Tobias Böhm

Bio: Tobias Böhm is an academic researcher. The author has contributed to research in topics: Bed load & Saltation (geology). The author has an hindex of 6, co-authored 8 publications receiving 445 citations.

Entrainment and motion of coarse particles in a shallow water stream down a steep slope

Abstract: We investigate the entrainment, deposition and motion of coarse spherical particles within a turbulent shallow water stream down a steep slope. This is an idealization of bed-load transport in mountain streams. Earlier investigations have described this kind of sediment transport using empirical correlations or concepts borrowed from continuum mechanics. The intermittent character of particle transport at low-water discharges led us to consider it as a random process. Sediment transport in this regime results from the imbalance between entrainment and deposition of particles rather than from momentum balance between water and particles. We develop a birth–death immigration–emigration Markov process to describe the particle exchanges between the bed and the water stream. A key feature of the model is its long autocorrelation times and wide, frequent fluctuations in the solid discharge, a phenomenon never previously explained despite its ubiquity in both nature and laboratory experiments. We present experimental data obtained using a nearly two-dimensional channel and glass beads as a substitute for sediment. Entrainment, trajectories, and deposition were monitored using a high-speed digital camera. The empirical probability distributions of the solid discharge and deposition frequency were properly described by the theoretical model. Experiments confirmed the existence of wide and frequent fluctuations of the solid discharge, and revealed the existence of long autocorrelation time, but theory overestimates the autocorrelation times by a factor of around three. Particle velocity was weakly dependent on the fluid velocity contrary to the predictions of the theoretical model, which performs well when a single particle is moving. For our experiments, the dependence of the solid discharge on the fluid velocity is entirely controlled by the number of moving particles rather than by their velocity. We also noted significant changes in the behaviour of particle transport when the bed slope or the water discharge was increased. The more vigorous the stream was, the more continuous the solid discharge became. Moreover, although 90% of the energy supplied by gravity to the stream is dissipated by turbulence for slopes lower than 10%, particles dissipate more and more energy when the bed slope is increased, but surprisingly, the dissipation rate is nearly independent of fluid velocity. A movie is available with the online version of the paper.

Statistical description of sediment transport experiments

Abstract: A longstanding problem in the study of sediment transport in gravel-bed rivers is related to the physical mechanisms governing bed resistance and particle motion. To study this problem, we investigated the motion of coarse spherical glass beads entrained by a steady shallow turbulent water flow down a steep two-dimensional channel with a mobile bed. This experimental facility is the simplest representation of sediment transport on the laboratory scale, with the tremendous advantages that boundary conditions are perfectly controlled and a wealth of information can be obtained using imaging techniques. Flows were filmed from the side by a high-speed camera. Using image processing software made it possible to determine the flow characteristics such as particle trajectories, their state of motion (rest, rolling, or saltating motion), and flow depth. In accordance with earlier investigations, we observed that over short time periods, sediment transport appeared as a very intermittent process. To interpret these results, we revisited Einstein's theory on sediment and derived the statistical properties (probability distribution and autocorrelation function) of the key variables such as the solid discharge and the number of moving particles. Analyzing the autocorrelation functions and the probability distributions of our measurements revealed the existence of long-range correlations. For instance, whereas theory predicts a Binomial distribution for the number of moving particles, experiments demonstrated that a negative binomial distribution best fit our data, which emphasized the crucial role played by wide fluctuations. These frequent wide fluctuations stemmed particle entrainment and motion being collective phenomena rather than individual processes, contrary to what is assumed in most theoretical models.

Two-dimensional motion of a set of particles in a free surface flow with image processing

Abstract: A method to analyze bed load with image processing was developed. The motion of coarse spherical particles on a mobile bed entrained by a shallow turbulent flow down a steep channel was filmed with a high-speed camera. The water free surface and the particle positions were detected combining classical image processing algorithms. We developed a particle-tracking algorithm to calculate all particle trajectories and motion regimes, rolling or saltation. At constant slope, the contribution of the rolling particles to the solid discharge only slightly differed when the particle supply was increased. At a slope of 10%, it represented about 40%. In contrast, rolling became the major regime when the slope increased, at a slope of 15% it represented up to 80% of the total solid discharge.

Fluctuations of the solid discharge of gravity-driven particle flows in a turbulent stream.

Abstract: Substantial variations in the particle flux are commonly observed in field measurements on gravel-bed rivers and in laboratory experiments mimicking river behavior on a smaller scale. These fluctuations can be explained by the natural variability of sediment supply and hydraulic conditions. We conducted laboratory experiments of particle transport down a two-dimensional inclined channel, for which the boundary conditions were properly controlled. Most flow variables and the features of particle trajectories were measured using a high-speed camera. The particles were 6-mm glass beads entrained by a rapid, turbulent, supercritical water flow. Even under these well-controlled experimental conditions and despite steady supply, solid discharge exhibited significant variations with time. The objective of this paper was to pinpoint the origins of these fluctuations by investigating different flow conditions. Two experiments were done with a fixed (smooth or corrugated) channel bottom and two others were run with a mobile bed (involving layers of closely packed particles lying along the channel base, which could be entrained by the stream); in the latter case, two particle arrangements were tested. It was found that, to a large extent, fluctuations reflected the finite size of the observation window. For fixed beds, the characteristic time scale of fluctuations and their probability distribution can be predetermined by evaluating the mean and fluctuating velocities of a single particle. Solid-discharge fluctuations were exacerbated when the bed was mobile because (i) the moving solid phase and the stationary bed exchanged particles and (ii) collective entrainment of particles occurred.

Image processing for the study of bedload transport of two-size spherical particles in a supercritical flow

Abstract: Bedload sediment transport of two-size coarse spherical particle mixtures in a turbulent supercritical flow was analyzed with image and particle tracking velocimetry algorithms in a two-dimensional flume. The image processing procedure is entirely presented. Experimental results, including the size, the position, the trajectory, the state of movement (rest, rolling, and saltation), and the neighborhood configuration of each bead, were compared with a previous one-size experiment. Analysis of the solid discharge along the vertical displayed only one peak of rolling in the two-size bed, whereas three peaks of rolling appeared in the one-size case due to a larger collective motion. The same contrast is evidenced in spatio-temporal diagrams where the two-size mixtures are characterized by the predominance of saltation and a smaller number of transitions between rest and rolling. The segregation of fine particles in a bed formed by larger particles was analyzed taking into account the neighborhood configurations.

Turbulence in open-channel flows

Abstract: Part I presents the statistical theory of turbulence, and Part 2 the coherent structures in open-channel flows and boundary layers. The book is intended for advanced students and researchers in hydraulic research, fluid mechanics, environmental sciences and related disciplines. References Index.

Entrainment and motion of coarse particles in a shallow water stream down a steep slope

Abstract: We investigate the entrainment, deposition and motion of coarse spherical particles within a turbulent shallow water stream down a steep slope. This is an idealization of bed-load transport in mountain streams. Earlier investigations have described this kind of sediment transport using empirical correlations or concepts borrowed from continuum mechanics. The intermittent character of particle transport at low-water discharges led us to consider it as a random process. Sediment transport in this regime results from the imbalance between entrainment and deposition of particles rather than from momentum balance between water and particles. We develop a birth–death immigration–emigration Markov process to describe the particle exchanges between the bed and the water stream. A key feature of the model is its long autocorrelation times and wide, frequent fluctuations in the solid discharge, a phenomenon never previously explained despite its ubiquity in both nature and laboratory experiments. We present experimental data obtained using a nearly two-dimensional channel and glass beads as a substitute for sediment. Entrainment, trajectories, and deposition were monitored using a high-speed digital camera. The empirical probability distributions of the solid discharge and deposition frequency were properly described by the theoretical model. Experiments confirmed the existence of wide and frequent fluctuations of the solid discharge, and revealed the existence of long autocorrelation time, but theory overestimates the autocorrelation times by a factor of around three. Particle velocity was weakly dependent on the fluid velocity contrary to the predictions of the theoretical model, which performs well when a single particle is moving. For our experiments, the dependence of the solid discharge on the fluid velocity is entirely controlled by the number of moving particles rather than by their velocity. We also noted significant changes in the behaviour of particle transport when the bed slope or the water discharge was increased. The more vigorous the stream was, the more continuous the solid discharge became. Moreover, although 90% of the energy supplied by gravity to the stream is dissipated by turbulence for slopes lower than 10%, particles dissipate more and more energy when the bed slope is increased, but surprisingly, the dissipation rate is nearly independent of fluid velocity. A movie is available with the online version of the paper.

A probabilistic description of the bed load sediment flux: 1. Theory

Abstract: [1] We provide a probabilistic definition of the bed load sediment flux. In treating particle positions and motions as stochastic quantities, a flux form of the Master equation (a general expression of conservation) reveals that the volumetric flux involves an advective part equal to the product of an average particle velocity and the particle activity (the solid volume of particles in motion per unit streambed area), and a diffusive part involving the gradient of the product of the particle activity and a diffusivity that arises from the second moment of the probability density function of particle displacements. Gradients in the activity, instantaneous or time-averaged, therefore effect a particle flux. Time-averaged descriptions of the flux involve averaged products of the particle activity, the particle velocity and the diffusivity; the significance of these products depends on the scale of averaging. The flux form of the Exner equation looks like a Fokker-Planck equation (an advection-diffusion form of the Master equation). The entrainment form of the Exner equation similarly involves advective and diffusive terms, but because it is based on the joint probability density function of particle hop distances and associated travel times, this form involves a time derivative term that represents a lag effect associated with the exchange of particles between the static and active states. The formulation is consistent with experimental measurements and simulations of particle motions reported in companion papers.

Experimental evidence for statistical scaling and intermittency in sediment transport rates

Abstract: [1] Understanding bed load transport fluctuations in rivers is crucial for development of a transport theory and for choosing a sampling interval for “mean” transport rates. Field-scale studies lack sufficient resolution to statistically characterize these fluctuations, while laboratory experiments are limited in scale and hence cannot be directly compared to field cases. Here we use a natural-scale laboratory channel to examine bed load transport fluctuations in a heterogeneous gravel substrate under normal flow conditions. The novelty of our approach is the application of a geometrical/statistical formalism (called the multifractal formalism), which allows characterization of the “roughness” of the series (depicting the average strength of local abrupt fluctuations in the signal) and the “intermittency” (depicting the temporal heterogeneity of fluctuations of different strength). We document a rougher and more intermittent behavior in bed load sediment transport series at low-discharge conditions, transitioning to a smoother and less intermittent behavior at high-discharge conditions. We derive an expression for the dependence of the probability distribution of bed load sediment transport rates on sampling interval. Our findings are consistent with field observations demonstrating that mean bed load sediment transport rate decreases with sampling time at low-transport conditions and increases with sampling time at high-transport conditions. Simultaneous measurement of bed elevation suggests that the statistics of sediment transport fluctuations are related to the statistics of bed topography.