Sediment transport on rippled beds

Form resistance, which includes pressure drag on bed forms and pressure and viscous drag on bed particles in transport, is shown to be a major component of hydraulic roughness in steady, quasi‐uniform, two‐dimensional turbulent flow over mobile gravel beds. Dimensionless form shear stress exceeds dimensionless particle shear stress for values of about three times critical Shields stress in subcritical flow, and five times in supercritical flow. Theoretical analysis provides a physical basis for expressing friction factor as a function of particle friction factor, estimated by the Keulegan equation, and the ratio of form to particle shear stress, termed relative form shear stress. Dimensional reasoning and empirical modeling of flume data demonstrate that relative form shear stress depends on Shields stress and relative roughness in subcritical and upper supercritical flow regimes, and on relative roughness alone in the lower supercritical regime. In particular, for given Shields stress and increasing relative roughness, relative form shear stress increases in subcritical flow because of bed form influences but decreases in supercritical flow owing to transport rate effects. Predictive relations for relative form shear stress allow an explicit solution of the depth‐discharge problem for mobile gravel beds.

Force and torque model sensitivity and coarse graining for bedload-dominated sediment transport

Assessing sediment transport dynamics from energy perspective by using the instrumented particle

Fluctuations and particle transport in the scrape-off layer of TCV plasmas have been investigated by probe measurements and direct comparison with two-dimensional interchange turbulence simulations at the outer midplane. The experiments demonstrate that with increasing line-averaged core plasma density, the radial particle density profile scale length becomes broader. The particle and radial flux density statistics in the far scrape-off layer exhibit a high degree of statistical similarity with respect to changes in the line-averaged density. The plasma flux onto the main chamber wall at the outer midplane scales linearly with the local particle density, suggesting that the particle flux here can be parameterized in terms of an effective convection velocity. Experimental probe measurements also provide evidence for significant parallel flows in the scrape-off layer caused by ballooning in the transport of particles and heat into the scrape-off layer. The magnitude of this flow estimated from pressure fluctuation statistics is found to compare favourably with the measured flow offset derived by averaging data obtained from flow profiles observed in matched forward and reversed field discharges. An interchange turbulence simulation has been performed for a single, relatively high density case, where comparison between code and experiment has been possible. Good agreement is found for almost all aspects of the experimental measurements, indicating that plasma fluctuations and transport in TCV scrape-off layer plasmas are dominated by radial motion of filamentary structures.

<p>Despite the fact sediment transport has been studied for decades, there is still a need to gain a further insight on the nature and driving mechanisms of bed particle motions induced by turbulent flows, for the low transport stages where the particle transport is relatively intermittent. A custom designed and prototyped instrumented particle, embedded with inertial sensors is used herein to study its transport over hydraulically rough bed surfaces. The calibration and error estimation for its sensors is also undertaken before starting the experiments, to ensure optimal operation and estimate any uncertainties.</p><p>The observations and results of this research are obtained from experiments carried out at the University of Glasgow 12 meters long and 0.9 meters wide, tilting and water recirculating flume. The flume walls comprise of smooth transparent glass that enables observing particle transport from the side (also with underwater video cameras) and the bed surface generally is layered with coarse gravel.</p><p>The particle is initially located at the upstream end of the test configuration, fully exposed to the uniform and fully developed turbulent channel flow. The top and side cameras are set in their suitable positions to monitor and study the behaviour of particle motion by capturing the dynamical features of sediment motion and to not interfere with flow field that pushes particle downstream.<span> </span></p><p>Using the sensor data to calculate the kinetic energy for a range of sets of sediment transport experiments with varying flow rates and particle densities, the probability distribution functions (PDFs) of particle transport features, such as particle’s total energy, are generated which give information about particle interaction with the surface bed during its motion. In addition, the effects of different flow rates, particle densities on particle energy are assessed.</p>

Here we observe the spatial and temporal patterns that erosion fronts driven by pulsed radial wall jets develop in double ring arrays of pulse tubes within slurry mixing vessels with curved bottoms. Although erosion of unbounded particle beds driven by individual steady jets has been studied for decades, the patterns developed within mixing vessels as neighboring transient erosion fronts collide and the subsequent relaxation of the particle bed towards the vessel center when the jets stop (i.e., as the pulse tubes refill within mixing vessels) remain incompletely understood. Relaxation here refers to motion of fluidized particle beds that were driven toward the vessel seam by radial wall jets that subsequently return or relax from the seam toward the center of the vessel when the jets turn off. Relaxation does not refer to downward individual or hindered particle settling. Spatial variations in the particle bed due to these relaxing particle beds comprise an important “initial” condition to the mathematical description of the evolution of the jet driven erosion front, and erosion fronts other than the one that expands radially from the pulse tube axis have only recently been described. For example, Bamberger, et al. (2017) [9], recently evaluated five selected cases of erosion patterns found in vessels 15 and 70 inches in diameter with 2:1 semi-elliptical bottoms. A highlight of that study was the discovery of a second type of erosion front that forms at the plane of symmetry between two adjacent pulse tubes. As neighboring radial wall jets collide they form an upwelling sheet of fluid; this second type of erosion front forms immediately beneath this upwelling flow. However, variations in this type of planar erosion front have not been cataloged previously. In this study, we systematically probe the erosion fronts driven by these upwelling sheets in greater detail and evaluate the relaxation of the particle bed to its “initial” condition after the pulse ceases. Variations in the erosion patterns and particle bed relaxation are evaluated as a function of particle concentration, density, and size. This study specifically focusses on video images collected from the 15 inch vessel because it provides distinctive visualization of erosion pattern behavior. We find the upwelling sheets to be more influential on the erosion patterns at lower particle concentrations, making these findings particularly important to low solids concentration vessels. At lower particle concentrations, flow at the base of the plane of symmetry readily erodes particle beds. At higher particle concentrations, piles of unmobilized solids accumulate beneath colliding jets either because the erosion mechanism vanishes or because erosion at the plane of symmetry is slow compared to radial erosion. We also find that the upwelling sheets introduce a flow that drives erosion patterns from outer ring jets toward the vessel center along the curved vessel floor along the plane of symmetry between nozzles. We further find that the rate of particle bed relaxation back toward the vessel center after the pulse ceases may correlate with concentration, particle density, and size. Higher concentrations and particle densities relax faster. The rate at which the entire bed relaxes toward the vessel center is faster near the vessel seam but slows as the relaxing front approaches the vessel center. This paper discusses competing mechanisms to explain these observations, including particle rolling, bed avalanches, gravity driven fluidized bed motion, and suspended particle sedimentation.

Abstract. Understanding the mechanics of bed load at the flood scale is necessary to link hydrology to landscape evolution. Here we report on observations of the transport of coarse sediment tracer particles in a cobble-bedded alluvial river and a step-pool bedrock tributary, at the individual flood and multi-annual timescales. Tracer particle data for each survey are composed of measured displacement lengths for individual particles, and the number of tagged particles mobilized. For single floods we find that measured tracer particle displacement lengths are exponentially distributed; the number of mobile particles increases linearly with peak flood Shields stress, indicating partial bed load transport for all observed floods; and modal displacement distances scale linearly with excess shear velocity. These findings provide quantitative field support for a recently proposed modeling framework based on momentum conservation at the grain scale. Tracer displacement is weakly negatively correlated with particle size at the individual flood scale; however cumulative travel distance begins to show a stronger inverse relation to grain size when measured over many transport events. The observed spatial sorting of tracers approaches that of the river bed, and is consistent with size-selective deposition models and laboratory experiments. Tracer displacement data for the bedrock and alluvial channels collapse onto a single curve – despite more than an order of magnitude difference in channel slope – when variations of critical Shields stress and flow resistance between the two are accounted for. Results show how bed load dynamics may be predicted from a record of river stage, providing a direct link between climate and sediment transport.

<p>Bed particle motion as bedload entrainment in riverine flows is a topic of interest in scientific and engineering fields. It is responsible for erosion and sedimentation, essential for designing hydraulic structures and river and basin management. Stochastic processes govern the physics of coarse particle motion due to particle-particle (here, bed particles) and fluid-particle interrelations, yet not mainly considered for estimating and describing the bedload flux and motions. Therefore, authentic knowledge of bed particle behavior in different phases of entrainment and transport might lead to a better description of the phenomenon. This study contributes to applying a non-intrusive particle monitoring technique, i.e., an embedded micro-electromechanical system (MEMS) as “smart particle” [1], to explore and monitor the dynamics of the initial and the bed particle motion near- and above threshold conditions.</p><p><span>Additionally, the imaging technique was deployed to track and monitor the instantaneous particle velocity and displacement during the transport, which was also applied as a complementary technique to calibrate and assess the MEMS sensor results [2]. The dynamics of incipient particle motion and particle transport were evaluated in sets of hydraulic flume experiments (by applying the instrumented particle) for different flow conditions, which deliver distinct particle entrainment and transport regimes [3-5]. The stochastic frameworks, which best described the hydrodynamic aspects of the entrainment and transport conditions, were chosen and discussed in relation to the near riverbed surface flow hydrodynamic conditions for better comprehension of the conditions leading to incipient entrainment and relatively low bedload transport stages. </span></p><p> </p><p>References</p><p>[1] Valyrakis, M., Alexakis, A. (2016). Development of a “smart-pebble” for tracking sediment 2transport. River Flow 2016, MO, USA.</p><p>[2] Valyrakis, M., Farhadi, H. (2017). Investigating coarse sediment particles transport using PTV and “smart-pebbles”instrumented with inertial sensors, EGU General Assembly 2017, Vienna, Austria, 23-28 April 2017, id. 9980.</p><p>[3] Farhadi, H. and Valyrakis, M. (2021). Exploring probability distribution functions best-fitting the kinetic energy of coarse particles at above threshold flow conditions. In <em>EGU General Assembly Conference Abstracts</em> (pp. EGU21-1820).</p><p>[4] AlObaidi, K., Xu, Y., and Valyrakis, M. (2020). The Design and Calibration of Instrumented Particles for Assessing Water Infrastructure Hazards, Journal of Sensor and Actuator Networks, 2020, 9(3), pp.36(1-18), DOI: 10.3390/jsan9030036.</p><p>[5] AlObaidi, K. and Valyrakis, M. (2021). Linking the explicit probability of entrainment of instrumented particles to flow hydrodynamics. Earth Surface Processes and Landforms, 46(12), pp.2448-2465.</p>

Understanding incipient sediment transport is crucial for predicting landscape evolution, mitigating flood hazards, and restoring riverine habitats. Observations show that the critical Shields stress increases with increasing channel bed slope, and proposed explanations for this counterintuitive finding include enhanced form drag from bed forms, particle interlocking across the channel width, and large bed sediment relative to flow depth (relative roughness). Here we use scaled flume experiments with variable channel widths, bed slopes, and particle densities to separate these effects which otherwise covary in natural streams. The critical Shields stress increased with bed slope for both natural gravel (ρs = 2.65 g/cm3) and acrylic particles (ρs = 1.15 g/cm3), and adjusting channel width had no significant effect. However, the lighter acrylic particles required a threefold higher critical Shields stress for mobilization relative to the natural gravel at a fixed slope, which is unexpected because particle density is accounted for directly in the definition of Shields stress. A comparison with model predictions indicates that changes in local velocity and turbulence associated with increasing relative roughness for lighter materials are responsible for increasing the critical Shields stress in our experiments. These changes lead to concurrent changes in the hydraulic resistance and a nearly constant critical stream power value at initial motion. Increased relative roughness can explain much of the observed heightened critical Shields stresses and reduced sediment transport rates in steep channels and also may bias paleohydraulic reconstructions in environments with exotic submerged densities such as iron ore, pumice, or ice clasts on Titan.

Recent developments in the gyrokinetic theory have shown that, in a toroidal device, the Coriolis drift associated with the background plasma rotation significantly affects the small scale instabilities [A. G. Peeters et al., Phys. Rev. Lett. 98, 265003 (2007)]. The later study, which focuses on the effect of the Coriolis drift on toroidal momentum transport is extended in the present paper to heat and particle transport. It is shown numerically using the gyrokinetic flux-tube code GKW [A. G. Peeters and D. Strintzi, Phys. Plasmas 11, 3748 (2004)], and supported analytically, that the Coriolis drift and the parallel dynamics play a similar role in the coupling of density, temperature, and velocity perturbations. The effect on particle and heat fluxes increases with the toroidal rotation (directly) and with the toroidal rotation gradient (through the parallel mode structure), depends on the direction of propagation of the perturbation, increases with the impurity charge number and with the impurity mass to charge number ratio. The case of very high toroidal rotation, relevant to spherical tokamaks, is investigated by including the effect of the centrifugal force in a fluid model. The main effect of the centrifugal force is to decrease the local density gradient at the low field side midplane and to add an extra contribution to the fluxes. The conditions for which the inertial terms significantly affect the heat and particle fluxes are evidenced.

Longitudinal and lateral transport rates of uniform sediment and heterogeneous mixtures are measured experimentally with a laterally inclinable wind tunnel, and the sediment transport rates are formulated in terms of Shields stress, critical Shields stress and lateral inclination angle. The critical Shields stress of uniform and heterogeneous materials in air flow are observed to be much smaller than those in water flow. The critical shear velocity for each fraction size of heterogeneous mixtures does not depend on the size, which indicates that the incipient motion of sediment in air flow is the impact threshold. The amount of sediment transport in air flow increases at very large rate against Shields stress in the vicinity of the critical Shields stress. The ratio of lateral sediment transport to longitudinal one for heterogeneous mixtures is found to depend on the sediment size, because larger sizes feel the lateral gravitational force more than the finer ones.

The probability distribution of the fluctuating velocity in three dimensions and the near-bed shear stress (NBSS) of a channel with a deposit body were studied using mathematical statistics and the turbulent kinetic energy method, respectively. This analysis of the longitudinal and plane distributions of the NBSS under varying discharges, width ratios and lateral slopes will help further understanding of the laws of sediment incipient motion and transport in channels. It was found that the probability distribution of the near-bed vertical fluctuating velocity was closer to a normal distribution than that in the longitudinal and transversal directions. The NBSS did not change much in the upstream sections of the deposit body, but the difference between the left bank (near the deposit body) and the right bank (far away from the deposit body) was obvious in the sections near the deposit body and downstream. A high shear stress area was located in the transition zone between the main flow and the backflow. Introducing the backwater parameter β, an exponential relationship between the relative NBSS and β was determined, which will help in quick estimates of the NBSS in future practical projects.

Abstract

We present a mesoscopic description of the anomalous transport and reactions of particles in spiny dendrites. As a starting point we use two-state Markovian model with the transition probabilities depending on residence time variable. The main assumption is that the longer a particle survives inside spine, the smaller becomes the transition probability from spine to dendrite. We extend a linear model presented in Fedotov [Phys. Rev. Lett. 101, 218102 (2008)] and derive the nonlinear Master equations for the average densities of particles inside spines and parent dendrite by eliminating residence time variable. We show that the flux of particles between spines and parent dendrite is not local in time and space. In particular the average flux of particles from a population of spines through spines necks into parent dendrite depends on chemical reactions in spines. This memory effect means that one cannot separate the exchange flux of particles and the chemical reactions inside spines. This phenomenon does not exist in the Markovian case. The flux of particles from dendrite to spines is found to depend on the transport process inside dendrite. We show that if the particles inside a dendrite have constant velocity, the mean particle's position <x(t)> increases as t(μ) with μ<1 (anomalous advection). We derive a fractional advection-diffusion equation for the total density of particles.

The mass transfer rate in fluidized beds of inert particles (FIB) is shown to be dependent on the electrolyte flow velocity and the intensity of particle collisions with the electrode. The influence of particle size and density on the ratio of the magnitude of these two influences on the mass transfer rate in a FIB was studied. Use of particle materials of varying density in an FIB permits variation of the two effects. The influence of collision currents prevails in FIBs of low density materials, and the influence of interstitial velocity is dominant in beds of high density material. The ratio of these factors also depends on the size of particles of the same density. With smaller particle size the influence of collision currents is greater. Smoothing of mass transfer maxima in beds of particles both of small and high density is explained. The results establish a basis for the selection of FIB materials for electrochemical processes.