Search

The behavior of non-spherical particles in a shear-flow is of significant practical and theoretical interest. These systems have been the object of numerous investigations since the pioneering work of Jeffery a century ago. His eponymous orbits describe the deterministic motion of an isolated, rod-like particle in a shear flow. Subsequently, the effect of adding noise was investigated. The theory has been applied to colloidal particles, macromolecules, anisometric granular particles and most recently to microswimmers, for example bacteria. We study the Jeffery orbits of elongated particles subject to noise using Langevin simulations and a Fokker-Planck equation. We extend the analytical solution for infinitely thin needles ($\beta=1$) obtained by Doi and Edwards to particles with arbitrary shape factor ($0\le \beta\le 1$) and validate the theory by comparing it with simulations. We examine the rotation of the particle around the vorticity axis and study the orientational order matrix. We use the latter to obtain scalar order parameters $s$ and $r$ describing nematic ordering and biaxiality from the orientational distribution function. The value of $s$ (nematic ordering) increases monotonically with increasing P\'eclet number, while $r$ (measure of biaxiality) displays a maximum value. From perturbation theory we obtain simple expressions that provide accurate descriptions at low noise (or large P\'eclet numbers). We also examine the orientational distribution in the v-grad v plane and in the perpendicular direction. Finally we present the solution of the Fokker-Planck equation for a strictly two-dimensional (2D) system. For the same noise amplitude the average rotation speed of the particle in 3D is larger than in 2D.

Turbulent flows above a solid surface are characterised by a hydrodynamic roughness that represents, for the far velocity field, the typical length scale at which momentum mixing occurs close to the surface. Here, we are theoretically interested in the hydrodynamic roughness induced by a two-dimensional modulated surface, the elevation profile of which is decomposed in Fourier modes. We describe the flow for a sinusoidal mode of given wavelength and amplitude with RANS equations closed by means of a mixing-length approach that takes into account a possible surface geometrical roughness as well as the presence of a viscous sublayer. It also incorporates spatial transient effects at the laminar-turbulent transition. Performing a weekly non-linear expansion in the bedform aspect ratio, we predict the effective hydrodynamic roughness when the surface wavelength is varied and we show that it presents a non-monotonic behaviour at the laminar-turbulent transition when the surface is hydrodynamically smooth. Further, with a self-consistent looped calculation, we are able to recover the smooth-rough transition of a flat surface, for which the hydrodynamic roughness changes from a regime where it is dominated by the viscous length to another one where it scales with the surface corrugation. We finally apply the results to natural patterns resulted from hydrodynamic instabilities such as those associated with dissolution or sediment transport. We discuss in particular the aspect ratio selection of dissolution bedforms and roughness hierarchy in superimposed ripples and dunes.

We investigate experimentally the dissolution of an almost spherical butyramide particle during its sedimentation, in the low Reynolds high P\'eclet regime. The particle sediments in a quiescent aqueous solution, and its shape and position are measured simultaneously by a camera attached to a translation stage. The particle is tracked in real time, and the translation stage moves accordingly to keep the particle in the field of the camera. The measurements from the particle image show that the radius shrinking rate is constant with time, and independent of the initial radius of the particle. We explain this with a simple model, based on the sedimentation law in the Stokes' regime and the mass transfer rate at low Reynolds and high P\'eclet numbers. The theoretical and experimental results are consistent within $20\%$. We introduce two correction factors to take into account the non-sphericity of the particle and the inclusions of air bubbles inside the particle, and reach quantitative agreement. With these corrections, the indirect measurement of the radius shrinking rate deduced from the position measurement is also in agreement with the model. We discuss other correction factors, and explain why there are negligible in the present experiment. We also compute the effective Sherwood number as a function of an effective P\'eclet number.

Sand patches are one of the precursors to early-stage protodunes and occur widely in both desert and coastal aeolian environments. Here we show field evidence of a mechanism to explain the initiation of sand patches on non-erodible surfaces, such as desert gravels and moist beaches. Changes in sand transport dynamics, directly associated with the height of the saltation layer and variable transport law, observed at the boundary between non-erodible and erodible surfaces lead to sand deposition on the erodible surface. This explains how sand patches can form on surfaces with limited sand availability where linear stability of dune theory does not apply. This new mechanism is supported by field observations that evidence both the change in transport rate over different surfaces and in-situ patch formation that leads to modification of transport dynamics at the surface boundary.

Emergence and growth of sand dunes results from the dynamic interaction between topography, wind flow and sediment transport. While feedbacks between these variables are well studied at the scale of a single and relatively small dune, the average effect of a periodic large-scale dune pattern on atmospheric flows remains poorly constrained, due to a pressing lack of data in major sand seas. Here, we compare local measurements of surface winds to the predictions of the ERA5-Land climate reanalysis at four locations in Namibia, both within and outside the giant linear dune field of the Namib Sand Sea. In the desert plains to the north of the sand sea, observations and predictions agree well. This is also the case in the interdune areas of the sand sea during the day. During the night, however, an additional wind component aligned with the giant dune orientation is measured, in contrast to the easterly wind predicted by the ERA5-Land reanalysis. For the given dune orientation and measured wind regime, we link the observed wind deviation (over 50\textdegree) to the daily cycle of the turbulent atmospheric boundary layer. During the night, a shallow boundary layer induces a flow confinement above the giant dunes, resulting in large flow deviations, especially for the slower easterly winds. During the day, the feedback of the giant dunes on the atmospheric flow is much weaker due to the thicker boundary layer and higher wind speeds. Finally, we propose that the confinement mechanism and the associated wind deflections induced by giant dunes could explain the development of smaller-scale secondary dunes, which elongate obliquely in the interdune areas of the primary dune pattern., Comment: 47 pages, 23 figures. Boundary-Layer Meteorol (2022)

In landscape-scale experiments at the edge of the Gobi desert, we show that various dune types develop simultaneously under natural wind conditions. Using 4 years of high-resolution topographic data, we demonstrate that, depending on sand availability, the same wind regime can lead to two different dune orientations, which reflect two independent dune growth mechanisms. As periodic oblique dunes emerge from a sand bed and develop to 2 meters in height, we analyze defect dynamics that drive the non-linear phase of pattern coarsening. Starting from conical sand heaps deposited on gravels, we observe the transition from dome to barchan and asymmetric barchan shapes. We identify a minimum size for arm elongation and evaluate the contribution of wind reversals to its longitudinal alignment. These experimental field observations support existing theoretical models of dune dynamics boosting confidence in their applicability for quantitative predictions of dune evolution under various wind regimes and bed conditions.

Modern dune fields are valuable sources of information for the large-scale analysis of terrestrial and planetary environments and atmospheres, but their study relies on understanding the small-scale dynamics that constantly generate new dunes and reshape older ones. Here we designed a landscape-scale experiment at the edge of the Gobi desert, China, to quantify the development of incipient dunes under the natural action of winds. High-resolution topographic data documenting 42~months of bedform dynamics are examined to provide a spectral analysis of dune pattern formation. We identified two successive phases in the process of dune growth, from the initial flat sand bed to a meter-high periodic pattern. We focus on the initial phase, when the linear regime of dune instability applies, and measure the growth rate of dunes of different wavelengths. We identify the existence of a maximum growth rate, which readily explains the mechanism by which dunes select their size, leading to the prevalence of a 15~m-wavelength pattern. We quantitatively compare our experimental results to the prediction of the dune instability theory using transport and flow parameters independently measured in the field. The remarkable agreement between theory and observations demonstrates that the linear regime of dune growth is permanently expressed on low-amplitude bed topography, before larger regular patterns and slip faces eventually emerge. Our experiment underpin existing theoretical models for the early development of eolian dunes, which can now be used to provide reliable insights into atmospheric and surface processes on Earth and other planetary bodies., Comment: 36 pages, 19 figures (supplementary material included)

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 exhibits variations that lag behind the topography. We extract the in-phase and in-quadrature components from streamwise pressure profiles and compare them to hydrodynamic predictions calibrated on shear stress data., Comment: 17 pages, 7 figures

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 that Martian conditions belong to a previously unexplored saltation regime. The threshold wind speed required to initiate saltation is only quantitatively predicted by state-of-the art models up to a density ratio between grain and air of $4 \times 10^5$, but unexpectedly falls to much lower values for higher density ratios. In contrast, impact ripples, whose emergence is continuously observed on the granular bed over the whole pressure range investigated, display a characteristic wavelength and propagation velocity essentially independent of pressure. A comparison of these findings with existing models suggests that sediment transport at low Reynolds number but high grain-to-fluid density ratio may be dominated by collective effects associated with grain inertia in the granular collisional layer., Comment: 38 pages, 21 figures

The rheology of a 3-dimensional granular system consisting of frictional elongated particles was investigated by means of discrete element model (DEM) calculations. A homogenous shear flow of frictional spherocyliders was simulated, and a number of rheological quantities were calculated. In the framework of the $\mu(I)$ rheology, the effective friction was found to be a non-monotonic function of the aspect ratio for interparticle friction coefficient $\mu_p \lesssim 0.4$, while it was an increasing function for larger $\mu_p$. We reveal the microscopic origin of this peculiar non-monotonic behavior. We show the non-trivial dependence of the velocity fluctuations on the dissipation regime, and trace back the behavior of the normal stress differences to particle-level quantities., Comment: 13 pages + 3 pages supplementary material

Early-stage bedforms develop into mature dunes through complex interactions between wind, sand transport and surface topography. Depending on varying environmental and wind conditions, the mechanism driving dune formation and, ultimately, the shape of nascent dunes may differ markedly. In cases where sand availability is plentiful one mechanism suggested for triggering dune growth is linear stability theory. Until now, this theory has only been tested using field evidence in unidirectional winds. However, in many areas of the world and on other planets where aeolian processes act, wind regimes are often bimodal or multimodal. Here, we investigate field evidence of protodune formation under bimodal winds by applying linear stability analysis to a developing protodune field. Employing recent theoretical and experimental research, combined with in-situ wind, sediment transport, and topographic measurements during a month long field campaign at Great Sand Dunes National Park, Colorado, USA, we use a development of the linear stability theory to predict the spatial characteristics (orientation and wavelength) and temporal evolution (growth rate and migration velocity) of a protodune field. We find that the theoretical predictions compare well with measured dunefield attributes as characterized by high-resolution Digital Elevation Models measured using repeat terres trial laser scanning. Our findings suggest that linear stability theory is a quantitative predictor of protodune development on sandy surfaces with a bimodal wind regime. Our findings are significant as they offer critical validation of the linear stability theory for explaining the initiation and development of dunes towards maturity in a complex natural environment., Comment: 19 pages, 6 figures electronic ISSN: 2169-9011 print ISSN: 2169-9003

In zones of loose sand, wind-blown sand dunes emerge due the linear instability of a flat sedimentary bed. This instability has been studied in experiments and numerical models but rarely in the field, due to the large time and length scales involved. We examine dune formation at the upwind margin of the White Sands Dune Field in New Mexico (USA), using 4 years of lidar topographic data to follow the spatial and temporal development of incipient dunes. Data quantify dune wavelength, growth rate, and propagation velocity and also the characteristic length scale associated with the growth process. We show that all these measurements are in quantitative agreement with predictions from linear stability analysis. This validation makes it possible to use the theory to reliably interpret dune-pattern characteristics and provide quantitative constraints on associated wind regimes and sediment properties, where direct local measurements are not available or feasible., Comment: 15 pages, 3 figures

Compared to barchan dunes, the morphodynamics of linear dunes that elongate on a non-erodible bed is barely investigated by means of laboratory experiments or numerical simulations. Using a cellular automaton model, we study the elongation of a solitary linear dune from a sand source and show that it can reach a steady state. This steady state is analyzed to understand the physical processes at work along the dune. Crest reversals together with avalanche processes control the shape of transverse sections. Dune width and height decrease almost linearly with distance downstream until the minimum size for dunes. This is associated with a constant sand loss along the dune, which eventually compensates for the sediment influx and sets the dune length. This sand budget is discussed to distinguish an elongating linear dune from a barchan dune and to explain the complexity of linear dune fields in nature., Comment: 16 pages, 4 figures

Dune fields are commonly associated with periodic patterns that are among the most recognizable landscapes on Earth and other planetary bodies. However, in zones of limited sediment supply, where periodic dunes elongate and align in the direction of the resultant sand flux, there has been no attempt to explain the emergence of such a regular pattern. Here, we show, by means of numerical simulations, that the elongation growth mechanism does not produce a pattern with a specific wavelength. Periodic elongating dunes appear to be a juxtaposition of individual structures, the arrangement of which is due to regular landforms at the border of the field acting as boundary conditions. This includes, among others, dune patterns resulting from bed instability, or the crestline reorganization induced by dune migration. The wavelength selection in fields of elongating dunes therefore reflects the interdependence of dune patterns over the course of their evolution., Comment: 7 pages, 4 figures

Subaqueous and aeolian bedforms are ubiquitous on Earth and other planetary environments. However, it is still unclear which hydrodynamical mechanisms lead to the observed variety of morphologies of self-organized natural patterns such as ripples, dunes or compound bedforms. Here we present simulations with a coupled hydrodynamic and sediment transport model that resolve the initial and mature stages of subaqueous and aeolian bedform evolution in the limit of large flow thickness. We identify two types of bedforms consistent with subaqueous ripples and dunes, and separated by a gap in wavelength. This gap is explained in terms of an anomalous hydrodynamic response in the structure of the inner boundary layer that leads to a shift of the position of the maximum shear stress from upstream to downstream of the crest. This anomaly gradually disappears when the bed becomes hydrodynamically rough. By also considering the effect of the spatial relaxation of sediment transport we provide a new unifying framework to compare ripples and dunes in planetary environments to their terrestrial counterparts., Comment: 23 pages, 5 figures

Most terrestrial sand seas form at `horse' latitudes, where the wind direction exhibits seasonal variation. Here, we extend the two-dimensional linear stability analysis of a flat sand bed associated with a unidirectional wind to the three-dimensional case in order to account for multidirectional wind regimes. Focusing on the simplest case of bidirectional flow regimes, we show that the transition from transverse to oblique or longitudinal patterns is controlled by the transport ratio and the divergence angle between the two flows. Our predictions agree with previous results for dune orientation, and also provide a wider range of possible alignments depending on flow strength, especially when the two winds are perpendicular, at which the transition occurs. This analysis also predicts the selected pattern wavelength, which either decreases close to the transition angle for strong winds, due to a geometric effect, or increases at low winds, when the bed slope affects the transport. This theoretical analysis is complemented by analogous subaqueous experiments, where bedforms are submitted to alternate water flows. For transverse bedforms, the experimental data validate the model at strong flows, providing evidence for the predicted geometric effect, but also for the increase of the wavelength close to the transport threshold. For longitudinal bedforms, a discrepancy is observed, which we interpret as the sign of enhanced nonlinearities induced by the development of slip faces when the flow alternately blows on both sides of the dune., Comment: 27 pages, 12 figures

We theoretically investigate the pattern formation observed when a fluid flows over a solid substrate that can dissolve or melt. We use a turbulent mixing description that includes the effect of the bed roughness. We show that the dissolution instability at the origin of the pattern is associated with an anomaly at the transition from a laminar to a turbulent hydrodynamic response with respect to the bed elevation. This anomaly, and therefore the instability, disappears when the bed becomes hydrodynamically rough, above a threshold roughness-based Reynolds number. This suggests a possible mechanism for the selection of the pattern amplitude. The most unstable wavelength scales as observed in nature on the thickness of the viscous sublayer, with a multiplicative factor that depends on the dimensionless parameters of the problem., Comment: 13 pages, 7 figures

We study the rheology of dense granular flows for frictionless spherocylinders by means of 3D numerical simulations. As in the case of spherical particles, the effective friction $\mu$ is an increasing function of the inertial number $I$, and we systematically investigate the dependence of $\mu$ on the particle aspect ratio $Q$, as well as that of the normal stress differences, the volume fraction and the coordination number. We show in particular that the quasi-static friction coefficient is non-monotonic with $Q$: from the spherical case $Q=1$, it first sharply increases, reaches a maximum around $Q \simeq 1.05$, and then gently decreases, reaching back its initial value for $Q \simeq 2$. We provide a microscopic interpretation for this unexpected behavior through the analysis of the distribution of dissipative contacts around the particles: as compared to spheres, slightly elongated grains enhance contacts in their central cylindrical band, whereas at larger aspect ratios particles tend to align and dissipate by preferential contacts at their hemispherical caps., Comment: 5 pages, 5 figures

The rheology of dense granular flows is often seen as dependent on the nature of the energy landscape defining the modes of energy relaxation under shear. We investigate numerically the transition from soft to rigid particles, varying $S$, their stiffness compared to the confining pressure over three decades and the inertial number $I$ of the shear flow over five decades. We show that the rheological constitutive relation, characterized by a dynamical friction coefficient of the form $\mu(I)=\mu_c + a I^{\alpha}$ is marginally affected by the particle stiffness, with constitutive parameters being essentially dependent on the inter-particle friction. Similarly, the distribution of local shear rate mostly depends on the inertial number $I$, which shows that the characteristic timescale of plastic events is primarily controlled by the confining pressure and is insensitive to $S$. By contrast, the form under which energy is stored between these events, but also the contact network properties such as the coordination number and the distance to isostaticity, are strongly affected by stiffness, allowing us to discuss the different regimes in the $(S,I)$ phase space., Comment: 7 pages and 5 figues in main paper + 2 pages and 6 figures in supplementary material

Explaining the unexpected presence of dune-like patterns at the surface of the comet 67P/Churyumov-Gerasimenko requires conceptual and quantitative advances in the understanding of surface and outgassing processes. We show here that vapor flow emitted by the comet around its perihelion spreads laterally in a surface layer, due to the strong pressure difference between zones illuminated by sunlight and those in shadow. For such thermal winds to be dense enough to transport grains -- ten times greater than previous estimates -- outgassing must take place through a surface porous granular layer, and that layer must be composed of grains whose roughness lowers cohesion consistently with contact mechanics. The linear stability analysis of the problem, entirely tested against laboratory experiments, quantitatively predicts the emergence of bedforms in the observed wavelength range, and their propagation at the scale of a comet revolution. Although generated by a rarefied atmosphere, they are paradoxically analogous to ripples emerging on granular beds submitted to viscous shear flows. This quantitative agreement shows that our understanding of the coupling between hydrodynamics and sediment transport is able to account for bedform emergence in extreme conditions and provides a reliable tool to predict the erosion and accretion processes controlling the evolution of small solar system bodies., Comment: 37 pages, 13 figures, 1 table

The constitutive relations of a dense granular flow composed of self-propelling frictional hard particles are investigated by means of DEM numerical simulations. We show that the rheology, which relates the dynamical friction $\mu$ and the volume fraction $\phi$ to the inertial number $I$, depends on a dimensionless number $\mathcal{A}$, which compares the active force to the confining pressure. Two liquid/solid transitions -- in the Maxwell rigidity sense -- are observed. As soon as the activity is turned on, the packing becomes an `active solid' with a mean number of particle contacts larger than the isostatic value. The quasi-static values of $\mu$ and $\phi$ decrease with $\mathcal{A}$. At a finite value of the activity $\mathcal{A}_t$, corresponding to the isostatic condition, a second `active rigidity transition' is observed beyond which the quasi-static values of the friction vanishes and the rheology becomes Newtonian. For $\mathcal{A}>\mathcal{A}_t$, we provide evidence for a highly intermittent dynamics of this 'active fluid'., Comment: 7 pages, 7 figures, final version, accepted for publication in Europhys. Lett

A flexible sheet clamped at both ends and submitted to a permanent wind is unstable and propagates waves. Here, we experimentally study the selection of frequency and wavenumber as a function of the wind velocity. These quantities obey simple scaling laws, which are analytically derived from a linear stability analysis of the problem, and which also involve a gravity-induced velocity scale. This approach allows us to collapse data obtained with sheets whose flexible rigidity is varied by two orders of magnitude. This principle may be applied in the future for energy harvesting., Comment: 20 pages, 7 figures

Snow penitentes form in sublimation conditions by differential ablation. Here we investigate the physical processes at the initial stage of penitente growth and perform the linear stability analysis of a flat surface submitted to the solar heat flux. We show that these patterns do not simply result from the self-illumination of the surface --a scale-free process-- but are primarily controlled by vapor diffusion and heat conduction. The wavelength at which snow penitentes emerge is derived and discussed. We found that it is controlled by aerodynamic mixing of vapor above the ice surface., Comment: 11 pages, 10 figures

The aim of this article is to discuss the concepts of non-local rheology and fluidity, recently introduced to describe dense granular flows. We review and compare various approaches based on different constitutive relations and choices for the fluidity parameter, focusing on the kinetic elasto-plastic model introduced by Bocquet et al. [Phys. Rev. Lett 103, 036001 (2009)] for soft matter, and adapted for granular matter by Kamrin et al. [Phys. Rev. Lett. 108, 178301 (2012)], and the gradient expansion of the local rheology $\mu(I)$ that we have proposed [Phys. Rev. Lett. 111, 238301 (2013)]. We emphasise that, to discriminate between these approaches, one has to go beyond the predictions derived from linearisation around a uniform stress profile, such as that obtained in a simple shear cell. We argue that future tests can be based on the nature of the chosen fluidity parameter, and the related boundary conditions, as well as the hypothesis made to derive the models and the dynamical mechanisms underlying their dynamics., Comment: 15 pages, 8 figures, accepted for publication in Eur. Phys. J. E

The rheology of dense Brownian suspensions of hard spheres is investigated numerically beyond the low shear rate Newtonian regime. We analyze an athermal analogue of these suspensions, with an effective logarithmic repulsive potential representing the vibrational entropic forces. We show that both systems present the same rheology without adjustable parameters. Moreover, all rheological responses display similar Herschel-Bulkley relations once the shear stress and the shear rate are respectively rescaled by a characteristic stress scale and by a microscopic reorganization time-scale, both related to the normal confining pressure. This pressure-controlled approach, originally developed for granular flows, reveals a striking physical analogy between the colloidal glass transition and granular jamming., Comment: 6 figures, 6 pages

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 a compromise between this destabilizing mechanism and a diffusive downslope transport which stabilizes small wavelengths. The initial wavelength is set by the ratio of the sediment flux and the erosion/deposition rate, a ratio which increases linearly with the wind velocity. We show that this scaling law, in agreement with experiments, originates from an interfacial layer separating the saltation zone from the static sand bed, where momentum transfers are dominated by mid-air collisions. Finally, we provide quantitative support for the use the propagation of these ripples as a proxy for remote measurements of sediment transport., Comment: 21 pages, 12 figures

The dynamical mechanism at the origin of the non-local rheology of dense granular flows is investigated trough discrete element simulations. We show that the influence of a shear band on the mechanical behavior of a distant zone is contained in the spatial variations observed in the network of granular contacts. Using a micro-rheology technique, we establish that the exponential responses hence obtained, do not proof the validity of a mechanical activation process as previously suggested, but stem from the spatial relaxation of the shear rate as a direct consequence of a macroscopic non-local constitutive relation. Finally, by direct visualization of the local relaxation processes, we dismiss the kinetic elasto-plastic picture, where a flow is conceived as a quasi-static sequence of localized plastic events interacting through the stress field. We therefore conclude in favor of the jamming scenario, where geometrical constrains lead to coherent non-affine displacements along floppy modes, inherently non-local., Comment: Manuscript submitted to Phys. Rev. Lett. + Supplementary Material: 7 pages, 7 figures

We investigate the mechanical properties of inclined frictional granular layers prepared with different protocols by means of DEM numerical simulations. We perform an orthotropic elastic analysis of the stress response to a localized overload at the layer surface for several substrate tilt angles. The distance to the unjamming transition is controlled by the tilt angle $\alpha$ with respect to the critical angle $\alpha_c$. We find that the shear modulus of the system decreases with $\alpha$, but tends to a finite value as $\alpha \to \alpha_c$. We also study the behaviour of various microscopic quantities with $\alpha$, and show in particular the evolution of the contact orientation with respect to the orthotropic axes and that of the distribution of the friction mobilisation at contact., Comment: 9 pages, 6 figures. Granular Matter (2014), Special Issue in honor of Bob Behringer

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 migration is described as resulting from normal stresses, but is limited by turbulent mixing and shear-induced diffusion of particles. Using this framework, we theoretically investigate the transition between bedload and suspended load., Comment: 20 pages, 9 figures. Final version, accepted for publication in J. Fluid Mech

A granular material is observed to flow under the Coulomb yield criterion as soon as this criterion is satisfied in a remote but contiguous region of space. We investigate this non-local effect using discrete element simulations, in a geometry similar, in spirit, to the experiment of Reddy et al. (Phys. Rev. Lett., 106 (2011) 108301): a micro-rheometer is introduced to determine the influence of a distant shear band on the local rheological behaviour. The numerical simulations recover the dominant features of this experiment: the local shear rate is proportional to that in the shear band and decreases (roughly) exponentially with the distance to the yield conditions. The numerical results are in quantitative agreement with the predictions of the non-local rheology proposed by (Phys. Rev. Lett., 111 (2013) 238301) and derived from a gradient expansion of the rheology $\mu[I]$. The consequences of these findings for the dynamical mechanisms controlling non-locality are finally discussed., Comment: 6 pages, 5 figures

In nature, barchan dunes typically exist as members of larger fields that display striking, enigmatic structures that cannot be readily explained by examining the dynamics at the scale of single dunes, or by appealing to patterns in external forcing. To explore the possibility that observed structures emerge spontaneously as a collective result of many dunes interacting with each other, we built a numerical model that treats barchans as discrete entities that interact with one another according to simplified rules derived from theoretical and numerical work and from field observations: (1) Dunes exchange sand through the fluxes that leak from the downwind side of each dune and are captured on their upstream sides; (2) when dunes become sufficiently large, small dunes are born on their downwind sides (`calving'); and (3) when dunes collide directly enough, they merge. Results show that these relatively simple interactions provide potential explanations for a range of field-scale phenomena including isolated patches of dunes and heterogeneous arrangements of similarly sized dunes in denser fields. The results also suggest that (1) dune field characteristics depend on the sand flux fed into the upwind boundary, although (2) moving downwind, the system approaches a common attracting state in which the memory of the upwind conditions vanishes. This work supports the hypothesis that calving exerts a first-order control on field-scale phenomena; it prevents individual dunes from growing without bound, as single-dune analyses suggest, and allows the formation of roughly realistic, persistent dune field patterns., Comment: 22 pages, 12 figures, version accepted for publication in Geology

The rheology of dense granular flows is studied numerically in a shear cell controlled at constant pressure and shear stress, confined between two granular shear flows. We show that a liquid state can be achieved even far below the yield stress, whose flow can be described with the same rheology as above the yield stress. A non-local constitutive relation is derived from dimensional analysis through a gradient expansion and calibrated using the spatial relaxation of velocity profiles observed under homogeneous stresses. Both for frictional and frictionless grains, the relaxation length is found to diverge as the inverse square-root of the distance to the yield point, on both sides of that point., Comment: 5 pages, 4 figures

It has been conjectured by Bagnold [1] that an assembly of hard non-deformable spheres could behave as a compressible medium when slowly sheared, as the average density of such a system effectively depends on the confining pressure. Here we use discrete element simulations to show the existence of transverse and sagittal waves associated to this dynamical compressibility. For this purpose, we study the resonance of these waves in a linear Couette cell and compare the results with those predicted from a continuum local constitutive relation.

The river bar instability is revisited, using a hydrodynamical model based on Reynolds averaged Navier-Stokes equations. The results are contrasted with the standard analysis based on shallow water Saint-Venant equations. We first show that the stability of both transverse modes (ripples) and of small wavelength inclined modes (bars) predicted by the Saint-Venant approach are artefacts of this hydrodynamical approximation. When using a more reliable hydrodynamical model, the dispersion relation does not present any maximum of the growth rate when the sediment transport is assumed to be locally saturated. The analysis therefore reveals the fundamental importance of the relaxation of sediment transport towards equilibrium as it it is responsible for the stabilisation of small wavelength modes. This dynamical mechanism is characterised by the saturation number, defined as the ratio of the saturation length to the water depth Lsat/H. This dimensionless number controls the transition from ripples (transverse patterns) at small Lsat/H to bars (inclined patterns) at large Lsat/H. At a given value of the saturation number, the instability presents a threshold and a convective-absolute transition, both controlled by the channel aspect ratio {\beta}. We have investigated the characteristics of the most unstable mode as a function of the main parameters, Lsat/H, {\beta} and of a subdominant parameter controlling the relative influence of drag and gravity on sediment transport. As previously found, the transition from alternate bars to multiple bars is mostly controlled by the river aspect ratio {\beta}. By contrast, in the alternate bar regime (large Lsat/H), the selected wavelength does not depend much on {\beta} and approximately scales as H^(2/3)L^(1/3)/C, where C is the Ch\'ezy number., Comment: 22 pages, 12 figures, soumitted to J. Fluid Mech