Movable Bed Research Articles

Morphological properties of two-dimensional and three-dimensional bedforms in open channel flow: A flume experiments study

Bedforms are formed by sediment particles under the action of flow, which in turn affect flow and sediment movement. However, the fundamental mechanisms behind the formation and development of bedforms under varying flow conditions, the interconnection between sediment particle movement and bed morphology development, as well as the influence of bedforms on flow and sediment transport, are still not well understood. In the current study, the moveable bed load transport flume experiments under different flow conditions were done, and the development processes of two-dimensional and three-dimensional dunes formed under different flow intensities were simulated. The detailed structure of the bedforms was measured by laser scanning technology, the characteristics of the bedforms were analyzed in detail, and the relations between the formation of the bedforms and the movement of sediment particles are discussed. The results found that the correlation coefficients of the longitudinal profile curve can serve as a quick reference for distinguishing two-dimensional and three-dimensional dunes. When the crestline ratio is used as the criterion for two-dimensional and three-dimensional dunes, the relative amplitude of the dune crestline and the included angle with the flow direction should also be comprehensively considered. The lee side angles of dunes calculated using the triangle generalization method and local section tangent method are compared and show that the values obtained by the former method are only about half of that of the latter. It is also found that the lee side angles of dunes are related to the dune height. The superimposed dunes generally exist in the downstream area of the stoss side of the dunes. The local bed slopes on the stoss side of the dunes show reverse slopes. The superimposed dunes improve the local bed height and further increase the reverse slope degree of the stoss side. A streamwise ridge is an important form located in the upstream area of the dunes stoss side, and they are symmetrically distributed on both sides. Multiple streamwise ridges divide the stoss side of the dunes into relatively independent movement areas, restricting the movement of sediment particles to specific regions. According to the distribution characteristics of bed morphologies, the effects of dunes on sediment particle movement and flow energy consumption are analyzed.

Observations of wave run-up affected by dune scarp during storm conditions: a two dimensional large-scaled movable bed experiment

Artificial dunes serve as essential nature-based defenses against the increasing threats posed by climate change and rising sea levels along coastal regions. However, these man-made dunes are particularly susceptible to erosion during severe storm events, necessitating careful consideration of their design for effective coastal protection. Among the myriad factors influencing artificial dune design, wave run-up stands out as a paramount concern. Not only is wave run-up crucial in assessing the extent of coastal flooding, but it also plays a significant role in shaping shoreline dynamics. During intense storm events, wave run-up amplification leads to substantial erosion of sand dunes, forming dune scarps that resemble cliffs. To address these challenges, we conducted a series of innovative two-dimensional large-scale laboratory experiments using movable beds. These experiments aimed to provide a quantitative understanding of wave run-up characteristics on dune scarps. Additionally, our study explored the feasibility of using existing empirical formulas to predict the 2% exceedance of wave run-up (referred to as R2%) in such scenarios. Our results revealed a consistent trend in R2% values, irrespective of variations in the surf similarity parameter when wave run-up was influenced by a dune scarp. Notably, our findings recommend the adoption of the Stockdon empirical formula, incorporating beach slope from the still water level to the dune scarp toe, as an effective method for predicting R2% during highly erosive conditions. This approach can significantly enhance the design and functionality of artificial dunes, bolstering their capacity to safeguard coastal areas from the impacts of severe storms and erosion, thus contributing to resilient coastal ecosystems and sustainable coastal management.

Prediction of movable bed resistance in open channels with dune forms incorporating the effects of flow separation and water temperature

Flow separation behind the dune forms may have reduced the contact area between the flows and the bed surface, in addition to producing form drag in open channels. In this study, a novel predictor is developed based on the underlying mechanism of movable bed resistance across a dune-dominated bed. The mechanism is derived to a new formula based on the energy loss division approach to generalize the relationships among the grain drag, form drag and flow separation. The flow separation length is expressed to quantify the flow separation effect with a modified empirical method. Additionally, the water temperature effect is incorporated into the novel predictor due to the inclusion of fluid viscosity in both the roughness function and suspension number. A global database with a wide spectrum of measurements from the available literature was created to test the novel predictor. Approximately 83.3 % of flume data fall within a range of ± 30 % error, and ∼ 80.0 % of field data plot within this range. The optimized predictor has a better accuracy than the other four previously developed models in all five evaluation indicators. Furthermore, this predictor effectively reflects the impacts of water temperature on flow resistance to reproduce four variation modes. The diverse modes are jointly determined by suspension number and roughness Reynolds number. In actual river management, this predictor is used to interpret the effects of lower water temperature on sediment carrying capacity and flood routing. Seasonal variations in water temperature and the underlying effects of water temperature occur in rivers worldwide, which implies the need to pay more attention to this aspect in river management strategies.

Experimental investigation of pier scour depth and its scour hole pattern for different shapes

Local scour, a complex phenomenon in river flows around piers with movable beds, can damage bridge piers during high floods. Predicting scour depth accurately is vital for safety and economic reasons, especially for large bridges. This study using hydraulic flume laboratory experiments compared diamond, square, and elliptical pier models of different sizes under steady clear-water conditions considering different flow rates and discharge levels to identify the most efficient shape with less local scour. Local scour, a complex phenomenon in three-dimensional flow around piers in rivers with movable beds, can lead to detrimental effects on bridge piers due to high flood velocities. Accurate prediction of scour depth is crucial for economic and safety reasons, especially for large bridges with complex piers. Hydraulic engineers are keen on forecasting the equilibrium scour depth. To achieve this, laboratory testing compared diamond, square, and elliptical pier models under steady clear-water conditions to identify the most efficient pier shape with less local scour. This research provides valuable insights for optimizing pier design to enhance bridge stability and resilience against scour-induced risks. A variety of configurations, including different sizes and shapes of piers were experimented with in the flume using diamond, square, and elliptical shapes. The test results showed that the local scour depth around elliptical piers was around 29.16% less, and around diamond piers, it was approximately 16.05% less compared to the scour depth observed around square piers with the same dimensions. The researchers also observed distinct patterns of scouring around different pier shapes. Specifically, the square-shaped piers displayed the highest level of scouring depth, that is, 48 mm, followed by the diamond-shaped pier which experienced a scouring depth of 48 mm while the elliptical-shaped piers experienced the least amount of scouring depth, that is, 34 mm. The test results also demonstrated that pier size significantly influences scouring, with an increase in pier size from 3 × 3 cm2 to 5 × 5 cm2 leading to a rise in scour depth by 26.04%. Moreover, this study findings also elucidated that an increase in flow results in an increase of in scouring depth i.e., elevating the discharge from 0.0026 cumecs to 0.0029 cumecs led to a 28.13% increase in scouring depth for the identical pier size. These findings provide valuable insights into the hydraulic behavior of various pier shapes and can aid in the optimization of bridge design and hydraulic engineering practices. The investigations further revealed that local scouring is sensitive not only to pier dimensions but also to other critical parameters, including flow rate, time of exposure, and the size of a pier.

Integrated Prediction Model for Upstream Reservoir Sedimentation in a Weir: A Comprehensive Analysis Using Numerical and Experimental Approaches

In this study, a new empirical equation was established to predict the sedimentation volume resulting from the construction of a multi-purpose weir or low-head dam using experimental approaches. Applying the 1-D numerical model (STAFF), which is based on Exner’s equation, 2545 cases were simulated and laboratory experiments were conducted with various sediment particle sizes, channel slopes, inlet discharge, and outlet water elevation. Short-term predictions were conducted through laboratory experiments with movable bed, and the results indicated that dimensionless unit stream power and the Shields parameter exhibited the most significant correlation with dimensionless deposition volume. In particular, we analyzed the phenomenon in which the backwater effect and reservoir delta. Using a multiple regression approach, the developed empirical equation was validated for predicting sedimentation in the upstream reservoir of the weir.

Evaluating Manning's Roughness Coefficient for Flows with Equilibrium and Non-equilibrium Sediment Transport

One of the challenges in using Manning’s equation lies in accurately determining Manning’s roughness coefficient, especially due to sediment transport. The condition of sediment transport within a specific section of a river can be in equilibrium, meaning that the amount of sediment entering and exiting the segment is balanced or it can be in non-equilibrium, where there is an imbalance between the sediment entering and leaving the segment. Experiments were carried out in the laboratory to simulate both transport conditions, one involving sediment feeding (equilibrium condition) and the other without sediment feeding (non-equilibrium condition). A total of 180 mean velocity profiles were measured using an acoustic doppler velocimeter (ADV) in fixed and movable bed flows. The present experiment was combined with theoretical approaches to evaluate Manning’s coefficient in open channels under sediment transport-flow conditions and reach conclusive results. The shape of the velocity profile, u/U, for flows over a movable bed with sediment feeding is “slender” compared to those without sediment feeding. The presence of sediment transport affects the shape of the velocity profile, especially in the inner region, influencing Manning's roughness coefficient. This coefficient can be determined from two-point velocity measurements at z/H = 0.1 and 0.2 for fixed and movable bed flows with and without sediment feeding, respectively. On average, sediment feeding increases the coefficient by 19% compared to the non-sediment feeding case. KEYWORDS: Manning’s roughness coefficient, Velocity profile, Equilibrium and non-equilibrium, Sediment transport, Open-channel flow

Numerical Modeling of Sediment Transport and Bed Evolution in Nonuniform Open-Channel Flows

Abstract The shallow-water and multilayer hydrostatic models have been commonly used to analyze the problems of a sediment-laden, plane open-channel flow. The models are adequate to solve a quasi-hydrostatic flow problem, but their accuracy deteriorates as the e ects of the vertical acceleration gain in significance. Herein, a higher-order numerical model for treating the problems of unsteady, plane open-channel flow over a movable bed is proposed. In this model, the flow hydrodynamics is governed by the depth-averaged Boussinesq-type equations, and the bed morphodynamics is determined by an Exner-type equation and additional equations describing the non-equilibrium transports of suspended load and bed load. A hybrid finite-volume and finite-di erence scheme was used to discretize and solve the governing equations, yielding solutions that are in satisfactory agreement with the experimental data. Overall, the results of the proposed model for the temporal free-surface profile and bed evolution were fairly adequate. For the two particular cases considered, however, the quality of its results was moderately a ected by the e ects of the three-dimensional characteristics of the dam-break flow and the sliding of the dike body due to sub-surface flow. The results of this investigation highlight the importance of including a higher-order Boussinesq-type correction for refining sediment transport computations.

Non-intrusive measurements of wave nonlinearity over movable bed of sediment with different beach slopes

A series of laboratory experiments were undertaken to qualitatively investigate the evolution of wave nonlinearity over a movable bed of sediment with five different beach slopes under regular waves in a medium-scale wave flume. An innovative non-intrusive data collecting system, which mainly consists of three side-looking high-speed cameras, was developed to collect high-resolution and synchronous data on free-surface water elevation of waves and bed level changes without causing any disturbances to wave motions and the movable bed of sediment. On analyzing the collected experimental data, it is found that regular waves become nonlinear when they propagate to the shoaling zone and start breaking, and linear wave theory is quite accurate for calculating wave parameters such as orbital velocity with the correlation coefficient r2 = 0.8–0.95 before the waves break, but becomes less accurate after the waves break or are in the breaking zone with the smaller correlation coefficient r2 = 0.4–0.6. Four parameters, wave skewness Skη, asymmetry Ayη, Ursell number Ur, and Rocha number NP0, are introduced to describe the wave nonlinearity, of which Skη and Ayη are found to be of largest amplitudes at the wave breaking point and then start to decrease in the breaking zone and are almost unchanged for different beach slopes, while Ur further increases in the breaking zone and exceed the first larger value as waves approach to shoreline, but NP0 is almost linearly proportional to wave orbital velocity amplitude and quite sensitive to beach slope. The location of sandbar is found close to the wave breaking point in the wave flume and may be also considered as the point where wave nonlinearity becomes important for sediment transport in the surf zone, and the linear wave theory becomes less accurate.

Effect of wave motion on the scouring caused by a marine propeller jet: An experimental and numerical study

Bathymetry changes induced by marine propeller jets on movable beds are a crucial issue in harbors, especially in the maneuvering zone. The knowledge of the scour hole and deposition mound dimensions, due to propeller jets, is important in the context of sediment management.Although the presence of waves is well known in harbor environments, propeller jet scours are usually investigated under still water conditions neglecting the effect of wave interaction. Moreover, the interaction between waves and propeller jets can also occur in mooring out of harbors. For these cases, the interaction of wave induced hydrodynamics and propeller jets is a crucial issue that is still an open and challenging problem. This paper aims to address, for the first time, the knowledge gap by investigating the influence of waves on propeller jets in unconfined conditions, which in turn can lead to alterations in scour and deposition patterns. The study relies on a specific experimental investigation. The selection of the parameters of the experimental tests is based on the results of prior analyses aimed to investigate the propeller jets induced scour and deposition in still water conditions and in the presence of a current. Hence, regular waves with different parameters (i.e. wave height and wave period) have been then reproduced in a wave flume where a propeller jet has been installed. The experimental tests aimed to get insight on the scour profiles as well as scour hole bathymetry induced by propeller jets under the influence of regular wave propagation. Numerical simulations have been also performed to investigate the effects of the wave-induced velocity acting on the propeller jets hydrodynamics. Spectral analysis has been then applied to characterize the complex scoured form and bedforms on the bathymetry configuration induced by the tested propeller jet and waves.

The effect of upstream soil type on the amount of catchments sediment

ABSTRACT Mud filled by upstream surface runoff is one of the problems in maintaining the reservoir and dam. The material of upstream bed has a significant effect on the filling of reservoirs. In the present work, the filling rate of the reservoir from the upstream movable bed is investigated by using the Herschel–Bulkley model in both shear-thickening and shear-thinning modes. For this, a two-phase Newtonian-non Newtonian SPH code was developed that has special capabilities such as turbulence effects, surface tension, free surface, and particle displacement. This computational code is then evaluated by the experimental results in addition to finally used to investigate the main problem mentioned above. Five different models of movable beds with are considered, and the filling rate of the downstream tank with these materials is discussed. The results show that among the parameters of the Herschel–Bulkley model, the yield stress is more effective than other factors.

A comprehensive study of various regressions and deep learning approaches for the prediction of friction factor in mobile bed channels

Abstract A fundamental issue in the hydraulics of movable bed channels is the measurement of friction factor (λ), which represents the head loss because of hydraulic resistance. The execution of experiments in the laboratory hinders the predictability of λ over a short period of time. The major challenges that arise with traditional forecasting approaches are due to their subjective nature and reliance on various assumptions. Therefore, advanced machine learning (ML) and artificial intelligence approaches can be utilized to overcome this tedious task. Here, eight different ML techniques have been employed to predict the λ using eight different input features. To compare the performance of models, various error metrics have been assessed and compared. The graphical inferences from heatmap data visualization, Taylor diagram, sensitivity analysis, and parametric analysis with different input scenarios (ISs) have been carried out. Based on the outcome of the study, it has been observed that K Star in the IS1 with correlation coefficient (R2) value equal to 0.9716 followed by M5 Prime (0.9712) and Random Forest (0.9603) in IS2 and IS4, respectively, have provided better results as compared to the other ML models to predict λ in terms of least errors.

Numerical study of the dam-break flood over natural rivers with macroscopic rocks on movable beds

This paper presents a three-dimensional model of dam break flows over fixed and movable beds. As the consequences of a dam break, the model considers the transport of solid particles and deposition due to the momentum of the flow. The movement of the free surface of water and mud is performed by Newtonian and non-Newtonian fluid models, and the solid macroscopic particles movement is carried out by the discrete phase model (DPM) and macroscopic particle model (MPM) models. It has been detected that the model was reliable and well balanced, and could accurately capture the dam break flow movement in complex terrain. Moreover, using the proposed model, a partial dam break of the Mynzhylky Dam was simulated. Even more in the calculation, the presence of mud sediment and solid particles were taken into account, which is very close to the real dam break problem.

TSUNAMI RUN-UP CONSIDERING TIME VARIATION OF DENSITY OF INUNDATION WATER

Aiming for the advancement of tsunami load, historical and/or prospective tsunami scale evaluations, practical empirical formulas for evaluating friction factor K of inundation flow and density ρ of inundation water over a movable bed, which can be applied to a tsunami run-up theory, are proposed using experimental data whose amount (range) is increased (expanded) by carrying out additional experiments on ρ and run-up of inundation flow with sediment, and verification data of the above theory under a uniformly sloping movable bed condition are provided. Series solutions with a higher universality to the run-up of tsunami inundation flow with sediment over a uniformly sloping movable bed, in which both K and ρ depend on time, are derived under the conditions depending on an incident bore height h1 at shoreline (or an initial stored water depth), bed slope i, median particle diameter d50 of initial bed material, and examples of the solutions are shown. The solutions are applicable to the case that ρ is independent on time, i.e., the case of inundation flow without sediment over a movable bed or fixed bed. Including the case of inundation flow without sediment, validity of one of the solutions is also verified through a comparison with the verification data on run-up distance.

A consistent multi-resolution particle method for fluid-driven granular dynamics

Granular dynamics driven by fluid flow is ubiquitous in many industrial and natural processes, such as fluvial and coastal sediment transport. Yet, their complex multiphysics and multi-scale nature challenge numerical models’ accuracy and efficiency. Here, we develop a new multi-resolution mesh-free particle method, based on an enhanced weakly-compressible Moving Particle Semi-implicit (MPS) method, to study the dynamics of rapid fluid-driven granular erosion. We propose and validate a novel multi-resolution multiphase MPS formulation for the consistent and conservative form of the governing equations, including particle stabilization techniques. First, we discuss the numerical accuracy and convergence of the proposed approximation operators through two numerical benchmark cases: the multi-viscosity Poiseuille flow and the multi-density hydrostatic pressure. Then, coupling the developed model with a generalized rheology equation, we investigate the water dam-break waves over movable beds. The particle convergence study confirms that the proposed multi-resolution formulation predicts the analytical solutions with acceptable accuracy and order of convergence. Validating the multiphase granular flow reveals that the mechanical behavior of this fluid-driven problem is highly sensitive to the water-sediment density ratio; the bed with lighter grains experiences extreme erosion and interface deformations. For the bed with a heavier material but different geometrical setups, the surge speed, and the transport layer thickness remain almost identical (away from the gate). Furthermore, while the multi-resolution model accurately estimates the global sediment dynamics, the single-resolution model underestimates the flow evolution. Overall, the qualitative and quantitative analysis of results emphasizes the importance of multi-scale multi-density interactions in fluid-driven modeling.

Scour around the single emergent cylinder due to subcritical and supercritical approach flow conditions

ABSTRACT Flume experiments with a uniform cohesionless sand with d 50 = 0.9 m m were utilized in the current study to examine the local scour process around a single emergent cylinder under various geometrical circumstances and with a various flow characteristic that simulates an inundating tsunami flow. This single emergent cylinder represents a piloti-type column located over a movable bed material because piloti-type columns are used to elevate the building structures from the ground level. In the experiments, it was noted that the maximum scour depth probably occurs at the cylinder’s upstream face, resembling local scour around a scaled-down bridge pier in an open channel. Additionally, the scour hole around the cylinder is shallower the smaller they are, as are the horseshoe vortices that surround them. Furthermore, the effects of the surface bow-wave, hydraulic jump detachment and the wall-jet over the front face of the emerging cylinder were used to identify the relationship concerning the scouring pattern and selected flow characteristics over a piloti-type emergent column under tsunami flow. Empirical formulae have been finally developed to determine the maximum scour depth in front of the cylinder, which is beneficial to characterize the stability of the piloti-type columns, considering the specified Froude number conditions.

Design Scour Levels for Dune Revetments and Seawalls

A new method to determine design scour levels for dune revetments and seawalls is presented. The method is based on the thesis that toe scour is a function of the nearshore incident wave energy and was calibrated with results from several moveable bed model studies covering a large range of scales. The method determines scour levels to a still water level datum defined at the incident wave-breaking location. Therefore, the method incorporates many more parameters than those that pertain to existing methods including tidal stage, storm surge, wave setup, wave period, and seabed slope. However, application of the method is not difficult with a methodology being presented. The sensitivity of the method to variations in the values for the input parameters is examined and the limits of their applicability are presented. Recommendations for further research are given.

Prediction model of outburst debris flow triggered by landslide dam failure considering the erosion process

The formation of outburst debris flow is different from other types of debris flow as it is formed by the gradual erosion of the riverbed by the unsteady and rapid outburst flow triggered by landslide dam failure. However, a prediction model for outburst debris flow that comprehensively considers the erosion effect has not yet been established. In this paper, the shallow water equation is used to describe the motion of outburst flow. This study proposes a method for constructing a virtual unit and resetting the terrain variables to reproduce the wet and dry boundary. An erosion model considering the effect of hindered erosion is introduced. By combining the shallow water equations, a debris flow prediction model that considers the entire erosion process of outburst flow is thus proposed. The established model is verified by numerical experiments on the evolution of dam-break flow on a dry fixed bed and on a moveable bed; additionally, it is verified by physical experiments on the formation of outburst debris flow. Combined with the calculation results of erosion models with and without a hindered erosion effect, the erosion model without the hindered erosion effect overestimates the flow concentration in this paper. The simulation results are closer to the actual values when considering the effect of hindered erosion in the analysis of outburst debris flow formation. The proposed model in this paper can be used as a tool to predict the occurrence of outburst debris flow.

Discussion of “Prediction of Flow Resistance in an Open Channel over Movable Beds Using Artificial Neural Network” by Satish Kumar, Jnana Ranjan Khuntia, and Kishanjit Kumar Khatua

Discussion of “Prediction of Flow Resistance in an Open Channel over Movable Beds Using Artificial Neural Network” by Satish Kumar, Jnana Ranjan Khuntia, and Kishanjit Kumar Khatua

Closure to “Prediction of Flow Resistance in an Open Channel over Movable Beds Using Artificial Neural Network” by Satish Kumar, Jnana Ranjan Khuntia, and Kishanjit Kumar Khatua

Closure to “Prediction of Flow Resistance in an Open Channel over Movable Beds Using Artificial Neural Network” by Satish Kumar, Jnana Ranjan Khuntia, and Kishanjit Kumar Khatua

Hydrologic and geomorphic effects on the reduction of channel discharge capacity in the Middle Yangtze River

A systematic increase in the occurrence of flood events has been noted in rivers worldwide. However, our understanding remains unclear of how the flood level is affected by the change in channel discharge capacity. Therefore, the reduction of channel discharge capacity was quantified in the Middle Yangtze River (MYR) based on extensive measured data. It is confirmed that the variation in channel discharge capacity is a superposition result of channel-morphology and channel-resistance changes, as well as the change in local base-level at the outlet. Then a series of numerical simulations were carried out to quantitatively identify the contribution of each factor to the reduction of channel discharge capacity in the MYR for the years of 2004 and 2020. Simulated results reveal that channel degradation increased the flow passage area, helping the channel to convey floods, with the effect being weakened along the reach; however, the decline in flood level under the same discharge was not observed, which was primarily attributed to the increases in channel resistance and local base-level at the outlet. These two factors accounted for 16–91 % and 9–84 % of the total impact at four hydrometric stations in the MYR. It should be noted that the dominant factor to influence the discharge capacity varied greatly at different stations, which depended on the degree of bed-material coarsening, the distance from the confluence of lakes, etc. At the stations immediately downstream of the dam, the contribution of the increased movable bed roughness usually played a more essential role; while at the stations close to the outlet with the confluence of large lakes, the increase in local base-level became the main factor that accounted for the rise of high-flood levels under the specified large discharge.