Sediment Concentration Profiles Research Articles

Estimation of the suspended sediment concentration in ice-covered channels based on the gravitational theory

Rivers in cold high latitude northern regions usually freeze during winter, thereby forming an ice cover on the water surface. The additional ice cover significantly changes the flow characteristics of the rivers and hence affects the process of water and sediment transport. Understanding the vertical profile of suspended sediment concentration (SSC) in ice-covered channel flows is helpful for investigating the sediment deposition and the bed morphology of rivers located in cold regions. To predict the SSC distribution in ice-covered channels, this study is based on the gravitational theory and puts forward a new SSC model by dividing the flow underneath the ice cover into the upper ice layer and the lower bed layer with the maximum streamwise velocity and the zero Reynolds shear stress as the interface. The calculated results of the new SSC model agree well with the collected experimental data, and the accuracy of the prediction results is evaluated by error analysis. Besides, the differences in the governing equations and the prediction accuracy between the gravitational theory and the diffusion theory are discussed, and thus the pros and cons of the proposed SSC model are illustrated. Although the gravitational theory has the controversial point, the validation results and discussions demonstrate that adopting the gravitational theory to estimate the SSC distribution in ice-covered channels is effective. The theoretical approach used herein can provide some guidance for studying the sediment-laden flow of freezing rivers in high-latitude northern regions.

Modified stochastic diffusion particle tracking model driven by skew Brownian motion: Analysis of sediment particle motion in turbulent flow under the effects of ejection and sweep.

Turbulent bursting events have been classified into outward interactions (Q1), ejections (Q2), inward interactions (Q3), and sweeps (Q4) in various studies. Ejections (Q2) and sweeps (Q4) have been identified as significant contributors to time consumption, momentum flux, and sediment flux. Additionally, research has shown that the distribution of these events varies nonuniformly at different bed elevations. Despite extensive investigations into the nonuniform distribution of turbulent bursting events, their impact on sediment transport has been rarely explored. In this work, we developed a modified stochastic diffusion particle tracking model (SD-PTM) driven by skew Brownian motion (SBM) using the stochastic Lagrangian approach to scrutinize sediment particle movement in turbulent flows. The model incorporates turbulent characteristics derived from a direct numerical simulation dataset, allowing for a comprehensive analysis of sediment particle dynamics. Moreover, the proposed model accounts for the nonuniform spatial distribution of ejection and sweep events, as well as the particle movement direction during these events. Numerical simulations of the model were conducted to trace sediment particle trajectories in the streamwise and vertical directions. The analysis of sediment transport involved calculating the variance of particle trajectories to examine anomalous diffusion. The model's performance was evaluated by comparing it with flow velocity and sediment concentration profiles obtained from measurements in previous studies. In conclusion, our study suggests that the motion of sediment particles in turbulent flow can be thoroughly investigated under extreme flow conditions using the modified SD-PTM driven by SBM.

Evolution of suspended sediment concentration profiles in the partially and periodically stratified Changjiang Estuary during dry season

A better understanding of how the vertical profile of suspended sediment concentration (SSC) is influenced by multiple factors is required to better understand the hydrodynamics and sediment dynamics of estuaries. Based on in situ measurements obtained during a spring-neap cycle in the estuarine turbidity maximum (ETM) of the Changjiang Estuary in January 2015, we investigate the intratidal evolution and controlling mechanisms of SSC profiles. The results show that during the dry season the ETM was characterized by periodic salinity stratification, low SSC, suspended sediments with reduced grain size, and low sediment availability for resuspension. Three types of SSC profiles were identified, i.e., profiles with two-layer, linear and quasi-uniform structures. The shapes of the SSC profiles varied with time and generally deviated from the equilibrium profile due to the highly variable hydrodynamic and sediment conditions. During ebbs of spring and intermediate tides, the SSC profiles generally evolved from a two-layer to a quasi-uniform structure via a linear structure. Analysis shows that the linear and quasi-uniform profiles occurred under the combination of vertically well-mixed salinity, negligible resuspension, low settling velocity associated with very fine grains, and shallow water depth. Such an evolution pattern can be well reproduced using a one-dimensional numerical model, with the diffusion coefficient being parabolically distributed in the water column and the four factors mentioned above. The findings reported here imply a high variability of SSC profiles in estuarine environments.

Wave-supported fluid mud and sediment vertical mixing under winter storm

Data from 5 monthly field observations of the modern Yellow River delta demonstrate the formation of the fluid mud layer (FML) above the seabed under continuous storms and the sediment resuspension and vertical mixing over the FML. It was observed that the storm wave-related oscillatory flows during winter were mainly in energetic regime (400<ReΔ<1200). The high concentration sediment is trapped in a thin layer stably stratified above the seabed due to the formation of the wave-supported fluid mud (WSFM) layer. Above the WSFM, the total velocity spectral flux E(f) at z=0.7 m is decreased by approximately 14%∼22%, indicating a significantly decreased sediment carrying capacity of the flow. To explore detailed flow and sediment dynamics within the WSFM, a series of experiments in a wide wave flume with WSFM generated were carried out. The velocity and sediment concentration profiles measured over the water depth suggested that the sediment was confined in a thin FML even in high ReΔ regimes (ReΔ>480), and the behavior of FML can transition between a laminar to turbulent with varying wave orbital velocity and Rib. Laminar fluid mud dominates when uw<45 cm/s and ReΔ<518, resulting in exceptionally high viscous dissipation of wave energy. This can explain the observed significant decrease of E(f) during the onset of storm wave recession. Once the fluid mud layer forms, stronger flow with uw>45 cm/s (Rib<0.2) can disturb the interfacial wave of the fluid mud and the flow above it, which cause strong entrainment of the fluid mud layer and sediment mixing into the water column.

Vertical Distribution of Suspended Sediment Concentration in the Unsaturated Jingjiang Reach, Yangtze River, China

The Rouse formula and its variants have been widely used to describe the vertical distribution of the sediment concentration in sediment-laden flows in equilibrium. Han’s formula extends the Rouse formula to non-equilibrium regimes, where the diffusive flux is still assumed to be Fickian. The turbulent flow and suspension regimes downstream of a mega-reservoir, e.g., the Three Gorges Reservoir, usually exhibit fractal and unsaturated properties, respectively. To characterize the non-Fickian dynamics of suspended sediment and the non-equilibrium regime in natural dammed rivers, this study proposes a new formula for the concentration profile of unsaturated sediment based on the Hausdorff fractal derivative advection–dispersion equation. In addition, we find that the order of the Hausdorff fractal derivative is related to the sizes of the sediment and the degrees of non-equilibrium. Compared to Rouse and Han’s formulae, the new formula performs better in describing the sediment concentration profiles in the Jingjiang Reach, approximately 100 km below the Three Gorges Dam.

Positive Feedback Between the Tidal Flat Variations and Sediment Dynamics: An Example Study in the Macro‐Tidal Turbid Hangzhou Bay

AbstractTidal flat variations (curvature) in macro‐tidal turbid bays highly correlate with sediment dynamics. Interactions between tidal flats and sediment dynamics in macro‐tidal turbid estuaries, like Hangzhou Bay, China, have been studied through a fully validated 3D sediment model by considering high‐turbidity, flocculation, and water‐sediment density coupling. Numerical results show that the circulation and sediment flux in the curvature of Andong tidal flat have similar magnitudes in the along‐estuarine and lateral directions, demonstrating the important impact of the geometry on hydrodynamics and sediment transport processes. Sediment moves toward the southern/northern bank near the bottom/surface level in curvature. Tidally averaged net sediment flux is southward in the curvature. Tidal flat reclamation changes the curvature of the tidal channel, and modulates the circulation and sediment transport, and then feeds back to the tidal flat evolution subsequently. Bottom friction, nonlinear advection, and centrifugal force are dominant forces for inducing the lateral circulation, followed by the Coriolis force and sediment‐induced baroclinic process. Lateral circulation combined with the suspended sediment concentration (SSC) profile controls the distribution of instantaneous and tidally averaged net sediment fluxes in the curvature. The sediment flux positively correlates with the curvature of channel bends. The increased curvature of channel bends enhances the southward sediment fluxes mainly by increasing the effects of the centrifugal force, nonlinear advection, and Coriolis force on the lateral circulation and SSC. This study revealed a two‐way feedback system between tidal flat and sediment dynamics, which contributes to the impact of anthropogenic activities on geomorphological evolution of similar estuaries worldwide.

Analytical Eddy Viscosity Model for Turbulent Wave Boundary Layers: Application to Suspended Sediment Concentrations over Wave Ripples

Turbulence related to flow oscillations near the seabed, in the wave bottom boundary layer (WBBL), is the phenomenon responsible for the suspension and transport of sediments. The vertical distribution of turbulent eddy viscosity within the WBBL is a key parameter that determines the vertical distribution of suspended sediments. For practical coastal engineering applications, the most used method to parameterize turbulence consists in specifying the shape of the one-dimensional-vertical (1DV) profile of eddy viscosity. Different empirical models have been proposed for the vertical variation of eddy viscosity in the WBBL. In this study, we consider the exponential-type profile, which was validated and calibrated by direct numerical simulation (DNS) and experimental data for turbulent channel and open-channel flows, respectively. This model is generalized to the WBBL, and the period-averaged eddy viscosity is calibrated by a two-equation baseline (BSL) k-ω model for different conditions. This model, together with a β-function (where β is the inverse of the turbulent Schmidt number), is used in modeling suspended sediment concentration (SSC) profiles over wave ripples, where field and laboratory measurements of SSC show two kinds of concentration profiles depending on grain particles size. Our study shows that the convection–diffusion equation, for SSC in WBBLs over sand ripples with an upward convection term, reverts to the classical advection–diffusion equation (ADE) with an “apparent” sediment diffusivity εs*=α εs related to the sediment diffusivity εs by an additional parameter α associated with the convective sediment entrainment process over sand ripples, which is defined by two equations. In the first, α depends on the relative importance of upward convection related to coherent vortex shedding and downward settling of sediments. When the convective transfer is very small, above low-steepness ripples, α≈1. In the second, α depends on the relative importance of coherent vortex shedding and random turbulence. When random turbulence is more important than coherent vortex shedding, α≈1, and “apparent” sediment diffusivity reverts to the classical sediment diffusivity εs*≈ εs. Comparisons with experimental data show that the proposed method allows a good description of both SSC for fine and coarse sand and “apparent” sediment diffusivity εs*.

Fractional derivative modeling for sediment suspension in ice-covered channels.

Characterizing the anomalous diffusion behavior of sediment transport is a key factor in calculating sediment concentration. This study attempts to seek an equation that captures the nonlocal movement feature of the transport of an ensemble of sediment particles on ice-covered channels with a steady uniform flow field. Given that the fractional advection-dispersion equation with a noninteger order on the space term is nonlocal and able to describe the long-distance transport, a mathematical model with the Caputo fractional derivative is proposed to estimate the vertical diffusion of suspended sediment particles in the ice-covered channel. Results show that the fractional derivative model has a good predictive ability to the suspended sediment concentration as compared to the measurements. Especially in regions close to the undersurface of the ice cover, the proposed model matches better with experiments than the existing analytical model. Sensitivity analyses indicate that the strength of the turbulent diffusion effect dominates the uniformity of the sediment concentration profile. Besides, the sediment concentration is more sensitive to the variation of the boundary roughness than to the change of the sediment settling velocity. It should be noted that the sediment concentration reduces with the decrease of the order of the fractional derivative, which differs from the findings in previous studies.

Application of Hausdorff fractal derivative to the determination of the vertical sediment concentration distribution

The Rouse formula and its variants have been widely used to calculate the steady-state vertical concentration distribution for suspended sediment in steady sediment-laden flows, where the diffusive flux is assumed to be Fickian. Turbulent flow, however, exhibits fractal properties, leading to non-Fickian diffusive flux for sediment particles. To characterize non-Fickian dynamics of suspended sediment, the current study proposes a Hausdorff fractal derivative based advection-dispersion equation (HADE) model, where the Fickian diffusive flux in the Rouse model is replaced by a fractal derivative re-scaled using a constant diffusivity. The order of the Hausdorff fractal derivative is designed to characterize the influence of the multi-fractal turbulence structure on sediment diffusion. Applications show that the HADE model, with the analytical solution expressed using a stretched exponential function, can accurately describe the observed vertical concentration profiles for suspended sediment with different sizes. This improvement well captures the non-exponential decay of the vertical sediment concentration in turbulent flow. Further analyses of measured sediment concentration profiles reveal that the Hausdorff fractal order decreases with the Rouse parameter, which describes the stronger impact of turbulent flow and a more uniform sediment concentration profile for smaller particles. Model comparisons also show that the HADE model provides better performance in describing the sediment concentration profiles than the improved Rouse formula and the standard fractional derivative advection-dispersion equation (FADE), which either under- or over-estimates vertical displacement of sediment particles, likely due to coherent turbulent structures.

Numerical investigation of sheet flow driven by a near-breaking transient wave using SedFoam

Sheet flow driven by a near-breaking transient wave is numerically investigated using SedFoam, a two-phase Eulerian sediment transport model in the OpenFOAM framework. SedFoam resolves the full profile of sediment transport processes within the bottom boundary layer based on closures for intergranular stresses and fluid–particle interactions. Compared with large-scale wave flume data, good agreements are obtained for streamwise flow velocity profiles, sediment concentration profiles, and the sheet flow layer thickness. Model results show near-bed velocity and sediment profile evolution within the sheet flow layer. Intense sediment suspension trailing the wave crest generates stable density stratification that dampens near-bed turbulent kinetic energy and contributes to decreasing bed shear stress. Results suggest that the buoyant flux dominates turbulent kinetic energy dissipation after the passing of the wave crest, coinciding with the reduction of bed shear stress. The instantaneous upper bound of the sheet flow layer exists in different log-law regimes under the transient wave, giving rise to a near-bed velocity profile that is highly dependent on the variable sheet flow layer wall unit. The effect of the profile shape parameter on bedload sediment transport is studied where the bedload predicted using the time-varying optimal profile shape parameter yields good agreement compared to the directly modeled bedload. Modeled sediment transport rates demonstrate that reduced bed shear stress caused by density stratification limits bedload and results in a suspended load-dominant mode.

Submarine channels formation driven by turbidity currents interacting with an erodible bed.

In this article, we explore the submarine channel formation driven by the interaction of turbidity currents with an erodible bed. The theoretical analysis considers the three-dimensional continuity and momentum equations of the fluid phase, and the advection–diffusion and Exner equations of the solid phase. The governing equations are linearized by imposing periodic perturbations on the base flow. We study the response of both the base flow (profiles of velocity and suspended sediment concentration) and perturbations (growth rate and perturbation fields) to changes in key parameters related to the flow and sediment transport. The growth rate and the critical wavenumber are examined for a given quintet formed by the gravitational parameter, longitudinal bed slope, sediment concentration at the edge of the driving layer, Rouse number and erosion coefficient. The critical wavenumber reduces with an increase in gravitational parameter, longitudinal bed slope, sediment concentration at the edge of the driving layer and erosion coefficient, while it increases with the Rouse number. For the submarine channel formation, we identify the upper threshold values for the gravitational parameter, longitudinal bed slope, sediment concentration at the edge of the driving layer and erosion coefficient and the lower threshold value for the Rouse number.

Lateral Variation of Tidal Mixing Asymmetry and Its Impact on the Longitudinal Sediment Transport in Turbidity Maximum Zone of Salt Wedge Estuary

The lateral bathymetry in the estuary results in different degrees of tidal mixing asymmetry, which has significant impacts on the longitudinal sediment transport by changing the temporal variation of vertical eddy diffusion. This study focus on the lateral variation of tidal mixing asymmetry and longitudinal sediment transport at the landward boundary of turbidity maximum zone in the North Channel of Yangtze estuary, which is a typical time-dependent salt wedge estuary. A transect survey was carried out in December, 2018; five vertical profiles of flow velocity, salinity and suspended sediment concentration were simultaneously measured covering a spring tidal cycle. Analysis of the data revealed that, after the maximum ebb, the stratification in the main and secondary channel was stronger than that on the shoal. In the channel, during ebb tide, the stronger stratification restrained the turbulent mixing induced by vertical shear, vertical mixing during the flood tide was stronger than that during ebb tide and vertical mixing coefficients ranged from 0.06 to 0.12, showing regular tidal mixing asymmetry over a flood–ebb tidal cycle. Therefore, stronger eddy diffusion caused by vertical mixing resulted in higher suspended sediment concentrations during flood tide, the larger landward tidally averaged sediment transport rate was induced by tidal pumping with the transportation of flood tidal current and the net sediment transport over a flood–ebb tidal cycle in the channel was landward. Meanwhile, on the shoal, under the effect of vertical shear, the vertical mixing during flood tide was weaker than that during ebb tide; vertical mixing coefficients ranged from −0.27 to −0.02, showing the reversed tidal mixing asymmetry. Higher suspended sediment concentration was transported seaward by the ebb current, the tidally averaged sediment transport rate by both tidal pumping and advection was seaward and the net sediment transport was seaward. Furthermore, large river discharge increased the seaward advection sediment flux on the surface layer in the main channel, resulting in the seaward tidally averaged sediment flux. Strong resuspension increased the seaward advection sediment flux near the bottom in the main and secondary channel, resulting in the seaward tidally averaged sediment flux.

A random displacement model of sediment transport in ice-covered alluvial channel flows.

There is a need for developing efficient models to simulate the sediment transport phenomenon in ice-covered alluvial channel flows, which is essential in enriching the theory of riverbed evolution. This study establishes a random displacement model parameterized with the time-averaged streamwise velocity U(z), the sediment settling velocity ωs(z), and the turbulent diffusion coefficient Dz(z) to calculate the suspended sediment concentration and the longitudinal dispersion coefficient for ice-covered alluvial channels. The proposed model is first validated to determine if it could be used to predict the sediment concentration profiles by comparing to limited experiments published in the literature. Results show that the simulations agree well with the measurements except for the underestimated concentration near the ice cover boundary. Once validated, the random displacement model is applied to explore the variation law of the suspended sediment concentration and the longitudinal dispersion with different sediment particle release modes. The sediment concentration and the stable value of the longitudinal dispersion coefficient for a given flow condition in the dynamic equilibrium state are not affected by the change of the particle release mode. The Fickian time required for the longitudinal dispersion coefficient converging to a constant, however, has a close relationship with the particle release mode and increases as the water depth increases.

Review of Suspended Sediment Transport Mathematical Modelling Studies

This paper reviews existing studies relating to the assessment of sediment concentration profiles within various flow conditions due to their importance in representing pollutant propagation. The effects of sediment particle size, flow depth, and velocity were considered, as well as the eddy viscosity and Rouse number influence on the drag of the particle. It is also widely considered that there is a minimum threshold velocity required to increase sediment concentration within a flow above the washload. The bursting effect has also been investigated within this review, in which it presents the mechanism for sediment to be entrained within the flow at low average velocities. A review of the existing state-of-the-art literature has shown there are many variables to consider, i.e., particle density, flow velocity, and turbulence, when assessing the suspended sediment characteristics within flow; this outcome further evidences the complexity of suspended sediment transport modelling.

A Simplified Concept to Test Erosion or Sedimentation Potential along a Tidal River in the Ganges-Brahmaputra-Meghna Delta

The Payra is a tidal river with meandering planform in which around 6.5 km long landmass is formed naturally during the last 40 years that is selected for an establishment by the Government of Bangladesh. However, the site experiences intermittent erosion at several locations and poses threat to the newly developed infrastructures. In the present study, a Rouse type simple model is used to estimate the equilibrium profiles of suspended sediment concentration below which the system is likely to be eroded and regarded as “Sediment Deficit System, SDS” and above which the system is likely to be sedimented and regarded as “Sediment Surplus System, SSS”. The model was then tested at the study reach using the measured flow-sediment data complemented by field observation and Landsat images-based planform analysis. The analysis revealed that the residual flow-sediment regime in the study site is representing the “sediment deficit system” that causes continuous threat for erosion throughout the tidal cycles. Therefore, the availability of new landmass should not be the only criterion for the quick selection of a project site, and residual flow-sediment regime needs to consider as an additional parameter for such decision-making process.

Modeling of Sediment Transport with a Mobile Mixed-Sand Bed in Wave Motion

A multilayer model is proposed to calculate time-dependent sediment velocity and concentration profiles with the resulting sediment transport. The model is developed here for the wave boundary layer. Measurable quantities are considered, namely, the values of transport during the wave crest and the wave trough, as well as total and net sediment transport values (averaged over the wave period) resulting from the summation and subtraction of their absolute values, respectively. The calculated value of the maximum stress at the bed during the wave period is verified by direct stress measurements. The model is tested for mixed sediments with different grain size distributions including semiuniform and poorly sorted grains. Transport calculations are carried out for acceleration-skewed oscillatory flows and waves described by Stokes’ first and second approximations. Comparison with the available small- and full-scale data from flumes and oscillating tunnels yields agreement typically within plus/minus a factor of two of the measurements.

Process-based suspended sediment carrying capacity of silt-sand sediment in wave conditions

The sediment carrying capacity is one of the fundamental issues in sediment simulation. It is of great importance both in theory and practice to develop process-based approaches for the sediment carrying capacity for a wider range of silt-sand sediment. The current study focuses on the approach for depth-averaged concentration of silt-sand sediment under non-breaking wave conditions. By integrating process-based suspended sediment concentration (SSC) profiles, new synthetic expressions for depth-averaged SSC for vortex rippled beds and sheet flow conditions were obtained. The proposed expressions involve several basic physical processes, including the effects of bed forms, stratification, hindered settling, mobile bed, etc. A number of experimental datasets were collected for verification and reasonable results were obtained. Discussions were made on the changes of sediment concentration under increasing wave dynamics conditions, which show that the proposed formulas can describe the phenomenon which has been observed in experimental tests that SSC does not always increase when wave dynamics increase due to the effects of bed forms. In short, the current research provides a process-based approach for wave-induced sediment carrying capacity, which is expected to be applicable for numerical modeling and engineering practice.

Analytical model for the suspended sediment concentration in the ice-covered alluvial channels

Ice cover formed on an alluvial channel can significantly alter the flow characteristics, such as the vertical distributions of streamwise velocity and shear stress, and hence the water and sediment transport process. The vertical profile of the suspended sediment concentration in the ice-covered alluvial channels with steady uniform flows is investigated in this study. To calculate the suspended sediment concentration, we are based on the Schmidt O’Brien equation and deduce an analytical model that employs an existing eddy viscosity model and a modified formula of the sediment fall velocity considering the common effects of the upper and lower boundaries. The proposed analytical model is then validated by using available experimental data reported in the literature. The predicted accuracy of the proposed model is evaluated through error statistics by comparing to previous modeled results. The relative concentration profiles of the suspended sediment are subsequently simulated by applying the validated analytical model with different characteristic parameters. Results show that the relative concentration decreases with the increase of both the ice cover roughness and the sediment fall velocity. The uniformity of the relative concentration distribution is closely related to the value of the proportionality parameter σ, revealing the physical mechanism that the more prominent the turbulent diffusion effect is, the more uniform the relative concentration profile is.

The Influence of Slipface Angle on Fluvial Dune Growth

AbstractDunes dominate the bed of sandy rivers and they respond to flow by changing shape and size, modifying flow, and sediment transport dynamics of rivers. Our understanding of and ability to predict dune adaptation, particularly dune growth and decay, remain incomplete. Here, we investigate dune growth from an initial flatbed in a laboratory setting by continuously mapping the 3D bed topography using a line laser scanner combined with a 3D camera. High‐resolution profiles of flow velocity and sediment concentration providing both bedload and suspended sediment fluxes were obtained by deploying Acoustic Concentration and Velocity Profiler technology. Our analysis reveals that the magnitude of the dune slipface angle, which determines flow separation and controls turbulence production, adjusts to the imposed flow at time scales similar to the evolution of dune height and length. The initiation of a flow separation zone intensifies through scour, and results in acceleration of the dune growth. Gradients in sediment transport and the rate of dune growth are inherently linked to spatial variations in slipface angles. During dune growth, the slipface angle evolves differently than the ratio of dune height to length, which immediately reaches its equilibrium value after dune initiation.

Analytical solutions for sediment concentration in waves based on linear diffusivity

Two kinds of analytical solutions are derived through Laplace transform for the equation that governs wave-induced suspended sediment concentration with linear sediment diffusivity under two kinds of bottom boundary conditions, namely the reference concentration (Dirichlet) and pickup function (Numann), based on a variable transformation that is worked out to transform the governing equation into a modified Bessel equation. The ability of the two analytical solutions to describe the profiles of suspended sediment concentration is discussed by comparing with different experimental data. And it is demonstrated that the two analytical solutions can well describe the process of wave-induced suspended sediment concentration, including the amplitude and phase and vertical profile of sediment concentration. Furthermore, the solution with boundary condition of pickup function provides better results than that of reference concentration in terms of the phase-dependent variation of concentration.