then decreasing leeside angle thereafter.The trends revealed herein show that the dune leeside angle is less under upper transport conditions than lower transport conditions, regardless of dune size.The relationship between leeside angle and suspension number revealed herein matches that reported by Naqshband and Hoitink (2020), who used low-density sediment in flows of lower Froude number.The present observations, specifically the decrease in leeside angle that occurs at the onset of suspended sediment flux, also support the contention of Naqshband and Hoitink (2020) that low-angle leesides may be related to sediment suspension rather than transitional Froude numbers, as the onset of the lowering of leeside angle here was at Fr ∼ 0.4 (Figure 2e).In addition, the decrease in leeside angle occurs before the suspension number equals unity, and at the onset of suspended sediment flux between the bedload and lower-mix experimental conditions.This result suggests that the effects of sediment suspension on dampening leeside turbulence or bypassing deposition in the crest and deposition of sediment on the dune leeside may occur before suspended sediment transport is the dominant sediment transport flux.The present analysis thus confirms the likely importance of sediment suspension as a mechanism that contributes to the lowering of dune leeside angle, but has been previously difficult to measure in the field and model in the laboratory.
Although the discussion above illustrates the key role of sediment suspension in forming low and intermediate dunes at higher transport stages and suspension numbers, it is also evident that intermediate dunes exist (11%-27%, Table S3 in Supporting Information S1) at lower transport conditions.In order to examine if the dunes documented herein are able to generate flow separation, the data for leeside angle and H/Y were plotted alongside previous indices for the onset of flow separation (Figure 7).These data demonstrate that the maximum percentage occurrence of dunes that do not reach the onset of permanent flow separation (leeside angle <17°) is 29% at low transport stage (THLD 15 case), as compared to 51% at high transport cases (UMIX 15 case, Figure 7 and Table S3 in Supporting Information S1).Thus, although their abundance is slightly less at low transport stages, dunes that do not experience permanent flow separation do exist under these conditions and thus a mechanism for their formation is required that does not involve the transport of suspended sediment.Exploratory analysis (Figure 4) reveals how bedform superimposition causes lowering of the dune leeside angle in the threshold experimental condition where the suspended load flux was zero.In these bedload dominated conditions, bedform superimposition may be the dominant process to lower dune leeside angles (Figure 6).When bedform superimposition occurs, smaller dunes migrate up and over the larger dune stoss side and crest and, as they do so, they lower the leeside angle of the large dune due to erosion in the reattachment region of the flow separation zone associated with the superimposed bedform.Reesink and Bridge (2009) found that when the superimposed bedform is greater than 25% of the large dune height, leeside slope reduction occurs as the smaller dune approaches the larger dune crest.Although detailed investigation of this mechanism requires higher temporal and spatial resolution data than available herein, the present exploratory analysis provides an example of how the leeside angle may become lower due to bedform superimposition.In this case, when the leeside angle of the large dune begins to lower, the superimposed bedforms near the large dune crest possess H S /H L = 0.23 and leeside angle = 17°(Figure 4).Since H S /H L is lower than 0.25 and the leeside is <24°, this suggests that the process of crestal erosion may occur at a lower H S /H L than proposed by Reesink and Bridge (2009), and also at leeside angles lower than those required for permanent flow separation.In this case, flow acceleration over the superimposed bedform, and intermittent or developing permanent flow separation, may generate increased bed shear stresses that lower the leeside angle of the larger dune through crestal erosion.The increased bed shear stresses associated with superimposed bedforms (Bennett & Best, 1996) have also been shown to increase suspended sediment flux by producing resuspension events (Frias & Abad, 2013).This increase in transport stage may also shift the dominant process from bedform superimposition to sediment suspension (Figure 6), providing a feedback to sediment suspension that is related to intermittent flow separation.It is also inevitable that this process is not constrained to a 2D profile but instead bedform superimposition occurs across the dune field at various times, producing a complex three-dimensional pattern of crestal erosion due to superimposition.The increase in turbulence associated with 3D dunes compared to 2D dunes also leads to complex erosional patterns and sediment pulses (Hardy et al., 2021), and future work would benefit from investigating the formation of superimposed bedforms and their influence on dune morphology and the three-dimensionality of dune crestlines.Additionally, it is difficult to investigate the mechanism of bedform superimposition at higher transport stages, where dune celerity may be greater than the sampling frequency and acoustic detection of the bed surface also becomes difficult.Thus, understanding the importance of superimposition at higher transport stages remains a subject worthy of future study, especially as suspension begins to dominate sediment transport and where the importance of superimposition remains unclear.

Implications
The present analyses illustrate the distinct differences in leeside angle between dunes formed in the lower and upper transport stages and provide key insights into the formation of low and intermediate angle dunes in shallow flows.First, these data show that dunes that do not experience permanent flow separation can form in shallow flows, predominantly when suspended sediment is the major sediment transport flux, but also at lower sediment transport stages.Bradley andVenditti (2019a, 2019b) noted that dunes in suspension-dominated flows are longer and flatter than those in bedload-dominated flows, and the present analysis of these data shows that those relationships are related to lowering of the leesides.Past work (Kostaschuk & Venditti, 2019) has speculated that low and intermediate angle dunes do not form in shallow flows, and that their formation is linked to the presence of liquefied leeside avalanches that require greater flow depths.However, the present analysis demonstrates that low and intermediate angle dunes can form in flows as shallow as 0.15 m, and thus the processes that result in their formation are not a phenomenon solely confined to deep flows (Best et al., 2020;Bradley & Venditti, 2017;Kostaschuk & Venditti, 2019).
The dominance of lower angle dunes in suspension-dominated flows (lower-mix to suspension cases herein) is similar to that found in large rivers (Cisneros et al., 2020).However, the mean leeside angle and steepest slope of dunes in large rivers are lower than the experimental suspension cases, and distributions of leeside angle in these rivers are more widely spread than in the experimental suspension cases (Figure 3 and Table 1).The positive skewness of both the upper transport experiments and large rivers shows that these distributions are shifted toward lower leeside angles with tails extending to higher angles.Leeside angles in large rivers have the most positively skewed distribution, with the lowest leeside angle values and steep slopes compared to the experimental cases.These data illustrate how the characteristics of dune leesides revealed by the experimental data have clear parallels with large rivers, and provide clarification on some of the processes that dominate their formation.
In shallow flows under lower transport conditions, these data show 11%-29% of dunes are at low or intermediate angles and do not reach the onset of permanent flow separation (Figure 7; percentage abundance found between 0 under the dashed line) being similar to previous work that suggests most dunes would not possess fully developed permanent flow separation (Best & Kostaschuk, 2002;Kostaschuk & Villard, 1996;Kwoll et al., 2016;Lefebvre & Winter 2016).Under these lower transport conditions, bedform superimposition may provide a Journal of Geophysical Research: Earth Surface 10.1029/2023JF007520 mechanism to generate lower angle leeside slopes.In addition, dunes formed under low and high transport conditions will influence flow differently due to their different leeside angles.Under lower transport conditions, flow resistance produced through form drag from flow recirculation associated with high-angle leesides (>24°) will be greater than that produced over low and intermediate angle dunes (Kwoll et al., 2016;Lefebvre & Winter 2016;Ma et al., 2022).Under lower transport conditions, a greater percentage of angle-of-repose dunes exist (up to 54%), which past literature has used to predict flow resistance, suggesting that flow roughness and resistance predictions in bedload-dominated rivers may not require substantial modification.However, most dunes reported herein have leesides <24°(Figure 7) and therefore do not possess fully developed, permanent flow separation.Under the same flow depth in the present experiments at high transport conditions, a higher percentage of dunes likely either exhibit no permanent flow separation or no fully developed permanent flow separation (Figure 7).Under lower transport conditions, between 71% and 89% of dunes reach the onset of permanent flow separation, whereas this figure reduces to 56%-88% in high transport conditions (Figure 7).Using results from recent modeling that predict bed shear stress associated with dunes with leesides ranging from 10, 20, and 30° ( Kwoll et al., 2016), it can be speculated that the bed shear stress over dunes of the same height and under the same flow depth will be at least 10% less under high rather than low transport conditions.Incorporating these flow resistance and bed shear stress reductions for low-and high-transport stages into morphodynamic and flood risk models, especially in cases where rivers are undergoing variable flow conditions and transitions in sediment transport capacity, holds important consequences for understanding and managing many of the world's finegrained rivers (Ma et al., 2022).

Conclusions
To aid understanding of the processes responsible for the formation of low-angle dunes, bedform maps were analyzed from shallow flow (0.15-0.25 m deep) laboratory experiments detailing dune morphology.The experimental cases ranged from the threshold of sediment transport to bedload-and suspended-load dominated transport.This analysis reveals the presence of low and intermediate angle dunes in all shallow flows and that such dunes become more prevalent at higher transport stages.Past research has suggested that several potential factors may lead to the formation of dunes that do not experience permanent flow separation, including the influence of sediment suspension, the occurrence of bedform superimposition, the presence of liquefied leeside avalanches, and the influence of bedform crestline three-dimensionality.The present analysis confirms that the percentage of low and intermediate dunes increases in suspension-dominated flows, suggesting sediment suspension is key, but the occurrence of intermediate angle dunes in bedload-dominated flows also indicates that superimposition may play a role in the formation of low and intermediate dunes.The occurrence of low-angle and intermediate dunes that do not experience permanent flow separation in shallow (0.15 m) flows confirms that the role of liquefied avalanches, which has been speculated to be related to pore pressures generated under deep flows, cannot be a control.From limited data, the negligible difference between leeside angles across threedimensional dune crestlines under different transport conditions suggests that three-dimensionality in dune crestline shape does not appear to be a key factor influencing leeside angle.Future research should investigate how the dune leeside angle may change under unsteady flows, especially when transport stages are most likely to vary between bedload and suspended load dominated.Such considerations may be critical to better predicting flow resistance and flood stage in alluvial channels.

Figure 1 .
Figure 1.Schematic representation of the four mechanisms proposed in previous studies to cause the formation of low-angle dunes.

Figure 2 .
Figure 2. Relationship between leeside angle and: (a) flow depth, (b) relative dune height, (H/Y), (c) suspension number (u * /w s ), (d) transport stage (τ/τ * c ), and (e) Froude number (Fr) for all experiments.The average values of the individual scans are represented as pale colored symbols, whereas the average values for all scans per transport and flow depth condition are shown as bold outlined symbols.Dashed horizontal lines on the y-axis represent leeside angle values at 10°and 24°.Values for suspension number, transport stage, and Froude number for each scan are fromBradley and Venditti (2019a).Ιn (c) solid vertical line represents suspension number equal to 1, and in (e) solid and dashed vertical lines denote Froude number equal to 0.84 and 1, respectively.In panel (c), additional data represented as stars is fromNaqshband and Hoitink (2020).In panels (c-e) the dashed curve represents a polynomial regression fit to the average values of transport and flow depth condition pairs, with the dotted curves showing the 95% confidence intervals of the regression.

Figure 3 .
Figure 3. Distributions of leeside angle (filled) and steep slopes (outlined) for all experiments (a-l) and from the worlds large rivers (m).Dashed lines represent the leeside angles at 10°and 24°.See Table2for descriptive statistics of leeside angle distributions and TableS2in Supporting Information S1 for descriptive statistics of steep slope distributions.

Note.
The acronyms represent different transport and flow depth condition pairs: transport cases are Threshold = THLD, Bedload = BDLD, Lower-mix = LMIX, Upper-mix = UMIX, and Suspension = SPSN and flow depths range from 15 = 0.15 m, 20 = 0.20 m, and 25 = 0.25 m. a The data for the worlds big rivers represent the average values of the data set reported by Cisneros et al. (2020).

Figure 4 .
Figure 4. Visualization of the influence of bedform superimposition on dune morphology, showing (a) leeside angle and (b) relative height ratio, H S /H L , as linked to (c) successive longitudinal bed profiles and (d) 3D bedform maps (i-iv).In panel (a) blue markers denote the leeside angle of large dunes and gray markers denote superimposed bedforms.Note that values for superimposed bedforms do not exist when these bedforms are absent.The vertical-axes in (c) and (d), taken from the centerline and area around the centerline, depict a consistent 10 cm elevation range, with a 10-min time interval between successive profiles.Dashed lines represent leeside angles at 10°and 24°and H S /H L = 0.25.

Figure 5 .
Figure 5. Box and whisker plot of leeside angle measured across lobes, straight crests, and saddles (see inset definition diagram) in the THLD 15, BDLD 15, and SPSN 15 cases.The first quartile, median, and third quartile are shown by the bottom, middle and top lines bounding each box, with the minimum and maximum values shown as the bottom and top whiskers, respectively.For the SPSN case, only two values were available.Dashed lines represent the leeside angles of 10°and 24°.

Figure 6 .
Figure 6.Schematic summary of the relative significance of transport stage, grain size and bed shear stress and their influence on whether sediment suspension or bedform superimposition is the principal formative mechanism producing low and intermediate angle dunes.

Figure 7 .
Figure7.Hotspot graphs showing the potential for flow separation for all experiments.The relative dune height (H/Y) is plotted against lee-side angle for (a, f, k) THLD, (b, g, l) BDLD, (c, h) LMIX, (d, i) UMIX, and (e, j) SPSN dunes over (a-e) 15 cm, (f-j) 20 cm, and (k, l) 25 cm flow depth.The white star symbol represents the average value for the leeside angle and H/Y for each case.Zones of no permanent flow separation (<10°), the onset of permanent flow separation (dashed line,Lefebvre & Winter 2016) and fully developed permanent flow separation (>24°) are indicated on each plot.Note how fewer dunes possess high leeside angles at greater transport stages.

Table 1 T
-Test Statistics of Leeside Angles for Transport-Flow Condition PopulationsNote.In this table, the critical t-number changes based on the reference population (as reported in Table

Table 2
Statistics for Distributions of Leeside Angle for All Experiments Presented in Figure3