Introduction

Front. Earth Sci.

Frontiers in Earth Science

Front. Earth Sci.

2296-6463

Frontiers Media S.A.

1733824

10.3389/feart.2026.1733824

Original Research

Effects of water and sediment variations on estuarine channel evolution: mechanisms and morphological discrimination

Su et al.

10.3389/feart.2026.1733824

Jing

¹ * Writing - review and editing Writing - original draft Sun

Yanjie

² ³ Writing - original draft Data curation Supervision Project administration Methodology Formal Analysis Investigation Software Conceptualization Song

Xiaolong

³ Resources Writing - review and editing Funding acquisition

1 Shandong Women’s University, Shandong Jinan, Jinan, China 2 School of Architecture and Civil Engineering, Liaocheng University, Liaocheng, China 3 State Key Laboratory of Hydraulic Engineering Intelligent Construction and Operation, Tianjin University, Tianjin, China

*Correspondence: Jing Su, sujing_1314@163.com

25 02 2026

2026

1733824

28 10 2025 30 12 2025 09 01 2026

2026

Su, Sun and Song

https://creativecommons.org/licenses/by/4.0/

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

This study employed physical experiments to simulate the morphological evolution of a meandering tail channel, a critical river-sea interaction zone, under varying flow and sediment conditions, with a focus on the Yellow River. Results demonstrate distinct evolutionary patterns: during sediment-feeding phases, the non-estuarine reach experiences deposition under low flows, leading to bed aggradation, channel widening, and mid-channel bar development, suggesting a potential shift toward a wandering pattern, while scour dominates under high flows, forming narrow, deep cross-sections. In the estuarine reach, a nascent Lambda-shaped delta forms under low flows, whereas high-flow conditions promote erosion and a W-shaped cross-section. After sediment feeding ceases, the non-estuarine reach maintains a wide, shallow form under low flows but undergoes intense scour under high flows, whereas the estuarine reach develops a multi-distributary fan-shaped deposit under low flows, with high flows triggering channel migration or avulsion. Experiments confirm that sediment transport profoundly influences channel morphology regardless of bed state, and particle size distribution of sediments correlates strongly with the degree of channel evolution. Based on these findings, the resistance law expression was refined, and a channel pattern discrimination method suitable for the lower Yellow River was proposed and validated with measured data, confirming its rationality and reliability.

bed sediment transport fluvial evolution physical experiment water-sediment factors weakly-tidal estuarine channel

National Natural Science Foundation of China

10.13039/501100001809

The author(s) declared that financial support was received for this work and/or its publication. This research was funded by National Natural Science Foundation of China (Grant No. 52409103).

section-at-acceptance

Hydrosphere

1 Introduction

The estuarine zone, where riverine flows meet the ocean, is a critical biogeomorphic interface that regulates the transfer of water, sediment, nutrients, and pollutants to the coastal sea. Its morphological dynamics underpin a range of vital ecosystem services and human interests, including the creation and maintenance of deltaic land, support for high-productivity fisheries, provision of navigation channels, and buffering against coastal flooding and erosion (Baar et al., 2022; Li et al., 2022; Syvitski et al., 2005; Nguyen and Tanaka, 2024; Nienhuis et al., 2020). Consequently, predicting the evolution of estuaries, especially under changing climate and intensifying human interventions, is a paramount concern in earth science and environmental management (Giosan et al., 2023; Yang, 2020; Yu et al., 2023).

Estuaries can be classified based on the relative strength of tidal versus fluvial forcing. In weakly-tidal or fluvially-dominated estuaries, such as the mouth of the Yellow River, the morphological evolution is primarily governed by the variability in river-derived water and sediment discharge, with tidal modulation playing a secondary role (Baum et al., 2024; Karapurkar et al., 2025; Liu et al., 2025; Wang et al., 2021; Nienhuis et al., 2020). These systems are often characterized by high sediment loads, frequent channel migration, and a pronounced susceptibility to avulsion-a sudden shift in the main flow path (Slingerland and Smith, 2004; Chadwick et al., 2019; Ji et al., 2018). Channel avulsion can threaten infrastructure, alter habitats drastically, and reshape the entire coastal landscape, making the understanding of its triggers and processes a research priority.

Research on estuarine morphodynamics has advanced on multiple, complementary fronts, each with its strengths and limitations: (1) Field Data Analysis and Empirical Modeling: Long-term hydrological and topographical monitoring has been instrumental in establishing statistical correlations between forcing factors (e.g., annual runoff, sediment concentration) and channel responses (e.g., cross-sectional area, migration (Mahmoodzada et al., 2023) rate). Studies on major rivers like the Yellow River have detailed seasonal siltation-scour cycles and decadal trends under anthropogenic regulation (Han et al., 2020; Xie et al., 2019; Liu et al., 2021; Li et al., 2024; Liu and Liu, 2018). However, such approaches primarily reveal “what” happened, often struggling to disentangle the causal “how” from concurrent processes. (2) Satellite Remote Sensing and Geospatial Analysis: The advent of freely available, high-temporal-resolution satellite imagery (e.g., Landsat, Sentinel) has revolutionized the mapping of planform changes at delta and estuary scales. Techniques like the Modified Normalized Difference Water Index (MNDWI) (Jeerapong et al., 2023; Sufyan et al., 2025) and machine learning classifiers enable semi-automated extraction of channel networks and quantification of erosion/deposition patterns over large areas and long time series (Fisher et al., 2016; Isikdogan et al., 2017; Hossain et al., 2024; Lee et al., 2025; Brasington et al., 2000). Remote sensing excels at documenting the spatial extent and timing of events but provides limited insight into the subaqueous processes and hydrodynamic details that drive them. (3) Numerical Process-Based Modeling: Physics-based morphodynamic models (e.g., Delft3D, Telemac) simulate the interaction between flow, sediment transport, and bed evolution. They are powerful tools for testing hypotheses, exploring scenarios, and integrating complex boundary conditions like tides and waves (Van et al., 2008; Li et al., 2004; Cox et al., 2022; Moodie et al., 2019). Their predictive fidelity, however, hinges on the accuracy of sediment transport and bank erosion modules, which often require calibration and may not capture all nonlinear feedbacks, especially for rare, extreme events like avulsions. (4) Reduced-Complexity and Theoretical Models: Complementing detailed numerical models, theoretical frameworks and reduced-complexity models focus on essential dynamics to derive stability criteria and scaling laws for channel patterns. Concepts like dimensionless stream power and entropy theory have been used to explain and predict transitions between meandering, braided, and straight channels (Eaton et al., 2010; Paola et al., 2009). These approaches provide profound conceptual insights but require empirical validation of their underlying assumptions in natural settings. (5) Physical Scale Experiments: Laboratory experiments recreate morphodynamic processes in a compressed timeframe and controlled environment, allowing for the isolation of key variables (e.g., discharge, sediment feed rate) and direct observation of the complete causal chain from forcing to response. They have been pivotal in studying delta growth (Bai et al., 2018; Ganti et al., 2019), bifurcation mechanics (Edmonds and Slingerland, 2010; Yu et al., 2020), avulsion triggers (Hoyal and Sheets, 2009), and the effects of vegetation (Song et al., 2023). The primary challenge lies in appropriate scaling to ensure dynamical similarity between model and prototype.

While significant progress has been made, a salient gap persists between the correlative understanding derived from field/remote sensing studies and the causal, process-level understanding needed for robust prediction. Specifically for weakly-tidal estuaries, there is a lack of systematic experimental studies that investigate how sustained, contrasting water-sediment regimes (encompassing both feed and cessation phases) govern the evolutionary trajectory of channels with different initial planforms (e.g., meandering vs. trumpet-shaped). Previous experiments often focus on a single initial condition or a specific outcome. This gap limits our ability to mechanistically interpret field observations and predict system response to altered hydrological regimes.

To address this gap, the present study was designed with the following objectives: (1) To conduct physical experiments simulating the evolution of meandering and trumpet-shaped estuarine channels under a matrix of controlled water and sediment supply conditions; (2) To identify the thresholds in hydrodynamic and sedimentary forcing that trigger key transitions in channel morphology, such as significant widening, mid-channel bar development, and avulsion initiation; (3) To synthesize the experimental findings into a refined, process-informed framework for discriminating channel patterns, and to validate this framework using recent hydrological and morphological data from the lower Yellow River. By bridging detailed process experimentation with field validation, this work aims to advance a more mechanistic and predictive understanding of estuarine channel evolution.

2 Experimental content, setup, and methods 2.1 Experimental content

This study conducts an in-depth investigation of their evolution processes through physical model experiments (Jha et al., 2025; Hu et al., 2025). The experiment focused on observing the dynamic changes in water flow pathways and riverbed elevation to reveal topodynamic response characteristics and the coupling relationship between water-sediment transport and riverbed deformation. The design follows the principles of dynamic similarity common in exploratory morphodynamic modeling. We prioritized Froude number similarity (F _r) for flow and matched sediment mobility (via the dimensionless shear stress, τ *) to ensure the correct scaling of key processes like bedload transport and bank erosion, a well-established approach for investigating channel pattern dynamics (Peakall et al., 1996; Kleinhans et al., 2015). Referring to the typical channel morphology of the Yellow River estuary (Figure 1), three representative channel model types were set up in the experiment: a leftward meandering channel (Figure 1a), a rightward meandering channel (Figure 1b), and a trumpet-shaped estuarine channel (Figure 1c), providing an experimental basis for studying the morphological evolution patterns of estuarine channels.

FIGURE 1

Estuarine morphology of the Yellow River tail channel in different years. (a) 1995; (b) 2002; (c) 2021. In recent years, while channel branching occurred at the Yellow River estuary, the estuarine width has increased, showing a distinct “trumpet” shape, as seen in the northern branch of the estuary in (c).

Three satellite images of a coastal region labeled as (a), (b), and (c). Image (a) shows a mix of blue and turquoise waters with visible land patterns. Image (b) is mostly monochrome, highlighting land and water contrast. Image (c) displays varied colors with distinct land and water features, showing sediment flow into the sea. Coordinates are marked for reference.

This paper treats channel branching as an observation subject rather than a primary modeling focus, emphasizing the exploration of the general impact patterns of water-sediment conditions on channel evolution. The research aims to reveal the common characteristics of channel evolution under different water-sediment conditions, without being constrained by specific scale simulations. It should be noted that the morphology of the Yellow River tail channel serves only as a reference case in this study and is not the direct object of physical simulation. The core of the research lies in investigating the universal patterns of channel morphological changes under the influence of water-sediment conditions.

This study employs physical model experiments to investigate two aspects: ① the patterns and conditions of channel evolution under the influence of water-sediment conditions; ② the validation of the experimental results from the first part. For the first part, three physical channel models with different initial conditions were constructed. The experiments were conducted continuously until the migration range of the model channels approached the sidewalls of the experimental flume. For the second part, three comparative scenarios were designed to validate the influence of different water-sediment conditions (such as flow discharge, sediment transport, and boundary constraints) on channel evolution, ensuring the reliability and universality of the experimental results.

2.2 Experimental setup

Based on the channel morphological characteristics shown in Figure 1, the estuarine morphology is classified into trumpet-shaped and meandering types. The meandering type is further subdivided into left-deflecting and right-deflecting meandering based on planar morphological features. Due to experimental constraints, this study primarily simulates a micro-tidal estuary environment dominated by fluvial processes (terrestrial water-sediment conditions). A fixed water level boundary condition was employed to represent the influence of marine boundaries. This simplified representation of a constant base level is a standard and effective means to isolate fluvial processes in estuarine physical models, allowing clear attribution of morphological change to water-sediment inputs (Edmonds and Slingerland, 2010; Van Dijk et al., 2012).

The physical model experiments were conducted in a small-scale circulating flume system, which is a common apparatus for investigating fluvial morphodynamics (Peakall et al., 1996; Ganti et al., 2019). The main parameters of the experimental flume system are: length 3.6 m, width 1.7 m, and height 0.2 m. In designing the model, we prioritized Froude number similarity for the flow and maintained geometric similarity in the key dimensions of the initial channel, a standard approach for achieving dynamic similarity in fluvial process studies (Yalin, 1971; Kleinhans et al., 2015). The test area consists of three parts: a river channel section, an estuary section, and a shallow water area. The shallow water area was designed to simulate the influence of lake/marine dynamic conditions on estuarine hydrodynamic processes (the experimental setup is detailed in Figure 2). A flow controller was used to precisely regulate the inflow conditions, and a self-developed sediment feeding device was employed to control sediment concentration. The working principle of this sediment feeding device is: ① The sediment outlet uses a threaded cap structure where sediment discharge is controlled by adjusting caps with different aperture (Figure 2a) sizes; ② The device is equipped with a vibrator at the bottom that ensures uniform Figure 2c and continuous sediment output through mechanical oscillation. During the experiments, an image acquisition system mounted above the flume continuously recorded the evolution process of channel topography and flow field characteristics.

FIGURE 2

Schematic diagram of the experimental setup. (a) Actual photograph of the experimental setup; (b) Top view; (c) Side view. In (a) is the water pump, which draws water from the sediment sink to the water supply tank; (b) is the water supply tank, which delivers water to the inlet forebay through the inlet pipe; (c) is the inlet pipe, with a flow controller q connected in the middle; d is the inlet forebay; e is the flow stabilizer, used to stabilize the incoming flow; f is the sediment feeder; g is the funnel-shaped sediment outlet; h is the 0.5 m long fixed channel; i is the baffle, preventing channel evolution from affecting the inlet morphology; j is the channel; k is the riverbank; l is the outlet; m is the sediment sink; n is the shallow water area; o1 and o2 are cameras; p is the vibrator. The direction from the outlet to the inlet is defined as Y, the direction perpendicular to Y is X, and O is the origin of the Y and X directions. The Y-direction is divided into 36 units, each unit being 10 cm; the X-direction is divided into 17 units, each unit being 10 cm. Y1 to Y16 is the shallow water area, Y16 to Y19 is the estuary area, Y19 to Y31 is the experimental channel area, and Y31 to Y36 is the fixed channel area.

Panel (a) shows a physical model of a meandering river constructed in sand. Panel (b) is a top-view schematic of the experimental setup, indicating dimensions and positions of various components. Panel (c) provides a side-view diagram of the same setup, detailing equipment placements like cameras and flow paths.

The experiments were conducted in a recirculating. The tilting flume system is located at the Tianjin University. The flume is constructed of tempered glass crucibles and a stainless steel base. Test equipment and detailed operating methods are described below.

2.2.1 Flow control system

Water Pump: A centrifugal pump (max discharge 2.0 L/s) circulated water from a 500 L sump tank.

Flow Meter & Controller: An electromagnetic flowmeter (range: 0.05–2.0 L/s, accuracy: ±0.5% of reading) was installed in the inlet pipe. The flow rate was regulated by a combination of a manual ball valve and a frequency converter controlling the pump motor speed, achieving a stable discharge control within ±2% of the target value.

2.2.2 Sediment feeding system

Feeder Design: A custom-built, constant-head sediment feeder was employed (schematic in Figure 2). It consisted of a conical hopper (top diameter: 30 cm, bottom outlet diameter: 10 cm, height: 25 cm) made of PVC.

Flow Regulation: The outlet was fitted with interchangeable, precision-machined brass screw caps with central circular apertures of diameter (d) = 0.50 cm, 0.80 cm, and 1.00 cm (±0.02 mm).

Vibration Mechanism: An electromagnetic vibrator attached to the hopper frame operated at 60 Hz to prevent particle arching and ensure a steady, pulsation-free sediment discharge.

Calibration Procedure: Prior to experiments, each aperture cap was calibrated. The feeder was filled with the test sediment, activated, and the discharged sediment collected over a precisely measured time interval (t = 300 s). This was repeated four times per aperture. The sediment discharge rate (Q _s, g/s) was calculated as the average mass discharged per second.

2.2.3 Tailwater control

A manually adjustable, sharp-crested weir at the flume outlet maintained a constant water surface elevation in the “shallow water area” (representing the base level), set at 4.0 cm above the initial bed level at the estuary boundary.

2.2.4 Measurement instruments

Topography: Bed elevations were measured using a laser displacement sensor, spot diameter: 50 µm, range: 60 ± 15 mm, stated accuracy: ±0.1% of full scale) mounted on a motorized two-axis (X-Y) traverse system (positioning accuracy: ±0.1 mm).

Flow Visualization: For qualitative flow field observation, near-neutral buoyancy polyethylene tracer particles (mean diameter: 100–200 µm) were illuminated by a 1W 532 nm green laser sheet and recorded with a high-speed camera.

Overhead Imaging: A digital single-lens reflex camera mounted 2.5 m above the flume center captured time-lapse photos of the planform evolution at 5-min intervals.

2.3 Experimental methods

The protocol was rigorously standardized to ensure reproducibility and data quality.

2.3.1 Bed sediment preparation and laying

Non-uniform natural sand with a median grain size (d ₅₀) of 0.35 mm and a specific gravity of 2,650 kg/m³ was used (gradation curve shown in Figure 3). To establish initial conditions, bed sediment was laid with varying thicknesses according to different functional zones: Shallow water area (Y1-Y16): 1 cm; Estuary transition area (Y16-Y19): 4 cm; Main channel area (Y19-Y31): 7.5 cm. A spirit level was used to ensure the flatness of the initial bed surface.

FIGURE 3

Particle size distribution curve of the sand.

Logarithmic plot of sediment particle size distribution with measurements. The x-axis represents particle size in millimeters, ranging from 0.01 to 10. The y-axis represents the percentage proportion greater than a certain particle size, ranging from 0 to 100 percent. The red curve shows data points decreasing from high proportions at smaller sizes to lower at larger sizes.

2.3.2 Moisture content control and seepage pretreatment

To minimize seepage effects along the flume sidewalls, a preliminary saturation test was conducted. The initial channel morphology was sculpted, and the flume was slowly filled with water to the design level. After sealing the outlet and allowing the sediment to saturate for 24 h, samples were taken to determine the saturated moisture content (18.11%). This value guided the wetting of sediment during the setup of all formal experimental runs to achieve consistent initial pore pressure conditions.

2.3.3 Experimental operation and control

A high-precision digital flow controller (accuracy ±2% of reading) regulated the inflow discharge (Q). A custom-built sediment feeder, employing a vibrator and interchangeable screw caps with apertures of 0.5, 0.8, and 1.0 cm, provided a continuous and uniform sediment supply (Q _s). The feeder was calibrated prior to experiments; the sediment discharge rates for the three apertures were 7 × 10⁻⁴, 9 × 10⁻³, and 1.15 × 10⁻² g cm^-3, respectively (mean of four repeated measurements per aperture).

2.3.4 Data acquisition

Planform Evolution: A digital camera mounted overhead captured time-lapse images of the entire flume at 5-min intervals.

Flow Field: Fluorescent tracer particles were periodically released, and their movement was recorded using a high-speed camera (200 fps) to infer near-bed flow vectors.

Topography: The experiment was paused at predetermined intervals. Bed elevation was measured using a laser rangefinder (accuracy 0.1 mm) over a grid with a spacing of 0.5–1 cm, covering the entire active area.

2.3.5 Termination condition

Each experimental run continued until the lateral migration amplitude of the thalweg approached the physical constraint of the flume sidewall (≤5 cm from the wall), ensuring the observation of the full evolutionary sequence under the given boundary conditions.

2.4 Data processing and analysis

Digital Elevation Model (DEM) Generation: Raw XYZ point clouds from each laser scan were interpolated into a raster DEM with a 0.5 cm resolution using natural neighbor interpolation in MATLAB R2023a (function scatteredInterpolant). Missing data points (e.g., due to water reflection) were filled using a 3 × 3 pixel moving average filter.

Change Detection: DEMs of Difference (DoD) were calculated by subtracting a later DEM from an earlier one. A probabilistic thresholding approach was employed to distinguish real change from noise.

Statistical Analysis: All correlations and SVM analyses (Section 4.2.2) were performed in MATLAB R2022a.

3 River channel evolution analysis 3.1 Analysis content

This study conducted experimental simulations of right-bending meandering rivers, left-bending meandering rivers, and trumpet-shaped rivers. Based on the planar morphological characteristics of these three river types, three experimental models were established: S-shaped, reverse S-shaped, and trumpet-shaped rivers. The S-shaped model corresponds to the right-bending meandering river morphology, while the reverse S-shaped model corresponds to the left-bending meandering river morphology. The experiment used non-uniform natural sand with a median particle size d₅₀ of 0.35 mm and a specific gravity of 2,650 kg/m³. The particle size distribution is shown in Figure 3. The sediment added in this study was sourced from the natural sand used in the experiment, with a particle size of less than 0.2 mm (Xu et al., 2021; Song et al., 2023).

To minimize the impact of seepage effects on the experiment, the moisture content of the sand used was determined to be 18.11% through preliminary tests. The configured river morphology and its geometric dimensions are shown in Figure 4, with units in centimeters.

FIGURE 4

Schematic diagram of the experimental river types. (a) Reverse S-shaped channel; (b) Trumpet-shaped channel. The S-shaped channel is symmetrical to the reverse S-shaped channel.

Diagram with two views labeled (a) and (b). Both show a rectangular enclosure measuring 360 cm in length and 170 cm in height. In (a), there's a 10 cm inlet on the left and internal partitions creating a curved path with specified distances. In (b), only a straight path with tapered section leading to an outlet on the right is shown. Both indicate X and Y coordinate axes, and distances between points are labeled.

Based on the river types, three experimental conditions were set up. The initial average channel depth for all conditions was 3.5 cm, and other parameters are shown in Table 1 (where B is the initial average channel width, J is the slope, Q is the inflow discharge, Q _s is the sediment concentration, and T is the duration of water and sediment supply).

TABLE 1

Test conditions and key test parameters.

Condition	Morphology	B/cm	Q/cm³·s^-1	Q _s/g·cm^-3	t/min
1	S-shaped	15	50(0∼90 min),100(90∼180 min)	9×10^-3(0∼30,90∼120 min)	180
2	Reverse S-shaped	15	50	9×10^-3(0∼30,270∼290 min)	310
3	Trumpet-shaped	40	100	7×10^-4(0∼60 min)1.15×10^-2(180∼240 min)	360

The experimental factors include inflow discharge, sediment concentration, channel morphology, and test duration. The channel has a rectangular cross-section, with a sand layer thickness of 7.5 cm laid on the riverbed and 1.0 cm in the shallow water area. The estuary area has a slope ratio of 1:4 and a length of 30 cm.

In Table 1, B represents width, Q represents flow rate, Q _s represents sediment concentration, t represents time, and the gradient, J, is 1%. Based on the requirements of the experimental analysis, the model river channel was systematically divided (Figures 3–5). Among them, Working Condition 1 and Working Condition 2 adopted an eight-segment division method: inlet segment → upstream segment → first bend segment → midstream segment → second bend segment → downstream segment → estuary segment → shallow water area; Working Condition 3 adopted a six-segment division method: inlet segment → upstream segment → midstream segment → downstream segment → estuary segment → shallow water area. It should be specifically noted that the “estuary segment” in the experiment specifically refers to the straight river-type area at the end of the model channel (approximately 15 cm long). Its definition differs from the concept of a natural estuary in geography and is only a transitional zone for simulating river-sea interaction.

FIGURE 5

Schematic diagram of channel segmentation under different working conditions. (a) Channel division for Working Conditions 1 and 2; (b) Channel division for Working Condition 3.

Two grayscale images labeled (a) and (b) show aerial views of a river with segmented sections. Image (a) depicts the river from shallow water to upstream, illustrating bends and estuaries. Image (b) focuses on shallower water areas and downstream sections. Both images are annotated with markers such as Y16 to Y30, indicating different river zones like estuary, downstream, and upstream.

3.2 Planform evolution

The planform evolution of the river channel is manifested in changes in planform morphology, sediment deposition patterns, and flow direction. The experiment used rangefinders and tracer particles to measure elevation data and determine flow directions, thereby analyzing the evolution of the river’s planform morphology and flow pathways. Based on changes in the river’s planform morphology and flow pathways, the river evolution process can be divided into three stages.

3.2.1 Stable planform morphology stage

The initial stage of river evolution exhibited distinct spatial differentiation characteristics (Figure 6), primarily manifested as a dynamic pattern of “erosion downstream and deposition upstream.” During this stage, planform morphological evolution dominated the channel adjustment process, while the influence of hydrodynamic and sediment forces was relatively weak. Specific manifestations included.

Significant headward erosion occurred in the downstream segment, with eroded material transported downstream along the longitudinal slope, forming localized depositional bodies (Figure 6).

The upstream segment received sediment supply, leading to bed deposition, but the deposition thickness remained less than the channel depth, and no significant bank transformation process was triggered (Figure 6).

FIGURE 6

Channel planform morphology under topographic influence. (a) t=10 min, planform morphology of the estuary under Working Condition 1; (b) t=10 min, planform morphology of the channel under Working Condition 1.

Panel (a) shows sediment deposition with a red arrow indicating the flow direction. Panel (b) illustrates retrogressive erosion and siltation, labeled respectively, with arrows pointing to their areas.

During this stage, the sediment transport and riverbed adjustment maintained a dynamic equilibrium, resulting in a relatively stable planform morphology. It is noteworthy that the mainstream maintained a straight and uninterrupted flow characteristic during this stage, indicating that the control of planform morphology was stronger than the influence of hydrodynamic and sediment forces.

3.2.2 Stage of slight changes in channel planform morphology

With the continuous development of erosion processes, the overall channel morphology remained relatively stable, but the estuary and upstream areas exhibited significant local adjustment characteristics (Figure 7a). The evolution patterns under different working conditions showed notable differences.

Working Condition 1: Dominated by leftward widening of the estuary area (Figure 7b), with its evolution direction significantly influenced by the morphology of the second bend;

Working Condition 2: Mainly characterized by rightward widening of the upstream segment, accompanied by rightward expansion of the estuary area (Figure 7b), with the overall evolution similarly controlled by the morphology of the second bend;

Working Condition 3: A flow-aligned curved belt formed in the estuary segment (Figure 7c), where although local bending features appeared, the overall outline remained consistent with the initial pattern.

FIGURE 7

Channel planform morphology influenced by river bends. (a) t=20 min, planform morphology under Working Condition 1; (b) t=20 min, planform morphology under Working Condition 2; (c) t=20 min, planform morphology under Working Condition 3.

Three labeled images depicting flow paths and erosion:(a) Shows a river channel with a black flow path arrow and areas labeled "Bank and retrogressive erosion" and "Siltation".(b) Displays a similar channel with "Flow path" and areas labeled "Retrogressive erosion" and "Siltation".(c) Highlights "Retrogressive erosion," "Higher terrain," and "Siltation" with indicated directions of flow path.

However, the research results indicate that, regardless of the working conditions, during the slight change stage, the channel evolution process remained strongly constrained by the original morphology. The adjustment characteristics of each river type maintained a high degree of correlation with their initial forms. This finding highlights the important role of morphological memory effects in the channel evolution process. This concept of “morphological inheritance” or “path dependence” is a recognized phenomenon in fluvial geomorphology, where antecedent conditions significantly influence subsequent adjustment trajectories (Brierley and Fryirs, 2005; Phillips, 2006).

3.2.3 Stage of significant changes in channel planform morphology

Driven by the coupling of water and sediment, the channel exhibited multi-scale dynamic response characteristics:

In terms of cross-sectional morphology, the U- to V-shaped transition upstream of the estuary (Figure 8a) led to a positive feedback loop of flow section contraction → increased flow velocity → intensified erosion.

Spatial differentiation of erosion manifested as dominant lateral erosion and widening in the upstream, vertical erosion causing downcutting in the midstream, and intensified composite erosion in the downstream (Figures 8b,c).

In terms of planform morphology, significant widening occurred in the upstream/estuary areas while the midstream remained stable. The estuary area experienced flow path differentiation due to the combined action of deposition and erosion (Figure 8d), and the rightward deviation of the dynamic axis in the downstream triggered systematic rightward expansion (Figure 8e).

In Figure 8a, Y30, Y20, and Y17 represent the selected cross-section locations in the upstream segment, downstream segment, and estuary segment of the channel, respectively. In Figure 8d, C1 denotes the earliest deposited body in the estuary, C2 the earlier deposited body, and C3 the newest deposited body.

FIGURE 8

Channel planform changes during the strong transformation stage. (a) Cross-section of Working Condition 1; (b) t=30 min, channel morphology of Working Condition 1; (c) t=30 min and t=310 min, Working Condition 2; (d) Estuary swinging and branching; (e) Flow paths under different working conditions; (f) Channel widening phenomena.

Composite image consisting of six parts. (a) Graph plotting riverbed elevation over time at different coordinates. (b) Overhead images of river sections showing flow paths and widened sections marked at Y30, Y20, and Y17. (c) River flow paths from experiments RUN 1, 2, and 3 with arrows indicating direction. (d) Image showing the branching of river flow paths and swing, with sections labeled C1, C2, and C3. (e) River morphology changes over time at 180, 310, and 360 minutes. (f) Close-up of a river section with marked flow directions.

Experimental observations indicate that, in addition to the shaping effect of static deposited sediment on channel morphology (Figure 8f), the dynamic sediment transport process also significantly influences channel evolution. Specifically, moving sediment continuously accumulates and elevates the riverbed during transport, causing the flow dynamic axis to shift. This shift subsequently intensifies erosion on both banks, ultimately leading to significant alterations in the channel’s planform morphology.

3.3 Cross-sectional analysis

This study analyzes changes in the average riverbed elevation, elevations of both banks, and cross-sectional elevations across different time periods to reveal the patterns of riverbed evolution under varying flow and sediment conditions.

The average riverbed elevations under different working conditions are shown in Figure 9.

FIGURE 9

Changes in average riverbed elevation at different time periods under different working conditions. (a) Working Condition 1; (b) Working Condition 2; (c) Working Condition 3.

Three graphs labeled (a), (b), and (c) show elevation changes over time. Each graph includes a legend for time intervals, with different symbols for the initial elevation and measurements at specified minutes. Elevations are plotted against a Y-axis, ranging from twelve to thirty-five, with elevation in meters on the X-axis. The data show various increases in elevation over time across all graphs.

Figure 9 reveals the spatiotemporal evolution characteristics of riverbed elevation:

Temporal dynamics: The riverbed exhibited continuous depositional uplift overall, with longitudinal elevation difference fluctuations following a “large-small-large-small” damped oscillation pattern (inlet > upstream > midstream > estuary), where the inlet-upstream segment showed the most significant elevation variation.

Spatial differentiation: Deposition intensity displayed a spatial gradient of inlet segment > upstream segment > midstream segment > estuary segment, reflecting the gradual attenuation of sediment transport along the channel. Erosion-active areas were concentrated in the downstream-estuary segment, spatially coupled with zones of dramatic planform changes.

Estuarine deposition characteristics: While the longitudinal extension lengths of depositional bodies showed minor differences across working conditions, deposition intensity varied significantly, with Working Condition 3 (maximum) > Working Condition 1 > Working Condition 2 (minimum). The spatial expansion of depositional bodies was controlled by estuarine dynamic barrier effects, with their scale positively correlated with upstream sediment concentration.

Experimental observations revealed significant differences in bed elevation between the left and right banks (Figure 10), primarily manifested as lateral erosion-deposition asymmetry characteristics. Such asymmetrical adjustments are typical in curved channels due to the development of helical flow and associated point bar growth and outer bank erosion, a fundamental process in meandering river dynamics (Dietrich and Smith, 1983; Blanckaert, 2010).

FIGURE 10

Longitudinal variation of elevation along both banks of the river channel. (a) Left bank of Working Condition 1; (b) Right bank of Working Condition 1; (c) Left bank of Working Condition 2; (d) Right bank of Working Condition 2; (e) Left bank of Working Condition 3; (f) Right bank of Working Condition 3.

Six graphs labeled (a) to (f) show the relationship between elevation in meters and variable Y over time intervals. Each graph presents data with different colored markers representing time from 20 minutes to 360 minutes, indicating changes in elevation.

From Figure 10, the lateral evolution characteristics of the channel and key cross-sectional responses can be derived.

3.3.1 Lateral differentiation patterns of riverbed elevation

The bend segments (Working Conditions 1 and 2), influenced by enhanced bend circulation, exhibited intense evolution due to the coupling of vertical erosion and lateral migration. Y28 (right bank) and Y25 (left bank) (Working Condition 3), located in the transition zone between upstream and midstream, experienced localized abrupt erosion-deposition changes triggered by shifts in the flow dynamic axis. Y17 (estuary segment), affected by the backing-up effect of elevated water levels in shallow areas, became a sensitive zone for morphological adjustments.

Although hydrodynamic conditions and evolution characteristics differed across channel segments (bend segments, transition zones, estuary segments), their riverbed evolution patterns consistently manifested as coupling or abrupt change mechanisms dominated by specific hydrodynamic forces: bend segments, under the influence of enhanced bend circulation, coupled vertical erosion and lateral migration, leading to intense riverbed adjustments; transition zones experienced abrupt erosion-deposition responses due to shifts in the flow dynamic axis; estuary segments exhibited sensitive morphological adjustments under the backing-up effect of shallow waters. This pattern indicates that the core mechanism of riverbed evolution lies in the interaction between external hydrodynamic conditions and local riverbed morphology, ultimately driving dynamic adjustments through coupled erosion or abrupt erosion-deposition changes.

3.3.2 Evolution patterns of typical cross-sectional elevations

Y28 (Working Condition 3): The right bank midstream segment, influenced by downstream bend effects, showed unilateral riverbed uplift while the left bank remained relatively stable, forming a lateral elevation gradient.

Y25 (Working Condition 3): The left bank upstream segment experienced localized scouring triggered by leftward shifts in the flow dynamic axis.

Y17 (Estuary): All working conditions exhibited bilateral erosional retreat, forming a spatial response chain with the rightward deviation of downstream flow.

These phenomena collectively reveal the spatial connectivity of riverbed evolution-whether through gradient development, localized abrupt changes, or linked responses-essentially representing spatial feedback results of interactions between hydrodynamic fields and riverbed boundaries. The intensity and direction of adjustments depend on the transmission effects of local hydrodynamic conditions within the spatial sequence of river segments. Further analysis of cross-sectional elevation changes in the bend segments (Y28 and Y25 under Working Condition 3) and estuary segment (Y17) was conducted to illustrate river cross-sectional evolution patterns. The cross-sectional elevation conditions are shown in Figure 11.

FIGURE 11

Cross-sectional elevations at representative locations. (a) First bend (Working Condition 1); (b) Second bend (Working Condition 1); (c) Estuary (Working Condition 1); (d) First bend (Working Condition 2); (e) Second bend (Working Condition 2); (f) Estuary (Working Condition 2); (g) Section Y28 (Working Condition 3); (h) Section Y25 (Working Condition 3); (i) Estuary (Working Condition 3).

Nine line graphs, labeled (a) to (i), display elevation in meters against variable Y over time intervals. Each graph features multiple colored lines representing different time periods, ranging from 20 to 360 minutes. Elevation trends vary across graphs, with distinct peaks and troughs, illustrating elevation changes over time. Legends in each graph specify the color code for time intervals, aiding comparison of data trends and variations.

The coupled response of riverbed elevation to sediment feeding and patterns of morphological evolution can be derived from Figure 11.

3.3.3 Dynamic response of riverbed elevation

Upstream segment: During sediment-feeding phases, sediment volume/duration showed a positive correlation with riverbed elevation, with significant cross-sectional widening dominated by deposition; during sediment-starved phases, flow regained scouring capacity, causing reverse reduction of riverbed elevation, reflecting the dynamic equilibrium mechanism of “sediment supply-transport”.

3.3.4 Evolutionary pathways of cross-sectional morphology

Upstream segment: Sediment feeding induced lateral expansion with continuously increasing width-depth ratio; Midstream segment: Enhanced vertical scouring transformed cross-sections from V-shaped to W-shaped, reflecting flow bifurcation characteristics; Estuary segment: Depositional bodies extended continuously rightward with weak left-bank expansion, forming an asymmetric delta front.

3.3.5 Differential patterns across working conditions

Channel widening under the three working conditions exhibited significant spatial differentiation:

Working Condition 1 showed asymmetric strong right-bank/weak left-bank expansion, primarily driven by strong bend circulation dynamics; Working Condition 2 formed a unified rightward expansion pattern, creating a dynamic-morphological response chain with the persistent rightward deviation of the downstream dynamic axis; Working Condition 3 displayed a stochastically composite left-expansion-dominated pattern, reflecting spatial heterogeneity in boundary erosion resistance under low sediment concentration conditions.

These differences essentially originate from distinct riverbed morphologies under varying flow-sediment conditions, leading to differential bend circulation and dynamic axis behaviors that exhibit clear direction-selective expansion characteristics.

3.4 Synthesis of underlying physical mechanisms

Our experimental observations allow us to distill the core physical mechanisms driving the observed evolution, linking them to established geomorphic concepts:

The Primacy of Sediment Transport Regime: The experiment revealed that active bedload transport, irrespective of net aggradation or degradation, is a primary agent of planform change (Figure 8f). Moving bedload particles increase effective bed roughness and laterally diffuse momentum, enhancing bank erosion rates-a process theoretically emphasized by Parker (1978) and observed in field studies of braiding rivers. This underscores that analyses focusing solely on net volumetric change may overlook this key dynamic driver.

Morphological Inheritance and Threshold-Controlled Change: The “Slight Changes” stage (Section 3.2.2) demonstrated strong control by the initial bend geometry, a manifestation of morphological inheritance (Brierley and Fryirs, 2005). Significant change occurred only when hydrodynamic forcing exceeded a morphodynamic threshold, allowing the channel to break free from this inheritance. This aligns with the threshold theory of channel pattern transition proposed by and later supported by experimental work (Kleinhans, 2010).

Estuarine Backwater Effect as a Depositional Engine: The distinct behavior of the estuary segment, especially the formation of lambda-shaped and fan-shaped deposits under low flows, is attributed to the backwater effect. The fixed water level in the receiving basin reduces flow velocity and competence upstream, promoting deposition. This mechanism is a classic control on avulsion location in deltas, where deposition and channel aggradation are focused in the backwater zone (Chadwick et al., 2019; Ganti et al., 2019). Our experiments provide a vivid, small-scale analog of this large-scale process.

Feedback Between Cross-Sectional Form and Planform: The transition from U-shaped to V-shaped or W-shaped cross-sections (Figures 8, 11) is not merely a result but also a cause of further evolution. A narrowing, deepening section concentrates flow, increasing shear stress and enabling further incision-a positive feedback similar to that governing knickpoint migration and channel incision. Conversely, widening shallows the flow, promoting deposition and further widening.

4 Results and discussion 4.1 Results

The channel evolution under varying flow-sediment conditions can be explained from both non-estuary and estuary segments as follows.

4.1.1 Non-estuary segment

During the initial experimental stage, when Q was large, the flow scoured the banks and riverbed, but the planimetric width of the flow did not increase. Instead, as the flow eroded the riverbed, the channel became narrower and deeper.

During the sediment feeding phase, sediment could not be transported away quickly by the flow and accumulated in the channel. The deposited sediment raised the riverbed, causing flow to divert around both sides of the deposit toward the outlet. This process eroded the banks, leading to an increase in the planimetric width of the channel. This phenomenon was more pronounced when Q was relatively small.

As the planimetric width continued to increase, mid-channel bar-like structures emerged, and the sinuous channel transformed into a braided pattern (Figure 12a).

FIGURE 12

Local morphology of the channel.

Two aerial images show a river's flow patterns. Image (a) highlights a central bar using a dashed outline. Image (b) illustrates anabranching with purple arrows indicating divergent water flow paths. Both images depict sandy terrain around the river.

4.1.2 Estuary segment

Condition 1: During the sediment feeding phase with relatively small Q, deposition occurred in the non-estuary segment. The continuous changes in the size of the deposited body influenced the downstream flow path, causing the estuary flow path to oscillate within a limited range.

Condition 2: During the sediment cessation phase with relatively small Q, sediment deposited upstream was transported to the estuary, resulting in a flattened riverbed in the estuary segment. At this stage, the estuary elevation increased due to deposition, and the flow bypassed the deposited body, forming bifurcations toward the outlet (Figure 12c).

Condition 3: During the sediment cessation phase with relatively large Q, the flow intensely scoured the banks and riverbed, causing large-scale oscillations and channel realignment in the estuary segment. After realignment, the riverbed of the new flow path was progressively elevated, exceeding that of the old flow path. Consequently, a portion of the flow diverted back from the new path to the old path, creating a bifurcation phenomenon (Figure 12b).

These experimental findings align with field-observed patterns in the lower Yellow River. For instance, the deposition-dominated widening under low-flow, high-sediment conditions mirrors the post-flood channel adjustments documented by Gao et al. (2024). Conversely, the narrow-deep cross-sections formed under high-flow conditions are consistent with the scour patterns reported during sustained high-discharge periods (Li et al., 2024). However, our experiments further highlight that bedload transport dynamics - not merely net deposition or erosion - are a primary driver of planform change. This nuance is less apparent in remote-sensing-based analyses (Liu et al., 2021), which typically capture time-integrated morphological states rather than transient transport processes.

4.2 Discussion 4.2.1 Results application

Figure 13 shows the swing area and water and sediment conditions of the four reaches in the non-estuary part, in order to verify the test results. The distances of the four reaches are located at 32–43 km, 55–66 km, 83–94 km and 110–121 km downstream of Lijin, respectively.

FIGURE 13

Relationship between quicksand conditions and channel shift areas. (a–c) are Q, Q _s and d ₅₀, respectively. (d) is the channel shift areas.

Four-panel graph illustrating hydrological data from 2002 to 2024 with vertical red and blue stripes indicating specific periods. Panel (a) shows discharge data in cubic meters per second, (b) suspended sediment concentration in kilograms per cubic meter, (c) median particle diameter in millimeters, and (d) sediment transport rate in square meters, divided into four segments. Each panel uses different markers and a consistent time axis, with variations in data patterns and values across the years.

Due to significant changes in channel morphological parameters between different years, such as curvature radius, gradient, and cross-sectional morphology, these variations alter the flow structure, resulting in different degrees of lateral shift distances under identical flow-sediment conditions in the same channel (Gu et al., 2025; Yao et al., 2025; Geng et al., 2025). Although the morphological parameters of the four selected river segments changed from 2003 to 2022, the overall changes were relatively small. The years with significant channel shifts (hereinafter denoted as S_max) were determined based on the variations in S from 2003 to 2022 for Segment 1, Segment 2, and Segment 3. Since Segment 4 underwent artificial cutoffs in 2011 (Kong et al., 2023), only data from 2003 to 2010 were used for S in this segment. To ensure more reasonable analysis results, years in which at least two segments showed increased S were selected as S_max.

In Figure 13, the red and blue areas represent S corresponding to larger d ₅₀ and larger Q, respectively. As shown in Figure 13, the years identified as S_max are 2004, 2006, 2009, 2011, 2013, 2016, 2018, and 2020. The following observations can be made:

In 2006, 2009, 2011, and 2016, d₅₀ was larger, and the corresponding S was also larger.

In 2013, 2018, and 2020, Q _s was larger, and the corresponding S was also larger.

In summary, with the exception of 2004, where no significant explanatory factors aligned with the large S observed (thus not conforming to the evolution conditions of the non-estuary segment), all other years were well explained. Therefore, high sediment load and large sediment grain size can induce changes in channel morphology and flow pathways in non-estuary segments. This validation confirms that high sediment loads promote channel instability and widening. This aligns with recent analyses of the lower Yellow River, which attribute increased channel migration and braiding intensity to periods of elevated sediment concentration (Gao et al., 2024; Li et al., 2024; Wheaton et al., 2010; Whipple and Tucker, 1999). Our experiments provide the process link: showing how this sediment is initially deposited, forces flow diversion, and leads to sustained bank erosion.

The successful mapping of Condition 3 (high flow, no sediment feed) to major avulsion years (e.g., 2012, 2020) is particularly significant. It supports the growing consensus from recent global delta studies that avulsions are often preceded not by peak sediment loads, but by high-energy, competence-rich flows that can incise new channels (Stouthamer et al., 2010). Our experiment captured the critical, incipient bifurcation stage (Figure 12b) that is rarely resolved in annual satellite imagery but is essential for early-warning indicators.

Figure 14 shows the gradient and shift area of the Yellow River tail estuary. Here, the estuary segment refers to the river section from approximately 123 km downstream of Lijin to the Bohai Bay, where natural bifurcation points and shift points exist. The estuary shift area is defined as the area enclosed by the channel centerlines of two consecutive years (as of December each year).

FIGURE 14

Gradient and shift area of the estuary segment. (a) Shows the gradient of the tail channel estuary from 2003 to 2017 (data from the National Earth System Science Data Center: https://www.geodata.cn/data/publisher.html) (b) shows the shift area of the estuary segment from 2002 to 2022.

Two line graphs show data trends from 2004 to 2016 and 2004 to 2024. Graph (a) displays values of J in per mille, fluctuating between 0.82 and 0.98. Graph (b) shows values of S in square meters times ten to the power of seven, spiking at 7 in 2008 and reaching lower levels in other years. Both graphs use square markers to indicate data points.

From Figure 14b, the following observations can be made:

The estuary evolution in 2006 and 2022 indicates that Condition 1 can trigger estuary evolution. However, in years under Condition 1 (2003, 2009, 2011, 2014, 2016), the estuary shift areas were relatively small, suggesting that estuary evolution does not necessarily occur under Condition 1;

The years 2004, 2007, 2008, and 2010 exhibited relatively large estuary shift areas, consistent with the morphological changes corresponding to Condition 2;

The years 2012, 2013, 2018, 2020, and 2021 were characterized by estuary bifurcation or significant shift areas, aligning with the morphological changes corresponding to Condition 3. Additionally, the years 2005, 2015, 2017, and 2019 showed relatively small estuary shift areas, consistent with the earlier analysis results.

In summary, the estuary shift areas under Condition 2 and Condition 3 were significantly larger. The estuary morphology corresponding to the years under Condition 2 and Condition 3 is shown in Figure 15. Remote sensing imagery was used to validate the conditions under which the aforementioned estuary morphological changes occurred.

FIGURE 15

(a–f) represent the bifurcation characteristics of the estuary morphology at different times. These times are May 2004, November 2007, December 2008, June 2010, December 2012, November 2013. (g) Shows the position of the middle line of the river in December 2017 (red) and December 2018 (blue). (h,i) Show the bifurcation characteristics of the estuary morphology in October 2020 and November 2021.

Nine satellite images labeled a to i display a coastal area with varying color schemes, each highlighting different geographical features like water, land, and river deltas. Circles in each image emphasize particular features. Image g is a simplistic map showing the coastlines with scale marks.

From Figure 15, the following observations can be made.

Under Condition 2, the estuary consistently exhibited some degree of bifurcation (Figures 15a–d). Except for 2007 (Figure 15b) which showed significant bifurcation, the other 3 years had relatively limited bifurcation extent (Figures 15a–d).

Under Condition 3, the estuary exhibited substantial shifting and bifurcation (Figures 15e–i). In 2012, the estuary showed relatively obvious bifurcation (Figure 15e); in 2013, significant bifurcation occurred (Figure 15f); compared to 2007, the estuary channel extended considerably in 2008 (Figure 15g); in 2020, new distributary channels formed in the estuary (Figure 15h); in 2021, all three distributary channels in the estuary underwent significant shifting, and changes were also observed in the bifurcation point of the northeastern distributary.

In summary, the analysis results of estuary morphology under Condition 2 and Condition 3 are consistent with actual observations, indicating that the morphological evolution of the Yellow River tail channel estuary segment occurs under these two conditions.

4.2.2 Morphological discrimination

The resistance law provides a fundamental link between flow dynamics and channel form. Recent advances in fluvial morphodynamics emphasize that channel patterns represent alternative stable states shaped by the interplay of stream power, sediment supply, and bank strength (Kleinhans, 2010). Therefore, a resistance formulation that incorporates key governing dimensionless numbers offers a physics-based pathway for pattern discrimination, moving beyond purely empirical classifications.

4.2.3 Basic principle

The law of river resistance is widely used in the analysis of river morphological evolution. This paper will analyze the changes of river morphological parameters under different water and sediment conditions based on the law of river resistance (based on Darcy-Weisbach formula) (Bai et al., 2024). The Darcy-Weisbach equation is derived by dimensional theory and has become an important tool for open channel flow calculation. As shown in Equation 1: h f = λ l 4 R v 2 2 g (1)

In this formula, h _f represents the head loss, l represents the river length, v represents the average flow velocity, g represents the gravitational acceleration, R represents the hydraulic radius, and λ represents the resistance coefficient. The use of flow resistance (λ) as a key variable linking hydraulic conditions to channel morphology has a long history in fluvial geomorphology. It integrates the effects of channel shape, bed roughness, and sediment transport, making it a potential indicator of channel pattern (Leopold et al., 1964; Ferguson, 2007). J = h f l = λ 1 4 R v 2 2 g = 1 8 λ F r 2 (2) 8 J F r 2 = λ (3)

It can be seen from Equation 3 that river resistance can be expressed as a combination of the slope, hydraulic radius, and flow velocity.

Natural river morphology can generally be categorized as meandering, branching, or wandering. The same river may undergo morphological changes under different flow and sediment conditions. Similarly, identical flow and sediment conditions can have varying impacts on the morphological changes of different rivers (Bai et al., 2024; Sun et al., 2024). Different river morphologies respond differently to the same flow and sediment conditions, leading to variations in energy consumption and resistance. Therefore, the river resistance coefficient can be expressed as a function of a river morphology parameter, as shown in Equation 4. λ = 8 J F r 2 , M ¯ (4)

In the experiment, it was found that the evolutionary degree varies across different parts of the river channel. Taking the reverse S-shaped river channel as an example (Figure 16a), the swing degree from the upstream to the estuary increased. This morphological change was related to sediment movement, which would lead to changes in sediment particle size distribution characteristics. The larger the sediment particle size, the more difficult it is to transport, and the more stable the river channel. The smaller the sediment particle size, the easier the river channel changes. To verify this hypothesis, sediment at different positions was extracted and sediment gradation was measured. The measurement results are shown in Figure 16b.

FIGURE 16

River sampling location, morphology, and sediment particle size. (a) Sampling position; (b) Sediment gradation curve of sampling position.

(a) An aerial view of a sedimentary landscape highlighting labeled areas: Estuary, Downstream, Midstream, and Upstream with red boxes. (b) A line graph shows particle size distribution of sand in different regions: Estuary, Downstream, Midstream, Upstream, and Primary, with percentage on the y-axis and particle size in millimeters on the x-axis.

Experiments have revealed that the sediment particle size in river channels is a crucial factor influencing the planar morphology of the channel. Therefore, this study incorporates the bed sediment particle size to refine Equation 4.

Drawing on relevant research, this paper analyzes the impact of sediment particle size on channel morphology by integrating findings from the Nikuradse experiment. The analysis is as follows:

Through systematic research on fluid motion inside circular pipes, the Nikuradse experiment achieved groundbreaking progress. This study not only elucidated the intrinsic relationship between frictional resistance characteristics and flow parameters (Reynolds number, Re) as well as wall conditions (Δ/d), but also classified the flow into five distinct regimes based on flow characteristics. Building on this significant discovery, Alexander further expanded the scope of the research, extending the applicability of the theory to rectangular open-channel flows with artificially roughened walls. Experimental data demonstrated that the resistance laws in these channels exhibited a high degree of consistency with those observed in pipe flows. From this perspective, the flow evolution process in natural rivers can essentially be regarded as a macro-scale Nikuradse experimental system (Xin et al., 2019).

The expression for the resistance coefficient λ is established as follows: λ = f Re , Δ R , M ¯ (5)

In the formula, Δ refers to the absolute roughness.

Substitute Equation 5 into Equation 2. J = 1 8 f Re , Δ R , M ¯ F r 2 (6)

The river’s morphology parameter M ¯ can be expressed as Equation 7. M ¯ = F J F r 2 , Re , Δ R (7)

In Nikuradse’s classic study, systematic experimental research established a quantitative relationship between the frictional resistance coefficient, the Reynolds number, and the relative roughness. It should be noted that in pipe flow, relative roughness is defined as the ratio of the wall roughness protrusion height to the pipe diameter. For natural rivers, this parameter can be analogously represented as the ratio of the median bed sediment grain size d50 to the hydraulic radius R. Considering that this study focuses on the process of riverbed morphological evolution, the relative roughness is simplified to the expression d ₅₀ /h (where h is the cross-sectional average water depth). Given that the influence of the Reynolds number in open-channel flow is typically negligible (Song et al., 2023), the riverbed morphological characteristic parameter can ultimately be simplified to the following functional relationship: M ¯ = F J F r 2 , d 50 h (8)

In the following text, for convenience of graphical representation and descriptive clarity, the first term in Equation 6 is denoted as Ψ ₁, and the second term as Ψ ₂.

4.2.4 Classification of river morphology

Taking the lower reaches of the Yellow River (from Xiaolangdi to Lijin, as shown in Figure 17) as the study area, this study analyzes the channel pattern discrimination method for this reach under different flow and sediment conditions.

FIGURE 17

River morphology in different reaches of the lower Yellow River.

Map of the Yellow River showing its progression from Xiaolangdi to the river mouth. It passes through regions labeled braided, transitional/anabranching, meandering, and river mouth. Key locations include Xiaolangdi, Huayuankou, Jiahetan, Gaocun, Sunkou, Aishan, Luokou, and Lijin. A north arrow and a scale bar indicate orientation and distance.

This river reach can be divided into four typical segments: the section from Mengjin to Baihe-Gaocun is a wandering reach; the section from Gaocun to Taochengpu is a transitional reach; the section from Taochengpu to Lijin is a meandering reach; and the section downstream of Lijin belongs to the estuary reach. Among these, the wandering reach possesses unique geomorphological characteristics, manifested as alternating wide and narrow channel widths, forming a sinuous and winding morphology, with numerous sandbars and distributary channels distributed within the widened areas.

According to Google Earth satellite data, the channel pattern in the transitional reach from Gaocun to Sunkou tends towards the wandering type, while the section from Sunkou to Aishan tends towards the branching type. Based on reference (Xu and Zhao, 2013), this paper defines the segment from Huayuankou to Sunkou as a wandering reach, the segment from Sunkou to Aishan as a branching reach, the segment from Aishan to Luokou as a meandering reach, and the segment from Luokou to Lijin as a branching reach. For convenience in plotting and description, the wandering channel pattern is hereafter denoted by B, the branching pattern by A, and the meandering pattern by M. The hydrological and sediment data as well as the cross-sectional morphology data used in this paper are sourced from the annual Sediment Bulletins published on the Yellow River website and from reference (Xu and Zhao, 2013).

By calculating the two characteristic parameters in Equation 8 and annotating them with the corresponding annual river patterns, the scatter plot distribution for different river patterns can be obtained, as shown in Figure 18. In the figure, B represents the wandering pattern, A represents the branching pattern, and M represents the meandering pattern.

FIGURE 18

Scatter points of different river types in the lower reaches of the Yellow River. The wandering channel pattern is hereafter denoted by B, the branching pattern by A, and the meandering pattern by M.

Scatter plot showing data classified into three categories: squares (B), circles (A), and triangles (M). The x-axis represents $\psi_1$ values ranging from 0.000 to 0.045, and the y-axis represents $\psi_2$ values ranging from 0.02 to 0.12. Different symbols and colors indicate data groupings.

In Figure 18, the horizontal and vertical coordinates represent the characteristic parameters mentioned above. As can be seen from Figure 18, the boundaries between channel patterns in the lower reaches of the Yellow River are generally clear, with only minor areas of overlap between different types. To better delineate the boundaries between these different patterns, this paper innovatively employs a Support Vector Machine (SVM).

SVM is a supervised machine learning algorithm based on the principle of structural risk minimization, which is suitable for handling small-sample, nonlinear classification problems and has particular advantages in geomorphic data analysis (Sulak, 2025; Qudah et al., 2025). In the specific implementation, two dimensionless parameters calculated from field data (ψ ₁ = J/Fr ² and ψ ₂ = d ₅₀ /h) were used as input features and standardized. A Gaussian radial basis function kernel was employed to address the anticipated nonlinear decision boundaries in the feature space. The key hyperparameters of the model-the regularization parameter C and the kernel coefficient γ-were optimized through a grid search combined with 5-fold cross-validation. The final model was built using the scikit-learn library in MATLAB and trained on the training set with the optimized hyperparameters (C = 10, γ = 0.1). It achieved an overall classification accuracy of 94.7% on an independent test set, with precision and recall exceeding 0.92 for all three channel pattern classes (wandering, braided, and meandering), demonstrating the robustness of the model for channel pattern discrimination. The results of the river pattern classification based on SVM, including the decision boundaries generated in the ψ₁–ψ₂ feature space, are shown in Figure 19.

FIGURE 19

The results of river morphology boundary division based on SVM. The wandering channel pattern is hereafter denoted by B, the branching pattern by A, and the meandering pattern by M.

Scatter plot with contour regions and data points in a three-color scheme. The x-axis is labeled $\psi_2$ and the y-axis $\psi_1$. Red points represent category B, green points A, and blue points M. Three contour regions, purple, teal, and brown, cover different ranges of the plot.

The kernel function used by the SVM in the boundary delineation process is the Gaussian kernel function. By extracting the boundary points, the coordinates of the horizontal and vertical axes are obtained. Fitting these coordinate points yields the boundaries between the different river patterns, as shown in Table 2.

TABLE 2

Boundaries of different river patterns.

Morphology	Boundary
B and A (Boundary 1)	y = 0.038 + 0.025 × e − 2 × x − 0.023 0.01 2
A and M (Boundary 2)	y = 0.025 + 0.012 × e − 0.5 × x − 0.026 0.003 2

Table 2 shows the boundaries between different river patterns, where x represents Ψ ₁ and y represents Ψ ₂. When y > Boundary 1, the river pattern is wandering; when Boundary 1 > y ≥ Boundary 2, the river pattern is branching; and when y < Boundary 2, the river pattern is meandering.

Based on the results of this study, the river patterns of the Gaocun–Sunkou reach in 2022 and the Sunkou–Aishan reach in 2021 were identified to analyze the changes in the transitional reach. The calculated parameters are shown in Table 3. The results indicate that the river pattern of the Gaocun–Sunkou reach tends to be branching, and the pattern of the Sunkou–Aishan reach also tends to be branching.

TABLE 3

Design conditions.

Segment	J/‱	B/m	h/m	Q/m³·s^-1	d ₅₀/mm
Gaocun–Sunkou	1.201	733	3.5	6572	0.102
Sunkou–Aishan	1.372	629	4.2	4839	0.121

These results were verified using images from the Sentinel official website with the remote sensing images shown in Figure 20.

FIGURE 20

Sentinel image. (a) Gaocun–Sunkou; (b) Sunkou–Aishan.

Two satellite images in false color display a river flowing through agricultural and urban areas. Image (a) shows a broader section of the river, while image (b) focuses on a narrow, winding section. Red indicates vegetation, highlighting the surrounding fields.

As can be seen from Figure 20, the calculation results are consistent with the actual channel morphology. This indicates that the classification method proposed in this paper is accurate and can be applied to the analysis of river pattern evolution in the lower reaches of the Yellow River.

Through a comprehensive analysis of the flow and sediment conditions after the implementation of water and sediment regulation in the Yellow River since 2003, it can be concluded that following a significant reduction in sediment load and fluctuating changes in water volume, the river cross-sections generally exhibit a trend of channel degradation (becoming deeper). Wandering river patterns are transitioning towards branching patterns, and although branching rivers remain branched, many reaches are developing sinuous characteristics.

5 Conclusion

Through systematic physical experiments and field data validation, this study elucidates the mechanisms by which water and sediment variations drive the evolution of weakly-tidal estuarine channels. The principal findings are:

Process-Based Mechanisms Identified: We demonstrate that (a) active bedload transport is a critical, often overlooked, driver of planform change; (b) evolution proceeds via threshold-exceedance, where channels remain stable until forcing overcomes morphological inheritance; (c) the estuarine backwater effect is a key controller of deposition style and location.

Validated Evolutionary Pathways: The experimental conditions leading to channel widening, braiding, and avulsion were successfully mapped onto specific hydrological years in the lower Yellow River, validating the experimental approach. Notably, high-flow, sediment-starved conditions (post-flood scouring) were confirmed as a primary avulsion trigger.

An Improved Discriminative Framework: By incorporating both a stream power index (J/Fr ²) and relative roughness (d ₅₀ /h) into a resistance-based framework and classifying outcomes using a robust SVM algorithm, we developed a reliable method for discriminating channel patterns in the lower Yellow River. This method outperforms single-parameter approaches by capturing the interplay between flow energy and boundary resistance.

This research bridges controlled experimentation and field observation, providing not just correlative relationships but also causal, process-based explanations for estuarine channel evolution. The findings and the discriminative framework offer valuable insights for managing fluvial deltas under changing environmental conditions.

Data availability statement

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

Author contributions

JS: Writing – review and editing, Writing – original draft. YS: Writing – original draft, Data curation, Supervision, Project administration, Methodology, Formal Analysis, Investigation, Software, Conceptualization. XS: Resources, Writing – review and editing, Funding acquisition.

Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

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Edited by: Nan Xu, Hohai University, China

Reviewed by: Haimanot B. Atinkut, Bahir Dar University, Ethiopia

Daniel E. Kroes, Lower Mississippi Gulf Water Science Center, United States