An official website of the United States government
Abstract To date, there is no consensus on the probability distribution of particle velocities during bedload transport, with some studies suggesting an exponential‐like distribution while others a Gaussian‐like distribution. Yet, the form of this distribution is key for the determination of sediment flux and the dispersion characteristics of tracers in rivers. Combining theoretical analysis of the Fokker‐Planck equation for particle motions, numerical simulations of the corresponding Langevin equation, and measurements of motion in high‐speed imagery from particle‐tracking experiments, we examine the statistics of bedload particle trajectories, revealing a two‐regime distance‐time (L‐Tp) scaling for the particle hops (measured from start to stop). We show that particles of short hop distances scale asL~giving rise to the Weibull‐like front of the hop distance distribution, while particles of long hop distances transition to a different scaling regime ofL~Tpleading to the exponential‐like tail of the hop distance distribution. By demonstrating that the predominance of mostly long hop particles results in a Gaussian‐like velocity distribution, while a mixture of both short and long hop distance particles leads to an exponential‐like velocity distribution, we argue that the form of the probability distribution of particle velocities can depend on the physical environment within which particle transport occurs, explaining and unifying disparate views on particle velocity statistics reported in the literature.
more »
« less
Modeling Riverbed Elevation and Bedload Tracer Transport Resting Times Using Fractional Laplace Motion
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
- Award ID(s):
- 1854452
- PAR ID:
- 10530950
- Publisher / Repository:
- AGU
- Date Published:
- Journal Name:
- Journal of Geophysical Research: Earth Surface
- Volume:
- 129
- Issue:
- 7
- ISSN:
- 2169-9003
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract. Despite a rich history of studies investigating fluid dynamics over bedforms and dunes in rivers, the spatiotemporal patterns of sub-bedform bedload transport remain poorly understood. Previous experiments assessing the effects of flow separation on downstream fluid turbulent structures and bedload transport suggest that localized, intermittent, high-magnitude transport events (i.e., permeable splat events) play an important role in both downstream and cross-stream bedload transport near flow reattachment. Here, we report results from flume experiments that assess the combined effects of flow separation–reattachment and flow re-acceleration over fixed two-dimensional bedforms (1.7 cm high; 30 cm long). A high-speed camera observed bedload transport along the entirety of the bedform at 250 frames per second. Grain trajectories, grain velocities, and grain transport directions were acquired from bedload images using semiautomated particle-tracking techniques. Downstream and vertical fluid velocities were measured 3 mm above the bed using laser Doppler velocimetry (LDV) at 15 distances along the bedform profile. Mean downstream fluid velocity increases nonlinearly with increasing distance along the bedform. However, observed bedload transport increases linearly with increasing distance along the bedform, except at the crest of the bedform, where both mean downstream fluid velocity and bedload transport decrease substantially. Bedload transport time series and manual particle-tracking data show a zone of high-magnitude, cross-stream transport near flow reattachment, suggesting that permeable splat events play an essential role in the region downstream of flow reattachment.more » « less
-
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
-
Abstract Recent theoretical models and field observations suggest that fluvial bedload flux can be estimated from seismic energy measured within appropriate frequency bands. We present an application of the Tsai et al. (2012,https://doi.org/10.1029/2011gl050255) bedload seismic model to an ephemeral channel located in the semi‐arid southwestern US and incorporate modifications to better estimate bedload flux in this environment. To test the model, we collected streambank seismic signals and directly measured bedload flux during four flash‐floods. Bedload predictions calculated by inversion from the Tsai model underestimated bedload flux observations by one‐to‐two orders of magnitude at low stages. However, model predictions were better for moderate flow depths (>50 cm), where saltation is expected to dominate bedload transport. We explored three differences between the model assumptions and our field conditions: (a) rolling and sliding particles have different impact frequencies than saltating particles; (b) the velocity and angle of impact of rolling particles onto the riverbed differ; and (c) the fine‐grained alluvial character of this and similar riverbeds leads to inelastic impacts, as opposed to the originally conceptualized elastic impacts onto rigid bedrock. We modified the original model to assume inelastic bed impacts and to incorporate rolling and sliding by adjusting the statistical distributions of bedload impact frequency, velocity, and angle. Our modified “multiple‐transport‐mode bedload seismic model” decreased error relative to observations to less than one order of magnitude across all measured flow conditions. Further investigations in other environmental settings are required to demonstrate the robustness and general applicability of the model.more » « less
-
Abstract While the ecological significance of hyporheic exchange and fine particle transport in rivers is well established, these processes are generally considered irrelevant to riverbed morphodynamics. We show that coupling between hyporheic exchange, suspended sediment deposition, and sand bedform motion strongly modulates morphodynamics and sorts bed sediments. Hyporheic exchange focuses fine-particle deposition within and below mobile bedforms, which suppresses bed mobility. However, deposited fines are also remobilized by bedform motion, providing a mechanism for segregating coarse and fine particles in the bed. Surprisingly, two distinct end states emerge from the competing interplay of bed stabilization and remobilization: a locked state in which fine particle deposition completely stabilizes the bed, and a dynamic equilibrium in which frequent remobilization sorts the bed and restores mobility. These findings demonstrate the significance of hyporheic exchange to riverbed morphodynamics and clarify how dynamic interactions between coarse and fine particles produce sedimentary patterns commonly found in rivers.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1029/2024JF007771
