Spatial patterns of transport‐effective flow at three small confluences: Relation to channel morphology

The spatial patterns of transport‐effective flows at confluences and the relation of these patterns to channel morphology remain poorly understood. This field study uses acoustic Doppler current profiler measurements to explore the spatial structure of different transport‐effective flows at three small stream confluences where measurements of flow structure have been obtained previously using electromagnetic current meters or acoustic Doppler velocimeters for events incapable of mobilizing bed material or for transport‐effective events with much smaller discharges. Results show that flow accelerates from upstream to downstream for all six measured flows and that in each case a distinct region of velocity deficit exists within the confluence. Accelerating flow within this velocity‐deficit region eventually transforms into the high‐velocity core of flow downstream of the confluence. Patterns of secondary flow are indicative of helical motion, with some helical cells exhibiting senses of rotation inconsistent with patterns of streamline curvature defined by patterns of depth‐averaged velocity vectors—a type of fluid motion that contrasts with flow structure documented at lower stages. Channel form, especially bed morphology, generally reflects acceleration of flow at the confluences; all three sites exhibit zones of scour. Despite mobility of bed material during measured flows, channel morphology does not change substantially at any of the sites, but systematic change in channel form for two different transport‐effective events with different momentum flux ratios is observed at one of the three confluences. At this confluence, the type of change documented during the two events is consistent with previous work on changes in morphology before and after events with different momentum flux ratios. The results of this study improve understanding of the connections between flow structure and channel form at small lowland stream confluences.

Accelerating flow within this velocity-deficit region eventually transforms into the high-velocity core of flow downstream of the confluence. Patterns of secondary flow are indicative of helical motion, with some helical cells exhibiting senses of rotation inconsistent with patterns of streamline curvature defined by patterns of depthaveraged velocity vectors-a type of fluid motion that contrasts with flow structure documented at lower stages. Channel form, especially bed morphology, generally reflects acceleration of flow at the confluences; all three sites exhibit zones of scour.
Despite mobility of bed material during measured flows, channel morphology does not change substantially at any of the sites, but systematic change in channel form for two different transport-effective events with different momentum flux ratios is observed at one of the three confluences. At this confluence, the type of change documented during the two events is consistent with previous work on changes in morphology before and after events with different momentum flux ratios. The results of this study improve understanding of the connections between flow structure and channel form at small lowland stream confluences.  (Biron & Lane, 2008;Rhoads, 2020), which in turn can produce corresponding changes in bed-material transport, channel morphology and sedimentology (Best, 1988;Best & Rhoads, 2008;Nazari-Giglou et al., 2016;Rhoads et al., 2009). Factors that control the hydrodynamics of confluences include the junction angle, the symmetry of the confluence planform (whether the confluence is y-shaped or Y-shaped), the relative strength of the incoming flows as defined by the momentum flux ratio, characteristics of the confluence bed morphology, and density effects (Rhoads, 2020). As flows from separate streams combine, complex patterns of fluid motion develop within confluences. The development of zones of flow separation and flow stagnation, along with the formation of a distinct mixing interface between the confluent flows, has been well documented in the laboratory (Best, 1987) and in the field (Lewis & Rhoads, 2018;Rhoads & Kenworthy, 1995, 1998Rhoads & Johnson, 2018;. Understanding flow structure at confluences is not only important for linking fluid dynamics to processes of sediment transport and channel change at confluences (Rhoads et al., 2009), but is also relevant for evaluating the role of confluences in aquatic ecosystems and in the dispersal of river contaminants (Blettler et al., 2016;Gualtieri et al., 2020;Rice et al., 2008;Yu et al., 2020).
Based on the relation between bed elevations of contributing channels, confluences can be either concordant (contributing channels with the same bed elevation) or discordant (contributing channels with different bed elevations). Helical motion can develop at concordant confluences through mutual deflection of incoming flows, resulting in curvature of time-averaged trajectories of the moving fluid, also known as streamlines (Ashmore & Parker, 1983;Ashmore et al., 1992;Chen et al., 2017;Constantinescu et al., 2011Constantinescu et al., , 2012Constantinescu et al., , 2014Constantinescu et al., , 2016Mosley, 1976;Ramos et al., 2019Rhoads & Kenworthy, 1995, 1998. This streamline curvature results in centrifugal forces that are balanced in a depth-averaged sense by pressure-gradient forces associated with superelevation of the water within the confluence (Bradbrook et al., 2000;Weber et al., 2001). The development of helical motion at confluences can influence bed morphology and patterns of sediment transport by advecting momentum laterally and vertically, thereby altering spatial patterns of bed shear stress (Rhoads et al., 2009). It can also strongly influence patterns of mixing within and downstream from confluences (Lewis & Rhoads, 2015;Lewis et al., 2020;Lyubimova et al., 2020). At symmetrical confluences, mutual deflection results in curvature of depth-averaged streamlines of both incoming flows and the production of back-to-back counter-rotating helical cells that vary in relative size depending on the momentum flux of each incoming flow (Ashmore et al., 1992). At asymmetrical confluences, flow from the lateral tributary exhibits the greatest streamline curvature, resulting in a single dominant helical cell within the downstream channel (Rhoads & Kenworthy, 1995). Patterns of helical motion within confluences can be altered by the planform characteristics of the upstream channels, particularly curvature of these channels, which generates helical motion of incoming flows that can extend into the confluence (Luz et al., 2020;Riley & Rhoads, 2012;Riley et al., 2015;Rhoads & Johnson, 2018).
Patterns of fluid motion within confluences are also strongly influenced by discordance of the channel bed. At discordant confluences, flow from one of the contributing channels enters the confluence over a vertical step or steeply inclined ramp (Kennedy, 1984).
Recent research has suggested that under certain conditions density differences between the incoming flows can influence patterns of fluid motion in confluences, especially when buoyancy forces are similar in magnitude to inertial forces (Duguay et al., 2022a(Duguay et al., , 2022bGualtieri et al., 2019;Herrero et al., 2018;Laraque et al., 2009;Lewis & Rhoads, 2015;Ramon et al., 2013Ramon et al., , 2014Ramon et al., , 2016van Rooijen et al., 2020). The main effect of density differences is to initiate a spatially extended lock-exchange-like mechanism that promotes movement of the denser incoming flow beneath the less-dense incoming flow within and downstream of the confluence (Horna-Munoz et al., 2020). In extreme cases, this process can result in vertical stratification of the confluent flows. The extent to which even weak vertical stratification can modify the generalized flow patterns of confluences has been investigated computationally (Ramon et al., 2014(Ramon et al., , 2016Horna-Munoz et al., 2020;van Rooijen et al., 2020) and has been confirmed in the field at confluences where density effects are relatively strong (Herrero et al., 2018;Ramon et al., 2013), but extensive field investigations are lacking. Recent work suggests that even small density effects can produce local effects on flow structure in the vicinity of the mixing interface (Duguay et al., 2022a(Duguay et al., , 2022b. To date, most experimental, modeling, and field studies of threedimensional flow structure at confluences have focused on variations in controlling factors for a fixed discharge or over a relatively narrow range of discharges. Moreover, many field studies, particularly those at small confluences, have focused on measurements of flow during events that either were not capable of transporting most size fractions of bed material (Ashmore et al., 1992;De Serres et al., 1999;Rhoads & Kenworthy, 1995, 1998, 2008Sukhodolov & Sukhodolova, 2019Sukhodolov et al., 2017 or produced relatively minor mobilization of bed material (Boyer et al., 2006;Rhoads, 1996;Roy & Bergeron, 1990). As a result, understanding of changes in three-dimensional flow structure in response to variation in flow stage remains poorly constrained, hindering the development of a general conceptual model of confluence hydrodynamics. In field studies of small confluences, flow structure observed at low stages often is assumed to also occur at high stages, and channel changes documented during high flows are interpreted based on this assumption (Rhoads & Kenworthy, 1995). Field studies have been conducted at stages capable of mobilizing substantial amounts of bed material in large rivers, but generally do not include data at low stages for comparative purposes (Rhoads & Johnson, 2018;Riley & Rhoads, 2012;Riley et al., 2015).
The purposes of this study are (i) to analyze spatial patterns of flow at three small stream confluences at high stages capable of mobilizing virtually all sizes of material in the channel bed, referred to here as transport-effective stages, (ii) to compare these patterns to flow structure at low stages that either do not mobilize bed material or that produce only limited mobilization of this material, and (iii) to examine the effect of changes in the relative momentum fluxes of transporteffective incoming flows on channel form. A particularly noteworthy aspect of the study is that flow structure at all three confluences has been documented previously during events incapable of mobilizing any bed material or producing only limited mobilization of this material. Past investigations have indicated that large transport-effective events of the type documented herein can reshape the channel bed at one of the three confluences and have called for measurements during these types of events (Rhoads, 1996;Rhoads & Kenworthy, 1995;Rhoads et al., 2009). Although the study does not include direct measurements of active bed-material transport, it does assess whether bed material is mobilized by flows documented at the confluences, examines the extent to which channel morphology changes for different transport-effective conditions, and relates channel morphology, whether changing or static, to confluence flow characteristics. The results provide insight into flow patterns at confluences during transport-effective stages, the relation of these patterns to flow patterns at low stages, and the influence of transport-effective flows on confluence morphology.

| FIELD SITES
Three confluences in east-central Illinois were chosen for field measurements: the confluence of the Copper Slough with the Kaskaskia River (KRCS), the confluence of the Two-mile Slough with the Kaskaskia River (KRTMS), and the confluence of an unnamed tributary with the Saline Ditch (SALINE) (Figure 1). KRCS has been extensively studied as part of a long-term research project on the hydrodynamics and morphodynamics of confluences (Constantinescu et al., 2011(Constantinescu et al., , 2012(Constantinescu et al., , 2014(Constantinescu et al., , 2016Horna-Munoz et al., 2020;Lewis & Rhoads, 2015;Lewis et al., 2020;Rhoads & Kenworthy, 1995, 1998, 2004, 2008Rhoads et al., 2009). This work has noted, through before-and-after surveys of bed morphology (e.g., Rhoads et al., 2009), how specific events can reshape the channel bed, but, with one exception, has not directly measured flow characteristics during such events. Flow structure and patterns of bedload transport were documented at two cross-sections within the downstream channel during a bed-shaping hydrological event in July 1992 (Rhoads, 1996). Flow near peak stage of this event produced substantial change in channel bed morphology, but this change had already occurred by the time measurements were obtained on the receding limb of the hydrograph. Flow structure and mixing at relatively low flow stages have been investigated previously at KRTMS and SALINE , but past investigations have not examined the extent to which bed morphology is shaped by specific events at these confluences.
Land cover in the watersheds of the three confluences is predominantly (>85%) row-crop agriculture, almost all of which consists of corn and soybeans. All the confluences are set within trapezoidal ditches excavated to improve agricultural drainage. Because the ditches are earthen, erosional and depositional processes occur unimpeded, especially in the lowest part of the ditches where channels with deformable banks and beds can be defined ( Figure 3).
KRCS is an asymmetrical (y-shaped) confluence with a junction angle of $60 , while KRTMS and SALINE have approximately symmetrical (Y-shaped) planforms. KR and TMS meet at an angle of 36 , F I G U R E 1 Location map of the three confluences with accompanying aerial images (not to scale). [Color figure can be viewed at wileyonlinelibrary.com] while the junction angle at the SALINE confluence is 75 . At KRCS, the drainage area of KR (54 km 2 ) is 32% larger than the drainage area of CS (41 km 2 ), and at KRTMS KR drains twice the area (187 km 2 ) compared to TMS (98 km 2 ). The drainage area of the Saline Ditch at the confluence (38.7 km 2 ) is nearly identical to that of the unnamed tributary (38.6 km 2 ). At each confluence, the major and minor tributaries were defined on the basis of drainage area, with the major tributary having the largest drainage area.
Bed material at all three confluences consists of mixed sand and fine gravel   (Figure 2). SALINE and KRTMS have median particle sizes (d 50 ) corresponding to medium sand (0.35-0.50 mm); sand (0.063-2 mm) comprises 90% of the bed material at KRTMS and 75% of the bed material at SALINE. Bed material at KRCS is somewhat coarser, with d 50 in the granule size class (2-4 mm) and 43% of the bed material consisting of sand. Given the abundance of sand in the bed material, surficial armor layers do not develop at any of the sites.
All three confluences have beds that can be considered concordant; that is, the channels of the confluent tributaries have approximately the same bed elevations (Figure 3). Local differences in bed elevations are generally less than 0.2 m. These spatial variations in bed topography are not large enough to have a strong influence on flow structure throughout the water column at depths many times greater than the relief of the bed. Each confluence has lower bed elevations within the confluence than in the upstream channels, with depths of scour ranging from 0.3 to 0.6 m below upstream bed elevations ( Figure 3). Side slopes of the scour holes generally are less than 5 .  The M9 profiler (firmware version 2.0-3.0) has a nine-beam transducer system, two sets of 3 MHz and 1 MHz transducers for velocity measurements, and a single 0.5 MHz vertical echo sounder to measure depth (Boldt & Oberg, 2016). It features automated cell size adjustments for water depth, with bin sizes ranging from 0.1 to 0.4 m. Blanking of acoustic returns near the transducer head and side-lobe interference near the channel bed limit the domain of measurements to between 0.1 m below the water surface and 0.25 m above the channel bed.
Prior to initiating the ADCP measurements, a system test was conducted to ensure that the ADCP was operating properly. In addition, the compass of the instrument was calibrated to achieve error from calibration of less than 0.5 . Traverses at measurement crosssections were accomplished by mounting the ADCP on a catamaran and moving it back and forth between marked endpoints of each cross-section using ropes or by attaching the catamaran to a kayak and rowing the kayak between endpoints. Four to six traverses were performed at each cross-section. The time required to complete a transect varied between 1 and 3 min, depending on flow width. The duration of cross-section measurements ranged between 5 and 15 min and all measurement campaigns were completed within 1.5-3 h. The position of the ADCP within the confluence was determined by a differential global positioning system (dGPS) with submeter accuracy mounted on and time-synchronized with the ADCP.
The ADCP data were exported from Sontek's RiverSurveyorLive software into the Velocity Mapping Toolbox (VMT), a MATLAB-based GUI for post-processing of ADCP data (Parsons et al., 2013). VMT was used to average data for the four to six traverses into a single representation of local time-averaged velocities in the downstream (u), cross-stream (v), and vertical (w) directions. This averaging reduces the influence of outliers and measurement errors for individual transects on patterns of velocities within a cross-section. Previous work has demonstrated the value of VMT-based analysis of multiple traverses of ADCP data for identifying patterns of time-averaged threedimensional fluid motion at confluences (Gualtieri et al., 2018;Herrero et al., 2018;Li et al., 2022;Luz et al., 2020;Rhoads & Johnson, 2018;Riley & Rhoads, 2012;Riley et al., 2015;Yuan et al., 2021;Zhang et al., 2020). Secondary velocities (v s ) based on the Rozovskii method (Rozovskii, 1957), which defines components of secondary flow oriented perpendicular to the direction of the depthaveraged velocity ( u) at each vertical profile through the flow column, were also determined using VMT. Analysis of the pattern of v s -w vectors is effective for identifying coherent patterns of secondary flow at confluences where rotational motion of the fluid may be embedded within converging incoming flows exhibiting differential curvature of depth-averaged streamlines across the width of a confluence (Rhoads, 2020;Rhoads & Kenworthy, 1999). In particular, plots showing the spatial distribution of v s -w vectors throughout cross-sections are useful for identifying patterns of secondary circulation characteristic of helical motion oriented parallel to the direction of the flow.
Because the Rozovskii method always results in zero net secondary discharge locally over depth, it can yield complex, local patterns of secondary circulation that are difficult to interpret (Lane et al., 1999).
To identify coherent helical motion, the present study focuses on patterns of depth-scale secondary circulation that generally persist longitudinally from one cross-section to another.
The processed data from VMT were plotted in Tecplot 360 to interpret patterns of fluid motion for the different measured events.
These patterns were compared to patterns of fluid motion documented previously at the three confluences during low flows based on electromagnetic current meter (ECM) or acoustic Doppler velocimeter (ADV) measurements Rhoads, 1996;Rhoads & Kenworthy, 1995, 1998.
Comparison of the ADCP and ECM/ADV data provides the basis for documenting similarities and differences in flow structure, including the presence/absence of secondary motion during high versus low flows. It also informs how channel morphology is related to patterns of fluid motion during transport-effective flows. Whereas representations of 3D flow structure using ECM/ADV measurements are based on time-averaging of many velocity measurements at a few points throughout cross-sections in the confluences, those using ADCP measurements are based on time-averaging of a few measurements at many locations throughout the cross-sections. Thus, the two representations are complementary, but involve different tradeoffs between spatial resolution versus temporal resolution.
The relative importance of density effects associated with temperature differences in relation to inertial effects can be assessed using the densimetric Froude number: where U m is the reach-averaged velocity within and immediately downstream of the confluence, D is mean flow depth within and immediately downstream of the confluence, g 0 is the reduced gravity were not useful in this study for defining a sharp contrast in surface temperature within the confluences given the small temperature differences between the incoming flows, the short transit times of the ADCP across the transects, and the relatively slow response time of the thermal probe to changes in water temperature.
Immediately prior to commencing the ADCP measurements, a survey rod and automatic level were used to determine the elevation of the water surface (WSE) near the apex of the confluence relative to the local datum. The WSE, along with flow depths determined by the ADCP, provide the basis for determining elevation profiles of channel cross-sections for each campaign. The value of WSE obtained near the junction apex was used to compute cross-section elevations at each confluence; variation in WSE over distance was not considered.
Given the slopes of the confluences, this method could result in local absolute errors of about 6 cm or less in bed elevations; however, errors in elevation differences between campaigns for a given cross-section should be less than these absolute errors, given that eleva- measurements were obtained at comparatively low discharges using either electromagnetic current meters or ADVs. At KRCS, only one previous set of velocity measurements was collected at a total discharge exceeding 2.5 m 3 /s and this set included measurements only at two cross-sections within the confluence (Rhoads, 1996). The discharges for the present study are 7-22 times greater than those for previous studies at KRCS that included measurements at more than two cross-sections. At SALINE, the largest discharge in the present study is six times greater than the largest previously measured flow, whereas the smallest discharge in the present study is twice as large as the largest flow measured previously. At KRTMS, the largest discharge in the present study is nearly five times greater than the largest previously measured flow and the smallest discharge in the present study is 1.8 times greater than the largest flow measured previously.
The momentum flux ratio (M r ) is defined as where ρ is water density, Q is the discharge, U is mean cross-sectional  (Table 1). In the present study, events with values of M r > 1 and <1 were documented at two of the sites (KRCS and SALINE) ( Temperature differences between the confluent flows, based on data obtained from the thermal probe on the ADCP at cross-sections upstream of the confluence, are relatively small, ranging from to 0.4 to 1.5 C ( Table 2). Values of F D all exceed 10, indicating that inertial forces are much greater at these confluences than buoyancy forces.
The development of any time-averaged coherent fluid motion within the flows is therefore most likely the result of spatial and temporal variability in inertial forces, rather than a product of buoyancy effects. involves turbulent lateral transport of momentum by coherent vortices along the margins of these regions (Sabrina et al., 2021). This mechanism differs from advective lateral transport of momentum by the mean flow within the velocity-deficit region downstream of the region of flow stagnation (Rhoads & Sukhodolov, 2008). Rates of velocity increase within the velocity-deficit region are greatest for KRCS and lowest for KRTMS (Table 4). SALINE has rates between those of KRCS and KRTMS, but rates for this confluence are more variable than those for the other two confluences. The similarity in the rate of velocity increase at KRTMS, despite large differences in Q T on the two dates (   Figure 6). This acceleration is produced by a downstream decrease in the cross-sectional area of the flow (Figure 6), which in turn is related to a progressive decrease in channel cross-sectional area. The spatial patterns of vector magnitudes and U at SALINE are more complex than at the other two confluences, reflecting the comparatively complicated geometry of this confluence (Figures 4 and 6).
The downstream channel at this confluence narrows, then abruptly widens, before narrowing again, producing a downstream pattern characterized by acceleration, deceleration, and acceleration ( Figure 6). This pattern is especially pronounced on 04/01/2016, when the flow is confined by the channel banks, thereby accentuating changes in flow area over distance.  F I G U R E 5 Increase in minimum depth-averaged velocity vector magnitudes over distance (beginning at first cross-section downstream of the stagnation zone) within the velocity deficit region in the center of the three confluences. Curved lines represent logarithmic functions fitted to the data (see Table 4).

| Secondary flow
expands. For the high-momentum-ratio event at KRCS ( This fluid motion appears to interact with, and perhaps reinforce to some extent, the decaying clockwise motion on the right side of the downstream channel.
On both measurement dates, coherent motion is observed at where f s is the fraction of sand in the mixture. A similar relation is used to compute τ Ã sc , the critical dimensionless shear stress for sand fractions: where τ Ã sc 0 d g50 is the median grain size of the gravel fraction, and d s50 is the median grain size of the sand fraction.
Given that sand content of bed material at the three confluences exceeds 40% and at KRTMS is as high as 89%, the critical dimensionless shear stress for gravel is rather small (0.008) ( Table 5) compared to values of 0.045-0.053 often cited for rough gravel-bed streams (Rhoads, 2020), reflecting the high mobility of gravel fractions in these sandy confluences. The relatively small ratios of d g50 =d s50 at all three confluences yield values of τ Ã sc equal to or nearly equal to the value for f s = 1 (0.045) ( Table 5). Dimensionless critical bed shear stresses can be used to determine the dimensional critical bed shear stresses for sand (τ sci ) and gravel (τ gci ) grain-size fractions (d i ) as where ρ s is the sediment density (2650 kg/m 3 ).
Determining the actual bed shear stress acting on particles on the bed requires portioning the total bed shear stress into components associated with grain friction (τ 0 ) and other sources of boundary resistance (τ 00 ). Using the ADCP data on variation in velocities over depth to evaluate bed shear stress based on the law of the wall method (Rhoads, 2020) is prone to error because the ADCP does not measure velocities near the bed, which are critical for accurate shear stress estimates. Instead, the Keulegan equation is employed to obtain a first-order estimate of the bed shear stress acting on grains: where D 0 is the portion of the flow depth attributed to grain friction, S is slope, and k s is the grain roughness. The roughness k s is typically expressed as a multiple of a representative grain size of the bed material. Values of k s range from 1.0d 50 to 3.0d 90 (Garcia, 2008), with coarse sizes typically selected for natural rivers (Wilcock, 1996). To accommodate uncertainty in grain roughness, two estimates of k s were considered in the analysis of grain mobility: k s ¼ 0:84d 90 , the value calculated by Wilcock and Kenworthy (2002) based on experimental analysis of sand-gravel mixtures, and k s ¼ 2:8d 90 , a value more typical of natural rivers containing gravel (van Rijn, 1982;Wilcock, 1996). The slope (S) at each confluence is derived from lidar data available from the Illinois State Geological Survey's Geospatial Data Clearinghouse (Table 5) The total mean bed shear stress at a cross-section (τ b ), which includes all sources of flow resistance, is where g is gravitational acceleration (9.81 m/s 2 ). At a particular vertical column through the flow the bed shear stress can computed as where h is the local flow depth. The mean bed shear stress at a crosssection (τ 0 b ) associated with grain friction is or, alternatively, the grain bed shear stress can be computed locally (τ 0 bl ) as where h 0 is the portion of the local depth (h) related to grain friction as determined from Equation (7)  four different velocities within each confluence: min U, the minimum cross-sectional velocity (always the cross-section closest to the junction apex); max U, the maximum cross-sectional velocity; mean U, the mean cross-sectional velocity of all cross-sections, and max u, the maximum local depth-averaged velocity (Table 6).
Total mean bed shear stresses for the different velocities are 4-11 times greater than the corresponding bed shear stresses associated with grain friction, showing that other sources of flow resistance, such as bedforms, bars, bank vegetation, and turbulent motion, are dominant at these confluences (Table 6). This result is not surprising, given that confluences are known to be zones of high turbulent energy loss in river systems and that all the confluences have varied bed morphology and abundant bank vegetation. Although the sampling strategy for flow measurements, i.e. cross-sections oriented across the confluence, was not conducive for documenting the occurrence of bedforms within the confluences, ripples have been observed at KRCS (Rhoads, 1996) and KRTMS   or more of the bed material, and stresses for the mean cross-sectional velocities (mean U) can mobilize greater than 90% of the bed material at all three confluences (Table 6). Maximum depth-averaged velocities (max u) generate grain shear stresses that can entrain 99-100% of the particles on the bed. Overall, these results suggest that the measured T A B L E 6 Hydraulic conditions related to total bed shear stress, grain shear stress, and the percent of the bed material distribution mobilized (% mobile) for minimum, maximum, and mean cross-sectional velocities and for maximum depth-averaged velocities at each confluence for two different grain roughness estimates flows are highly transport-effective and have the potential to influence confluence morphology. Although the approach adopted here yields only first-order reach-averaged estimates of grain shear stresses, in highly turbulent environments like river confluences it seems likely that such estimates are conservative and that actual grain shear stresses may exceed these estimates.

| Changes in channel form
Comparison of cross-section elevation profiles reveals the extent to which channel morphology at each confluence changed between different measured transport-effective flows (Figures 11-13).  Figure 12). At KRTMS minor differences are evident in the lateral extent of the left channel bank at the upstream end of the confluence (cross-sections 3-5) on the two measurement dates, but otherwise the bed morphology for the two campaigns is remarkably similar, differing locally by a maximum of 0.25 m and in many places by less than 0.10 m (Figure 13).

| DISCUSSION
The results of this study contribute to the understanding of linkages at stream confluences among spatial patterns of transport-effective flows, characteristics of secondary fluid motion of these flows, the competence of these flows to mobilize sediment, and the possible effect of these flows on channel morphology. The ADCP measurements confirmed that a region of relatively low velocities that extends downstream from near the junction apex exists between zones of high velocity at all three confluences. This finding supports results of previous work at KRCS and SALINE based on large-scale particleimage velocimetry (Lewis & Rhoads, 2018). It also is consistent with 2D and 3D measurements of velocity components at the three F I G U R E 1 1 Changes in cross-section morphology at KRCS for the two measured flow events.
F I G U R E 1 2 Changes in cross-section morphology at SALINE for the two measured flow events.
F I G U R E 1 3 Changes in cross-section morphology at KRTMS for the two measured flow events confluences at low-flow stages that have documented a region of low velocities separating high-velocity cores of the incoming flows at cross-sections in the upstream part of the confluences Rhoads & Kenworthy, 1998;. Together, the findings here as well as those from previous work suggest that velocity-deficit regions are often an important aspect of the spatial pattern of flow at confluences. Previous conceptual models have emphasized flow stagnation near the upstream junction corner (Best, 1987), but the region of velocity deficit is distinct from the region of stagnation (Lewis & Rhoads, 2018), which is characterized by recirculating fluid and is bounded by conspicuous shear layers (Sabrina et al., 2021). In the region of velocity deficit, fluid is moving downstream, but at lower speeds than adjacent fluid constituting the high-velocity cores of the incoming flows. Fluid within this region accelerates over distance and eventually transforms into the high-velocity core of flow within the downstream channel.
Lateral advection and diffusion of momentum into the velocity-deficit region contribute to acceleration, as does change in flow geometry, particularly decreases in cross-sectional area within the downstream channel, which result in overall fluid acceleration. Interestingly, the downstream rate of increase in velocity at all three confluences conforms to a logarithmic relation. The velocity-deficit region also contains the interface between the two confluent flows and thus is a zone of mixing .
Large-scale flow separation, a well-studied aspect of confluence hydrodynamics in experimental and numerical contexts (Best & Reid, 1984;Qing-Yuan et al., 2009;Shakibainia et al., 2010), occurred only at one of the three confluences. Separation at SALINE was related mainly to the morphological configuration of the confluence, particularly local protrusion of the bankline and widening of the downstream channel. Separation can occur at the lowest stages at KRCS (Rhoads & Kenworthy, 1995;Lewis & Rhoads, 2018), especially when an exposed bar is located near the downstream junction corner, but was not evident for the high-stage flows documented here, which substantially inundated within-channel deposits that might be exposed at low flow as bars. Separation at KRTMS is inhibited by the low junction angle of this confluence, which prevents detachment of incoming flow from the channel banks.
The ADCP data indicate that patterns of secondary flow at the confluences are complex and do not necessarily conform to patterns that occur at total discharges much less than those documented in this study. Previous work at KRCS Rhoads & Kenworthy, 1995, 1998, including measurements at stages capable of partly mobilizing bed material (Rhoads, 1996), has shown that for M r ≤ 1 dual surface-convergent cells develop within the confluence (cross-sections A1 and A) with the clockwise-rotating cell on the left side of the confluence intensifying and expanding as flow moves through the downstream channel (cross-sections C and E) ( Figure 14). For M r > 1, dual surfaceconvergent cells also develop, but within the confluence (crosssections A1 and A) the cell on the left (CS) side of the confluence is larger than the cell on the right (KR) side (Rhoads, 1996;Rhoads & Kenworthy, 1998). Immediately downstream (cross-sections C and E), clockwise motion extends over most of the cross-section, similar to the pattern for M r ≤ 1. This basic structure of helical motion has been explained by curvature of streamlines defined by the spatial pattern of depth-averaged velocity vectors and associated local imbalances over depth between centrifugal and pressure-gradient forces (Rhoads & Kenworthy, 1998). Counterclockwise curvature of streamlines related to flow from the Copper Slough should generate clockwise helical motion, whereas clockwise curvature of streamlines related to flow from the Kaskaskia River should generate counterclockwise helical motion (Rhoads, 1996). Thus, at low stages, the "back to back" meander-bend analogy, sometimes invoked for confluences (Ashmore & Parker, 1983;Ashmore et al., 1992), seems to apply to KRCS. Mild counterclockwise curvature of the downstream channel reinforces clockwise helical motion generated by realignment of flow from the Copper Slough as it moves through the confluence, but weakens counterclockwise helical motion initiated upstream within the Kaskaskia flow.
F I G U R E 1 4 Generalized patterns of depth-averaged streamlines and secondary circulation at KRCS for M r > 1 and M r ≤ 1 for high and low flows. Patterns for high flow are based on results of this study, whereas those for low flow are based on findings reported in Kenworthy (1995, 1998), Rhoads (1996), Rhoads and Sukhodolov (2001), and Lewis et al. (2020). Solid blue lines with arrows indicate relatively strong circulation compared to the dashed blue lines with arrows (view is looking downstream). Area between streamlines near upstream junction corner represents velocity-deficit region. [Color figure can be viewed at wileyonlinelibrary.com] The results for KRCS show that a high, transport-effective flow with M r < 1 is characterized by strong helical cells on each side of the confluence (cross-sections A1 and A), but the cells are co-rotating rather than counter-rotating ( Figure 14). The counterclockwise rotation of the cell on the right side of the confluence is consistent with the clockwise pattern of streamline curvature within the confluence, as is the weakening of this cell as the sense of streamline curvature reverses to a counterclockwise pattern within the downstream channel ( Figure 14). that inertial forces are much greater than buoyancy forces, large-scale density effects, such as those associated with the lock-exchange mechanism (Horna-Munoz et al., 2020), seem unlikely to be a cause of strong secondary flow. The capacity of F D to capture local effects of relatively small density contrasts, which can produce helicity near the mixing interface (Duguay et al., 2022a(Duguay et al., , 2022b, remains uncertain, but rotation of the strong helical cell on the left side of KRCS on 12/29/2015 is opposite that expected based on density considerations (Duguay et al., 2022a(Duguay et al., , 2022b. Although dunes can develop within the sand and fine-gravel substrate of KRCS (Rhoads, 1996), these features typically produce periodic turbulent structures oriented in an inclined plane extending from bedform crests toward the surface (Best, 2005), rather than persistent streamwise helical motion. Flow separation over steep slopes in the channel bed associated with bed discordance or avalanche faces bounding a scour hole can generate helical motion of the flow (Bradbrook et al., 2001;McLelland et al., 1996). Exactly how steep the channel bed at a confluence must be to induce flow separation remains uncertain, but the steepest gradient of the channel bed along the path of the depth-averaged flow at the three confluences occurs at KRCS (Figures 3 and 4)  vertical (z) dimensions related to boundary effects can generate streamwise helical vortices (Nezu et al., 1993;Perkins, 1970). No solid boundary exists between the two confluent flows, so anisotropic turbulence would have to be related to hydrodynamic boundary effects, such as the development of a pronounced stagnation zone or velocity-deficit region separating these flows. This possible explanation is rather speculative because lateral gradients of streamwise velocity typically produce vertically oriented vortices along regions of lateral shear, rather than large streamwise-oriented vortices that extend over substantial portions of the channel cross-section (Chu & Babarutsi, 1988). On the other hand, numerical simulations suggest that weak turbulence-generated helical vortices can develop at confluences (Lyubimova et al., 2019). This motion is only spatially persistent on the SALINE side of the confluence (cross-sections 6, 8 and 10), where clockwise rotation is consistent with the pattern of streamline curvature (Figure 15). On both dates, the cell on the left side of the downstream channel provides a mechanism for advective transport of momentum into the prominent separation zone at this confluence. Previous measurements of flow structure at SALINE during low-stage events with M r < 1 either have failed to document helical motion  or have found only limited evidence for a clockwise-rotating cell on the left side of the confluence (Lewis & Rhoads, 2018;Lewis et al., 2020) ( Figure 15).
The lack of prominent and spatially persistent large-scale helical motion at KRTMS is consistent with past studies of flow structure at this confluence at low flow for M r < 1 . The relatively small angle of this confluence, which limits streamline curvature, is one possible reason why strong helical motion does not develop. High bed friction associated with bedforms, which likely develop within the sandy substrate at this site, and the relatively large width-depth ratio of the flow, probably also inhibit helical motion (Parsons et al., 2007). The virtual lack of any per- F I G U R E 1 5 Generalized patterns of depth-averaged streamlines and secondary circulation at SALINE for M r > 1 and M r < 1 for high and low flows. Patterns for high flow are based on results of this study, whereas those for low flow are based on findings reported in Lewis et al. (2020). Solid blue lines with arrows indicate relatively strong circulation compared to the dashed blue lines with arrows (view is looking downstream). Area between streamlines near upstream junction corner represents velocity-deficit region.
[Color figure can be viewed at wileyonlinelibrary.com] The analysis of particle mobility, while approximate, indicates that all flows at the three sites were highly competent to move large percentages of bed material. All three confluences exhibit a zone of scour within the downstream channel ( Figure 3) that reflects acceleration of flow and corresponding increases in sediment transport capacity within the confluences during all measured transport-effective flows (Figures 4 and 6). Even at SALINE, where mean cross-sectional velocity decreases locally within the downstream channel ( Figure 6), acceleration of flow is clearly evident when the separation zone along the left bank is excluded from consideration ( Figure 4). The general morphology of the confluences seems to be governed by this spatial pattern of flow, which is largely independent of momentum flux ratio.
KRCS is the only confluence out of three studied where bed morphology differs systematically with changes in M r . At this confluence, the change from a symmetrical to an asymmetrical cross-sectional shape in conjunction with deposition along the left bank of the downstream channel has been documented previously through surveys of channel morphology before and after formative events with M r > 1 and M r < 1 (Rhoads, 2020;Rhoads et al., 2009). The results here confirm that such differences in channel morphology are evident during formative events and thus likely caused by changes in the momentum flux ratio associated with these events. Deposition along the left bank has been attributed to spatial decreases in the bed shear stress and associated sediment transport capacity along a path around the downstream junction corner equidistant from the channel bank (Best & Rhoads, 2008;Rhoads & Kenworthy, 1995). This effect will be most pronounced for events with M r > 1 when the high-velocity core from the Copper Slough penetrates far into the confluence and deceleration of incoming flow from the Copper Slough around the downstream junction corner is most pronounced. Near-bed flow directed toward the left bank by clockwise helical motion may also sweep mobile bed material toward this bank during transport-effective flows (Rhoads et al., 2009).
The development of counterclockwise helical motion on the left side of KRCS for M r < 1 should contribute to bed erosion because near-bed currents directed toward the right bank will transport bed material away from the left bank. Thus, the development of this cell during transport-effective events with M r < 1 may be an important hydrodynamic feature shaping channel morphology. Moreover, during high-stage events with M r < 1, the high-velocity core of flow from the Copper Slough is confined to a position near the left bank so that the bed shear stress may actually increase from upstream to downstream near the downstream junction corner rather than decrease as it does when M r > 1. Such a spatial pattern of bed shear stress will also promote excavation of deposited sediment on the left side of the downstream channel.
The lack of systematic change in channel morphology with changes in M r of transport-effective events at KRTMS and SALINE may reflect less-pronounced M r -related variations in patterns of secondary flow at these two confluences compared to KRCS, and perhaps less abundant supplies of sediment from upstream, which can be a major factor influencing the adjustment of channel form at confluences (Bombar & Cardoso, 2020). At KRTMS, variation in M r was relatively minor compared to the other two confluences, and the dominance of flow from the Kaskaskia River at this confluence for both measured events may have constrained adjustments of the bed.
At SALINE, the substantial influence of the local bank protrusion and downstream increase in channel width on flow structure, particularly flow separation, appears to dominate the connection between flow and channel form, thereby limiting the effect of variations in M r on channel morphology.

| CONCLUSIONS
This study has shown that the structure of transport-effective flows at three small stream confluences includes: (1) distinct zones of maximum depth-averaged velocity within the two tributaries upstream of the confluence; (2) a region of velocity deficit near the upstream junction corner situated between zones of maximum velocity associated with each incoming tributary flow; (3) progressive acceleration of the flow within the velocity-deficit region with velocities increasing logarithmically over distance; (4) overall acceleration of the flow within the confluence relative to maximum mean cross-sectional velocities of the incoming flows; and (5) secondary flow related to large-scale F I G U R E 1 6 Generalized patterns of depth-averaged streamlines and secondary circulation at KRTMS for M r < 1 for high and low flows. Patterns for high flow are based on results of the highest high flow measured in this study (05/05/2017), whereas those for low flow are based on findings reported in Lewis et al. (2020). Solid blue lines with arrows indicate relatively strong circulation compared to the dashed blue lines with arrows (view is looking downstream). Area between streamlines near upstream junction corner represents velocity-deficit region. [Color figure can be viewed at wileyonlinelibrary.com] streamwise helical motion. Some cells of helical motion have a sense of rotation consistent with curvature of streamlines defined by depthaveraged velocity vectors, whereas others rotate in the opposite sense expected on the basis of streamline curvature. The latter finding contrasts with patterns of helical motion observed at low stages at these confluences and indicates that mechanisms other than streamline curvature can generate streamwise helicity during high flow stages. The cause of large-scale helical motion that does not conform to patterns of streamline curvature is unclear, but may be related to strong lateral shear along the margins of the region of velocity deficit within the confluences. Density effects (Horna-Munoz et al., 2020) and bed discordance (Bradbrook et al., 2001;Canelas et al., 2022;McLelland et al., 1996) have also been implicated in the development of helical motion at confluences. Evaluation of inertial versus density effects suggests that the former greatly exceed the latter at these confluences. Also, the confluences examined here do not exhibit substantial discordance. Further studies of flow at confluences are needed to document helical motion and to determine the factors responsible for this motion under specific conditions. The generalized analysis of particle mobility at the three confluences implies that all flows could transport a large percentage of the bed material. Thus, the flows could reshape the channel bed and perhaps also the channel banks. The general characteristics of the flows, particularly flow acceleration over distance-that is, convective acceleration-are consistent with the development of bed scour at all three confluences. Convective acceleration should produce increasing bed shear stress and a corresponding increase in bed material transport capacity that will result in net excavation of bed material. The lack of change in the maximum depth of scour for events of different magnitudes suggests that channel morphology has adjusted to maintain an equilibrium form that can accommodate a wide range of flow conditions. To some extent changes in scour depth may also be limited by substrate conditions. Past work at the confluence of the Kaskaskia River and Copper Slough has shown that exposure of glacial till on the channel bed can limit the depth of scour within the downstream channel (Rhoads & Kenworthy, 1995;Rhoads et al., 2009).
Change in the relative strengths of the incoming flows, as measured by momentum flux ratio, does not appear to result in substantial change in channel form at two of the three confluences examined in this study, whereas it is associated with systematic change at the con- Overall, this study has demonstrated that the bed morphology of the confluences is consistent with general spatial patterns of hydraulic conditions, that the morphology of these lowland confluences is relatively stable at the event timescale, and that patterns of secondary flow, especially helical motion, differ both among the confluences and at a particular confluence as the momentum flux ratio of the incoming flows varies. Changes in the pattern of helical motion may influence bed morphology when the motion is strong, and this motion interacts with upstream sediment supply. Otherwise, details of helical motion do not seem to have a major influence on channel form.