Sediment transport occurs when the nondimensional fluid shear stress $Θ$ at the bed surface exceeds a minimum value $Θ_c$. A large collection of data, known as the Shields curve, shows that $Θ_c$ is primarily a function of the shear Reynolds number ${\rm{Re}}_*$. It is commonly assumed that $Θ>Θ_c({\rm{Re}}_*)$ occurs when the ${\rm Re}_*$-dependent fluid forces are too large to maintain static equilibrium for a typical surface grain. A complimentary approach, which remains relatively unexplored, is to identify $Θ_c({\rm{Re}}_*)$ as the applied shear stress at which grains cannot stop moving. With respect to grain dynamics, ${\rm{Re}}_*$ can be viewed as the viscous time scale for a grain to equilibrate to the fluid flow divided by the typical time for the fluid force to accelerate a grain over the characteristic bed roughness. We performed simulations of granular beds sheared by a model fluid, varying only these two time scales. We find that the critical Shields number $Θ_c({\rm Re}_*)$ obtained from the model mimics the Shields curve and is insensitive to the grain properties, the model fluid flow, and the form of the drag law. Quantitative discrepancies between the model results and the Shields curve are consistent with previous calculations of lift forces at varying ${\rm Re}_*$. Grains at low ${\rm Re}_*$ find more stable configurations than those at high ${\rm{Re}}_*$ due to differences in the grain reorganization dynamics. Thus, instead of focusing on mechanical equilibrium of a typical grain at the bed surface, $Θ_c({\rm{Re}}_*)$ may be better described by the stress at which mobile grains cannot find a stable configuration and stop moving.
Sediment transport is studied as a function of the grain to fluid density ratio using two phase numerical sim- ulations based on a discrete element method (DEM) for particles coupled to a continuum Reynolds averaged description of hydrodynamics. At a density ratio close to unity (typically under water), vertical velocities are so small that sediment transport occurs in a thin layer at the surface of the static bed, and is called bed load. Steady, or 'saturated' transport is reached when the fluid borne shear stress at the interface between the mobile grains and the static grains is reduced to …
We present a thermodynamically consistent constitutive model for fluid-saturated sediments, spanning dense to dilute regimes, developed from the basic balance laws for two phase-mixtures. The model can represent various limiting cases, such as pure fluid and dry grains. It is formulated to capture a number of key behaviors such as: (i) viscous inertial rheology of submerged wet grains under steady shearing flows, (ii) the critical state behavior of grains, which causes granular Reynolds dilation/contraction due to shear, (iii) the viscous thickening of the fluid response due to the presence of…
A function for the bed-load sediment transport rate is derived. This is achieved from the first principle by using the entrainment probabilities of the sediment grains by rolling and lifting, and by introducing two travel lengths, respectively, for the first time. The predictions from the new bed-load function agree well with the experimental results over the entire experimental range and show significant improvement over the commonly used formula for bed-load transport rate. The new function shows that, in terms of contributing to the bed-load transport rate, the total entrainment probability…
Nonsuspended sediment transport (NST) refers to the sediment transport regime in which the flow turbulence is unable to support the weight of transported grains. It occurs in fluvial environments (i.e., driven by a stream of liquid) and in aeolian environments (i.e., wind-blown) and plays a key role in shaping sedimentary landscapes of planetary bodies. NST is a highly fluctuating physical process because of turbulence, surface inhomogeneities, and variations of grain size and shape and packing geometry. Furthermore, the energy of transported grains varies strongly due to variations of their f…
The critical fluid-shear stress for the onset of sediment transport, $θ_c$, varies with the history of applied shear. This effect has been attributed to compaction, but the role of shear jamming is unexplored. We examine the response of a granular bed to fluid-shear stress cycles of varying magnitude and direction, and determine isotropic and anisotropic contributions. Creep and bed-load transport result in direction-dependent strain hardening for $θ/θ_c < 4$. Dilation-induced weakening, and memory loss, occurs for larger stresses that fluidize the bed. Our findings provide a granular explanat…
Aeolian sand beds exhibit regular patterns of ripples resulting from the interaction between topography and sediment transport. Their characteristics have been so far related to reptation transport caused by the impacts on the ground of grains entrained by the wind into saltation. By means of direct numerical simulations of grains interacting with a wind flow, we show that the instability turns out to be driven by resonant grain trajectories, whose length is close to a ripple wavelength and whose splash leads to a mass displacement towards the ripple crests. The pattern selection results from …
We performed molecular dynamics simulations of granular beds driven by a model hydrodynamic shear flow to elucidate general grain-scale mechanisms that determine the onset and cessation of sediment transport. By varying the Shields number (the nondimensional shear stress at the top of the bed) and particle Reynolds number (the ratio of particle inertia to viscous damping), we explore how variations of the fluid flow rate, particle inertia, and fluid viscosity affect the onset and cessation of bed motion. For low to moderate particle Reynolds numbers, a critical boundary separates mobile and st…
The characteristic time-dependent viscosity of the intergranular pore-fluid in Buckingham's grain-shearing (GS) model [Buckingham, J. Acoust. Soc. Am. 108, 2796-2815 (2000)] is identified as the property of rheopecty. The property corresponds to a rare type of a non-Newtonian fluid in rheology which has largely remained unexplored. The material impulse response function from the GS model is found to be similar to the power-law memory kernel which is inherent in the framework of fractional calculus. The compressional wave equation and the shear wave equation derived from the GS model are shown …
Classical scaling relationships for rheological quantities such as the $μ(J)$-rheology have become increasingly popular for closures of two-phase flow modeling. However, these frameworks have been derived for monodisperse particles. We aim to extend these considerations to sediment transport modeling by using a more realistic sediment composition. We investigate the rheological behavior of sheared sediment beds composed of polydisperse spherical particles in a laminar Couette-type shear flow. The sediment beds consist of particles with a diameter size ratio of up to ten, which corresponds to g…
The flow within an oscillatory boundary layer, which approximates the flow generated by propagating sea waves of small amplitude close to the bottom, is simulated numerically by integrating Navier-Stokes and continuity equations. The bottom is made up of spherical particles, free to move, which mimic sediment grains. The approach allows to fully-resolve the flow around the particles and to evaluate the forces and torques that the fluid exerts on their surface. Then, the dynamics of sediments is explicitly computed by means of Newton-Euler equations. For the smallest value of the flow Reynolds …
Aeolian sediment transport is observed to occur on Mars as well as other extraterrestrial environments, generating ripples and dunes as on Earth. The search for terrestrial analogues of planetary bedforms, as well as environmental simulation experiments able to reproduce their formation in planetary conditions, are powerful ways to question our understanding of geomorphological processes towards unusual environmental conditions. Here, we perform sediment transport laboratory experiments in a closed-circuit wind tunnel placed in a vacuum chamber and operated at extremely low pressures to show t…
We study experimentally gravity-driven granular discharges of laboratory scale silos, during the initial instants of the discharge. We investigate deformable wall silos around their critical collapse height, as well as rigid wall silos. We propose a criterion to determine a maximum time for the onset of the collapse and find that the onset of collapse always occurs before the grains adjacent to the wall are sliding down. We conclude that the evolution of the static friction toward a state of maximum mobilization plays a crucial role in the collapse of the silo.
The wavelength at which a dune pattern emerges from a flat sand bed is controlled by the sediment transport saturation length, which is the length needed for the sand flux to adapt to a change of wind strength. The influence of the wind shear velocity on this saturation length and on the subsequent dune initial wavelength has remained controversial. In this letter, we present direct measurements of the saturation length performed in a wind tunnel experiment. In complement, initial dune wavelengths are measured under different wind conditions -- in particular after storms. Using the linear stab…
We present a detailed comparison of the rheological behaviour of sheared sediment beds in a pressure-driven, straight channel configuration based on data that was generated by means of fully coupled, grain-resolved direct numerical simulations and experimental measurements reviously published by Aussillous {\it et al.} (J. Fluid Mech., vol. 736, 2013, pp. 594-615). The highly-resolved simulation data allows to compute the stress balance of the suspension in the streamwise and vertical directions and the stress exchange between the fluid and particle phase, which is information needed to infer …
We show that a freshly sedimented granular bed settles and creeps forward over extended periods of time under an applied hydrodynamic shear stress, which is below the critical value for bedload transport. The rearrangements are found to last over a time scale which is millions of times the sedimentation time scale of a grain in the fluid. Compaction occurs uniformly throughout the bed, but creep is observed to decay exponentially with depth, and decreases over time. The granular volume fraction in the bed is found to increase logarithmically, saturating at the random close packing value $ϕ_{rc…
In steady sediment transport, sediment deposition is balanced by entrainment of bed particles by fluid forces or particle-bed impacts. Here we propose a proxy to determine the role of impact entrainment relative to entrainment by the mean turbulent flow: the "bed velocity" $V_b$, which is an effective near-bed-surface value of the average horizontal particle velocity that generalizes the classical slip velocity, used in studies of aeolian saltation transport, to sediment transport in an arbitrary Newtonian fluid. We study $V_b$ for a wide range of the particle-fluid-density ratio $s$, Galileo …
Aeolian sand transport is a major process shaping landscapes on Earth and on diverse celestial bodies. Conditions favoring bimodal sand transport, with fine-grain saltation driving coarse-grain reptation, give rise to the evolution of megaripples with a characteristic bimodal sand composition. Here, we derive a unified phase diagram for this special aeolian process and the ensuing nonequilibrium megaripple morphodynamics by means of a conceptually simple quantitative model, grounded in the grain-scale physics. We establish a well-preserved quantitative signature of bimodal aeolian transport in…
Predicting rapid and slower soil evolution remains a scientific challenge. This process involves poorly understood aspects of disordered granular matter and dense suspension dynamics. This study presents a novel two-dimensional experiment on a small-scale chip structure; this allows the observation of the deformation at the particle scale of a large-grained sediment bed, under conditions where friction dominate over cohesive and thermal forces, and with an imposed fluid flow. Experiments are performed at conditions which span the particle resuspension criterion, and particle motion is detected…
Starting from the physics on the grain scale, we develop a simple continuum description of aeolian sand transport. Beyond popular mean-field models, but without sacrificing their computational efficiency, it accounts for both dominant grain populations, hopping (or "saltating") and creeping (or "reptating") grains. The predicted stationary sand transport rate is in excellent agreement with wind tunnel experiments simulating wind conditions ranging from the onset of saltation to storms. Our closed set of equations thus provides an analytically tractable, numerically precise, and computationally…
This paper investigates numerically the hydraulic conveying of solids through a 90$^{\circ}$ elbow that changes the flow direction from horizontal to vertical, in the very-narrow case where the ratio of pipe to particle diameters is less than 5. We performed resolved CFD-DEM (computational fluid dynamics - discrete element method) computations, in which we made use of the IB (immersed boundary) method of the open-source code CFDEM. We investigate the effects of the water flow and particle injection rate on the transport rate and sedimentation by tracking the granular structures appearing in th…
Gravel-river beds typically have an "armored" layer of coarse grains on the surface, which acts to protect finer particles underneath from erosion. River bed-load transport is a kind of dense granular flow, and such flows are known to vertically segregate grains. The contribution of granular physics to river-bed armoring, however, has not been investigated. Here we examine these connections in a laboratory river with bimodal sediment size, by tracking the motion of particles from the surface to deep inside the bed, and find that armor develops by two distinct mechanisms. Bed-load transport in …
Addressing bedload flux variability due to grain shape effects and experimental channel geometry
South China University of Technology（华南理工大学）；Zhejiang University（浙江大学）；Aix-Marseille University（艾克斯-马赛大学）；Leipzig University（莱比锡大学）；National Taiwan University（台湾大学）
