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 dimensionless framework for predicting submarine fan morphology

Limited observations of active turbidity currents at field scales challenges the development of theory that links flow dynamics to the morphology of submarine fans. Here we offer a framework for predicting submarine fan morphologies by simplifying critical environmental forcings such as regional slopes and properties of sediments, through densimetric Froude (ratio of inertial to gravitational forces) and Rouse numbers (ratio of settling velocity of sediments to shear velocity) of turbidity currents. We leverage a depth-average process-based numerical model to simulate an array of submarine fans and measure rugosity as a proxy for their morphological complexity. We show a systematic increase in rugosity by either increasing the densimetric Froude number or decreasing the Rouse number of turbidity currents. These trends reflect gradients in the dynamics of channel migration on the fan surface and help discriminate submarine fans that effectively sequester organic carbon rich mud in deep ocean strata.

A dimensionless framework for predicting submarine fan morphology

A remarkable diversity exists in the morphology and dynamics of submarine fans, which influence the transport of microplastics, burial of organic carbon, subsea geo-hazards, and their potential to house geofluids and high-resolution paleo-environmental records. Like river deltas, submarine fan morphology is a product of evolving fluid and sediment transport fields, but unlike their terrestrial counterparts, we lack a unifying framework to predict their morphology. Here, we simplify critical environmental forcings, like regional slopes and sediment properties, through a dimensionless framework defined by the densimetric Froude number (ratio of inertial to gravitational forces) and Rouse number (ratio of settling velocity of sediments to shear velocity) of turbidity currents. We explore this framework by leveraging a depth-averaged numerical model and measure fan rugosity as a proxy for their morphological complexity. We show a systematic increase in rugosity by either increasing the densimetric Froude number or decreasing the Rouse number of the simulated flows. These changes reflect observed gradients in the dynamics of channel migration and help discriminate submarine fans that have the potential to impact global climate through sequestration of organic carbon.

Sedimentation Processes: Geomorphological evidence for staged sand dam construction

Steam sediment transport is a convolution of climate, weather, geology, topography, biology, and human influence. In addition to providing water and food security for dryland rural communities, sand dams—small weirs designed to trap only the coarse fractions of transported sediments in seasonal and ephemeral streams—illuminate many complexities of geomorphological dynamics. Sand dams store water in interstitial riverbed pores and the size of deposited sediment particles largely determines the recoverability of stored water: fine materials limit transmission and provide lower volumetric yield. Can a sand dam be designed for a particular reach-scale, hydro-sedimentary context to limit capture of fine particles? We argue that the Rouse number provides a useful criterion for identifying regimes where the target material grades are trapped. These ideas were tested using sediment data collected in Kenya and HEC-RAS numerical simulations to evaluate the sensitivity of sedimentation processes to spillway height. We show that constructing sand dams in stages results in more targeted trapping of coarse material. Surprisingly, sedimentation is shown to be more sensitive to variation in spillway height than the flood hydrograph, especially when a dam is short. A method for evaluating the need for spillway staging (essentially controlling the bedform) based on the modeled Rouse number allows evaluation of costs and expected benefits. Beyond sand dams, this supports the observation that for dryland streams with peaky flows and high sediment loading, local hydraulic controls are typically more diagnostic of streambed sediment composition than is the sediment source.

Formulae of Sediment Transport in Unsteady Flows (Part 2)

Sediment transport (ST) in unsteady flows is a complex phenomenon that the existing formulae are often invalid to predict. Almost all existing ST formulae assume that sediment transport can be fully determined by parameters in streamwise direction without parameters in vertical direction. Different from this assumption, this paper highlights the importance of vertical motion and the vertical velocity is suggested to represent the vertical motion. A connection between unsteadiness and vertical velocity is established. New formulae in unsteady flows have been developed from inception of sediment motion, sediment discharge to suspension’s Rouse number. It is found that upward vertical velocity plays an important role for sediment transport, its temporal and spatial alternations are responsible for the phase lag phenomenon and bedform formation. Reasonable agreement between the measured and the proposed conceptual model was achieved.

Entrainment and suspension of sand and gravel

Entrainment and suspension of sand and gravel is important for the evolution of rivers, deltas, coastal areas and submarine fans. The prediction of a vertical profile of suspended sediment concentration typically consists of assessing (1) the concentration near the bed using an entrainment relation and (2) the upward vertical distribution of sediment in the water column. Considerable uncertainty exists in regard to both of these steps, and especially the near-bed concentration. Most entrainment theories have been tested against limited grain-size specific data, and no relations have been evaluated for gravel suspension, which can be important in bedrock and mountain rivers, as well as powerful turbidity currents. To address these issues, we compiled a database with suspended sediment data from natural rivers and flume experiments, taking advantage of the increasing availability of high-resolution grain-size measurements. We evaluated 14 dimensionless parameters that may determine entrainment and suspension relations, and applied multivariate regression analysis. A best-fit two-parameter equation (r2 = 0.79) shows that near-bed entrainment, evaluated at 10 % of the flow depth, increases with the ratio of skin-friction shear velocity to settling velocity (u*skin / wsi), as in previous relations, and with Froude number (Fr), possibly due to its role in determining bedload-layer concentrations. We used the Rouse equation to predict concentration upward from the reference level, and evaluated the coefficient βi, which accounts for differences between turbulent diffusivities of sediment and momentum. The best-fit relation for βi (r2 = 0.40) indicates greater relative sediment diffusivities for rivers with greater flow resistance, possibly due to bed-form induced turbulence, and smaller u*skin / wsi; the latter effect makes the dependence of Rouse number on u*skin / wsi nonlinear, and therefore different from standard Rousean theory. In addition, we used empirical relations for gravel saltation to show that our relation for near-bed concentration also provides good predictions for coarse-grained sediment. The new relations are a significant improvement compared to previous work, extend the calibrated parameter space over a wider range in sediment sizes and flow conditions, and result in 95 % of concentration data predicted within a factor of nine.

An index concentration method for suspended load monitoring in large rivers of the Amazonian foreland

Because increasing climatic variability and anthropic pressures have affected the sediment dynamics of large tropical rivers, long-term sediment concentration series have become crucial for understanding the related socioeconomic and environmental impacts. For operational and cost rationalization purposes, index concentrations are often sampled in the flow and used as a surrogate of the cross-sectional average concentration. However, in large rivers where suspended sands are responsible for vertical concentration gradients, this index method can induce large uncertainties in the matter fluxes. Assuming that physical laws describing the suspension of grains in turbulent flow are valid for large rivers, a simple formulation is derived to model the ratio (α) between the depth-averaged and index concentrations. The model is validated using an exceptional dataset (1330 water samples, 249 concentration profiles, 88 particle size distributions and 494 discharge measurements) that was collected between 2010 and 2017 in the Amazonian foreland. The α prediction requires the estimation of the Rouse number (P), which summarizes the balance between the suspended particle settling and the turbulent lift, weighted by the ratio of sediment to eddy diffusivity (β). Two particle size groups, fine sediments and sand, were considered to evaluate P. Discrepancies were observed between the evaluated and measured P, which were attributed to biases related to the settling and shear velocities estimations, but also to diffusivity ratios β≠1. An empirical expression taking these biases into account was then formulated to predict accurate estimates of β, then P (ΔP=±0.03) and finally α. The proposed model is a powerful tool for optimizing the concentration sampling. It allows for detailed uncertainty analysis on the average concentration derived from an index method. Finally, this model could likely be coupled with remote sensing and hydrological modeling to serve as a step toward the development of an integrated approach for assessing sediment fluxes in poorly monitored basins.

An index concentration method for suspended load monitoring in large rivers of the Amazonian foreland

Because increasing climatic variability and anthropic pressures have affected the sediment dynamics of large tropical rivers, long-term sediment concentration series have become crucial for understanding the related socio-economic and environmental impacts. For operational and cost rationalization purposes, index concentrations are often sampled in the flow and used as a surrogate of the cross-sectional average concentration. However, in large rivers where suspended sands are responsible for vertical concentration gradients, this index method can induce large uncertainties in the matter fluxes. Assuming that physical laws describing the suspension of grains in turbulent flow are valid for large rivers, a simple formulation is derived to model the ratio (α) between index and average concentrations. The model is validated using an exceptional dataset (1330 water samples, 249 concentration profiles, 88 particle size distributions (PSDs) and 494 discharge measurements) that was collected between 2010 and 2017 in the Amazonian foreland. The α prediction requires the estimation of the Rouse number (P), which summarizes the balance between the suspended particle settling and the turbulent lift, weighted by the ratio of sediment to eddy diffusivity (β). Two particle size groups, washload and sand, were considered to evaluate P. Discrepancies were observed between the evaluated and measured P, that were attributed to biases related to the settling and shear velocities estimations, but also to diffusivity ratios β ≠ 1. An empirical expression taking into account these biases was then formulated to predict accurate estimates of β, then P (∆P = ±0.03) and finally α. The proposed model is a powerful tool for optimizing the concentration sampling. It allows for detailed uncertainty analysis on the average concentration derived from an index method. Finally, this model can be coupled with remote sensing and hydrological modeling to serve as a step toward the development of an integrated approach for assessing sediment fluxes in poorly monitored basins.

Theoretical Model of Suspended Sediment Concentration in a Flow with Submerged Vegetation

Vegetation in natural river interacts with river flow and sediment transport. This paper proposes a two-layer theoretical model based on diffusion theory for predicting the vertical distribution of suspended sediment concentration in a flow with submerged vegetation. The suspended sediment concentration distribution formula is derived based on the sediment and momentum diffusion coefficients through the inverse of turbulent Schmidt number ( S c t ) or the parameter η which is defined by the ratio of sediment diffusion coefficient to momentum diffusion coefficient. The predicted profile of suspended sediment concentration moderately agrees with the experimental data. Sensitivity analyses are performed to elucidate how the vertical distribution profile responds to different canopy densities, hydraulic conditions and turbulent Schmidt number. Dense vegetation renders the vertical distribution profile uneven and captures sediment particles into the vegetation layer. For a given canopy density, the vertical distribution profile is affected by the Rouse number, which determines the uniformity of the sediment on the vertical line. A high Rouse number corresponds to an uneven vertical distribution profile.

Mechanics of advection of suspended particles in turbulent flow

In this paper, we explore the mechanics and the turbulent structure of two-phase (fluid–solid particle) flow system, for the first time, by considering the dynamic equilibrium coupled with suspended solid particle concentration, fluid flow and energetics of the two-phase flow system. The continuity, momentum and turbulent kinetic energy (TKE) equations of the fluid and the solid phases are treated separately to derive a generalized relationship of the two-phase flow system aided by suitable closure relationships. The results obtained from the numerical solution of resulting equations show that the particle concentration and the TKE diminish with an increase in the Rouse number, while the horizontal velocity component increases. On the other hand, the TKE flux, diffusion and production rates increase with an increase in the Rouse number, while the TKE dissipation rate decreases. In the vicinity of the reference level (that is, the hypothetical level from which the particles come in suspension), the Kolmogorov number increases with an increase in the Rouse number. However, as the vertical distance increases, this behaviour becomes reverse. A close observation of the turbulent length scales reveals that the Prandtl's mixing length decreases with an increase in the Rouse number, but the Taylor microscale and the Kolmogorov length scale increase.