An official website of the United States government
Abstract Predicting the transport of bedload tracer particles is a problem of significant theoretical and practical interest. Yet, little understanding exists for transport in rivers in the presence of bedforms, which may trap grains and thereby influence travel distance. In a series of flume experiments with a sandy gravel bed in a large experimental flume, bed elevation and tracer travel distances were measured at high resolution for a range of discharges. As discharge increased, bedform height increased and bedform length decreased, increasing bedform steepness. For all tracer sizes and flow conditions, bedforms act as primary controls on the tracer travel distances. Bedform trapping increases linearly with the ratio of bedform height to tracer grain size, with 50% trapping efficiency for a ratio of two and 90% trapping efficiency for a ratio of four. A theoretical model based on the extended active layer formulation for sediment transport is able to capture much of the distribution of measured travel distances for all tracer sizes and discharges, providing a first connection between tracer transport theory and bedform trapping and indicating normal diffusion of tracers at relatively small timescales. Variable bedform geometry can influence trap efficiency for individual bedforms and the theoretical model can help identify “preferential trapping” conditions. The distribution of tracer travel distances for a mixture of grain sizes and variable discharge, as expected in natural rivers, displays heavy tail characteristics.
more »
« less
Streamwise and Vertical Dispersal of Tracer Stones in an Equilibrium Bed
Abstract Modeling transport, erosion, and deposition of nonuniform sediment over temporal intervals that are short compared to those characterizing channel bed aggradation and degradation remains an open problem due to the complex quantification of the sediment fluxes between the bed material load and the alluvial deposit. Parker, Paola, and Leclair in 2000 proposed a morphodynamic (PPL) framework to overcome this problem. This framework is used here to model the dispersal of a patch of gravel tracers in three different settings, a laboratory flume, a mountain creek, and a braided river. To simplify the problem, (a) the bed slope, bedload transport rate, and bed configuration are assumed to be constant in space and time (equilibrium), (b) sediment entrainment and deposition are modeled with a constant step length formulation, and (c) the PPL framework is implemented in a one‐dimensional (laterally averaged) model. Model validation against laboratory experiments suggests that, as the transport capacity of the flow increases, the maximum elevation‐specific density of sediment entrainment may migrate downward in the deposit. The comparison between model results and field data shows that the equilibrium solution can reasonably capture tracer dispersal. The equilibrium model can also reproduce subdiffusion and superdiffusion of a patch of tracers in the streamwise direction, depending on the magnitude of the short‐term bed level changes. Finally, the average tracer elevation in a cross‐section decreases in time because particles that are buried deep in the deposit are only rarely reentrained into bedload transport.
more »
« less
- Award ID(s):
- 1751926
- PAR ID:
- 10382544
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Water Resources Research
- Volume:
- 58
- Issue:
- 11
- ISSN:
- 0043-1397
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Vegetation provides habitat and nature‐based solutions to coastal flooding and erosion, drawing significant interest in its restoration, which requires an understanding of sediment transport and retention. Laboratory experiments examined the influence of stem diameter and arrangement on bedload sediment transport by considering arrays of different stem diameter and mixed diameters. Bedload transport rate was observed to depend on turbulent kinetic energy, with no dependence on stem diameter, which was shown to be consistent with the impulse model for sediment entrainment. Existing predictors of bedload transport for bare beds, based on bed shear stress, were recast in terms of turbulence. The new turbulence‐based model predicted sediment transport measured in model canopies across a range of conditions drawn from several previous studies. A prediction of turbulence based on biomass and velocity was also described, providing an important step toward predicting turbulence and bedload transport in canopies of real vegetation morphology.more » « less
-
Abstract Riverbed elevations play a crucial role in sediment transport and flow resistance, making it essential to understand and quantify their effects. This knowledge is vital for various fields, including river engineering and stream ecology. Previous observations have revealed that fluctuations in the bed surface can exhibit both multifractal and monofractal behaviors. Specifically, the probability distribution function (PDF) of elevation increments may transition from Laplace (two‐sided exponential) to Gaussian with increasing scales or consistently remain Gaussian, respectively. These differences at the finest timescale lead to distinct patterns of bedload particle exchange with the bed surface, thereby influencing particle resting times and streamwise transport. In this paper, we utilize the fractional Laplace motion (FLM) model to analyze riverbed elevation series, demonstrating its capability to capture both mono‐ and multi‐fractal behaviors. Our focus is on studying the resting time distribution of bedload particles during downstream transport, with the FLM model primarily parameterized based on the Laplace distribution of increments PDF at the finest timescale. Resting times are extracted from the bed elevation series by identifying pairs of adjacent deposition and entrainment events at the same elevation. We demonstrate that in cases of insufficient data series length, the FLM model robustly estimates the tail exponent of the resting time distribution. Notably, the tail of the exceedance probability distribution of resting times is much heavier for experimental measurements displaying Laplace increments PDF at the finest scale, compared to previous studies observing Gaussian PDF for bed elevation.more » « less
-
Abstract Aquatic vegetation has the potential to increase suspended sediment capture while also increasing sediment resuspension and bedload transport. Suspended sediment can induce density stratification, which modulates the turbulence in the water column. We derive a Rouse‐based formulation for suspended sediment concentration (SSC) including the effect of sediment‐induced density stratification. We perform Large Eddy Simulations of vegetated and non‐vegetated channels to explicitly highlight the effect of stratification on SSC profiles. We found that the impact of stratification is dominant in the near‐bed region within the bottom boundary layer, affecting both sediment resuspension and bedload transport. Stratification reduces the likelihood of both dominant sweep and ejection events in the near the bed region which may affect sediment entrainment and bedload transport. Modifications to existing models of sediment entrainment and bedload transport are suggested to account for the effects of sediment induced stratification in vegetated and non‐vegetated channels.more » « less
-
Abstract Accounting for the burial of tracer particles during bedload transport is an important component in the formulation of tracer dispersal in rivers. Herein we propose a modified active layer formulation, which accounts for the effect of burial and admits analytical solutions, enabling insightful exploration of the phenomenon of superdiffusion of bedload tracers at the intermediate timescale. This phenomenon has been observed in recent numerical results using the 2‐D Exner‐Based Master Equation. By assuming that tracers in the active layer can exchange with nontracer particles in the substrate layer to preserve mass, and that tracers entering the substrate layer get permanently trapped during the timescale of analysis, we are able to deduce governing equations for the tracer concentration in both layers. The active layer tracer concentration is shown to be governed by an advection‐diffusion equation with a sink term, and the increase of tracers in the substrate layer is driven by a corresponding source term. The solution for the variance of tracer population is analytically determined and can be approximated by the sum of a diffusion‐induced scaling (∝t1) and an advection‐induced scaling (∝t3) terms at the intermediate timescale, which explains the phenomenon of superdiffusion. The proposed formulation is shown to be able to capture the key characteristics of tracer transport as inferred by comparison with available results of numerical simulations.more » « less
