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 its threshold value. The number of grains transported per unit surface is therefore limited by the flux of horizontal momentum towards the surface. However, the fluid velocity in the transport layer remains almost undisturbed so that the mean grain velocity scales with the shear velocity u\ast. At large density ratio (typically in air), the vertical velocities are large enough to make the transport layer wide and dilute. Sediment transport is then called saltation. In this case, particles are able to eject others when they collide with the granular bed, a process called splash. The number of grains transported per unit surface is selected by the balance between erosion and deposition and saturation is reached when one grain is statistically replaced by exactly one grain after a collision, which has the consequence that the mean grain velocity remains independent of u\ast. The influence of the density ratio is systematically studied to reveal the transition between these two transport regimes. Based on the mechanisms identified in the steady case, we discuss the transient of saturation of sediment transport and in particular the saturation time and length. Finally, we investigate the exchange of particles between the mobile and static phases and we determine the exchange time of particles.
The transport of dense particles by a turbulent flow depends on two dimensionless numbers. Depending on the ratio of the shear velocity of the flow to the settling velocity of the particles (or the Rouse number), sediment transport takes place in a thin layer localized at the surface of the sediment bed (bedload) or over the whole water depth (suspended load). Moreover, depending on the sedimentation Reynolds number, the bedload layer is embedded in the viscous sublayer or is larger. We propose here a two-phase flow model able to describe both viscous and turbulent shear flows. Particle migrat…
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…
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 …
Here we compare two extreme regimes of non-suspended fluid-mediated particle transport, transport in light and heavy fluids ("saltation" and "bedload", respectively), regarding their particle fluctuation energy balance. From direct numerical simulations, we surprisingly find that the ratio between collisional and fluid drag dissipation of fluctuation energy is significantly larger in saltation than in bedload, even though the contribution of interparticle collisions to transport of momentum and energy is much smaller in saltation due to the low concentration of particles in the transport layer…
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…
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…
Here we address the old question in Aeolian particle transport about the role of midair collisions. We find that, surprisingly, these collisions do enhance the overall flux substantially. The effect depends strongly on restitution coefficient and wind speed. We can explain this observation as a consequence of a soft-bed of grains which floats above the ground and reflects the highest flying particles. We make the unexpected observation that the flux is maximized at an intermediate restitution coefficient of about 0.7, which is comparable to values experimentally measured for collisions between…
Wind tunnel measurements of the mean saltation length $L$ and of different proxies of the mean saltation height $H$ in saturated aeolian sand transport indicate that $L$ and $H$ are relatively insensitive to both the wind speed and grain diameter $d$. The latter result is currently unexplained and contradicts the theoretical prediction $L\propto H\propto d$. This prediction is based on the assumption that the characteristic velocity $\sqrt{\tilde gd}$ of bed grains ejected by the splash of an impacting grain controls the average saltation kinematics. Here, we show that a recent analytical salt…
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 …
A key interest in geomorphology is to predict how the shear stress $τ$ exerted by a turbulent flow of air or liquid onto an erodible sediment bed affects the transport load $M\tilde g$ (i.e., the submerged weight of transported nonsuspended sediment per unit area) and its average velocity when exceeding the sediment transport threshold $τ_t$. Most transport rate predictions in the literature are based on the scaling $M\tilde g\proptoτ-τ_t$, the physical origin of which, however, has remained controversial. Here we test the universality and study the origin of this scaling law using particle-sc…
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…
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…
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. …
We investigate the formation of subaqueous transverse bedforms in turbulent open channel flow by means of direct numerical simulations with fully-resolved particles. The main goal of the present analysis is to address the question whether the initial pattern wavelength scales with the particle diameter or with the mean fluid height. A previous study (Kidanemariam and Uhlmann, J. Fluid Mech., vol. 818, 2017, pp. 716-743) has observed a lower bound for the most unstable pattern wavelength in the range 75-100 times the particle diameter, which was equivalent to 3-4 times the mean fluid height. In…
Predicting the morphodynamics of sedimentary landscapes due to fluvial and aeolian flows requires answering the following questions: Is the flow strong enough to initiate sediment transport, is the flow strong enough to sustain sediment transport once initiated, and how much sediment is transported by the flow in the saturated state (i.e., what is the transport capacity)? In the geomorphological and related literature, the widespread consensus has been that the initiation, cessation, and capacity of fluvial transport, and the initiation of aeolian transport, are controlled by fluid entrainment…
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 …
Predicting transport rates of windblown sand is a central problem in aeolian research, with implications for climate, environmental, and planetary sciences. Though studied since the 1930s, the underlying many-body dynamics is still incompletely understood, as underscored by the recent empirical discovery of an unexpected third-root scaling in the particle-fluid density ratio. Here, by means of grain-scale simulations and analytical modeling, we elucidate how a complex coupling between grain-bed collisions and granular creep within the sand bed yields a dilatancy-enhanced bed erodibility. Our m…
Understanding the dynamics of fluid-driven sediment transport remains challenging, as it is an intermediate region between a granular material and a fluid flow. Boyer \textit{et al.}\citep{Boyer2011} proposed a local rheology unifying dense dry-granular and viscous-suspension flows, but it has been validated only for neutrally-buoyant particles in a confined system. Here we generalize the Boyer \textit{et al.}\citep{Boyer2011} model to account for the weight of a particle by addition of a pressure $P_0$, and test the ability of this model to describe sediment transport in an idealized laborato…
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…
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…
It is widely accepted that both ripples and dunes form in rivers by primary linear instability, the wavelength of the former scaling on the grain size, that of the latter being controled by the water depth. We revisit here this problem, using the computation of the turbulent flow over a wavy bottom performed in Part 1. The details of the different mechanisms controlling sediment transport are encoded into three quantities: the saturated flux, the saturation length and the threshold shear stress. Theses quantities are modelled in the case of erosion and momentum limited bed loads. This framewor…
The linear stability analysis of the equations governing the evolution of a flat sand bed submitted to a turbulent shear flow predicts that the wavelength $λ$ at which the bed destabilises to form dunes should scale with the drag length $L_{\rm drag} = \frac{ρ_s}{ρ_f} d$. This scaling law is tested using existing and new measurements performed in water (subaqueous ripples), in air (aeolian dunes and fresh snow dunes), in a high pressure CO$_2$ wind tunnel reproducing conditions close to the Venus atmosphere and in the low pressure CO$_2$ martian atmosphere (martian dunes). A difficulty is to d…
We review different aspects of subaqueous sediment transport. We discuss the static threshold and its dependency with longitudinal and transverse slopes, as well as cohesion. We describe the different regimes of transport: erosion and momentum limited bed load, and suspended load. In all these cases, we derive the expressions of the saturation flux $q_{\rm sat}$ and the saturation length $L_{\rm sat}$ and discuss their dependencies.
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 …
Using particle-scale simulations of non-suspended sediment transport for a large range of Newtonian fluids driving transport, including air and water, we determine the bulk transport cessation threshold $Θ^r_t$ by extrapolating the transport load as a function of the dimensionless fluid shear stress (`Shields number') $Θ$ to the vanishing transport limit. In this limit, the simulated steady states of continuous transport can be described by simple analytical model equations relating the average transport layer properties to the law of the wall flow velocity profile. We use this model to calcul…
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…
In the context of subaqueous ripple and dune formation, we present here a Reynolds averaged calculation of the turbulent flow over a topography. We perform a weakly non-linear expansion of the velocity field, sufficiently accurate to recover the separation of streamlines and the formation of a recirculation bubble above some aspect ratio. The basal stresses are investigated in details; in particular, we show that the phase shift of the shear stress with respect to the topography, responsible for the formation of bedforms, appears in an inner boundary layer where shear stress and pressure gradi…
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…
The settling of cohesive sediment is ubiquitous in aquatic environments. In the settling process, the silt particles show behaviors that are different from non-cohesive particles due to the influence of inter-particle cohesive force. While it is a consensus that cohesive behaviors depend on the characteristics of sediment particles (e.g., Bond number, particle size distribution), little is known about the exact influence of these characteristics on the cohesive behaviors. In the present work, three-dimensional settling process is investigated numerically by using CFD--DEM (Computational Fluid …
Many fast-flowing glaciers and ice streams move over beds consisting of reworked sediments and erosional products, commonly referred to as till. The complex interplay between ice, meltwater, and till at the subglacial bed connects several fundamental problems in glaciology including the debate about rapid mass loss from the ice sheets, the formation and evolution of subglacial landforms, and the storage and transport of subglacial water. In-situ measurements have probed the subglacial bed, but provide surprisingly variable and seemingly inconsistent evidence of the depth where deformation occu…
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）
Turbulent flows over wavy surfaces give rise to the formation of ripples, dunes and other natural bedforms. To predict how much sediment these flows transport, research has focused mainly on basal shear stress, which peaks upstream of the highest topography, and has largely ignored the corresponding pressure variations. In this article, we reanalyze old literature data, as well as more recent wind tunnel results, to shed a new light on pressure induced by a turbulent flow on a sinusoidal surface. While the Bernoulli effect increases the velocity above crests and reduces it in troughs, pressure…
