Direct validation of dune instability theory.

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 mo 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 with 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 underpins 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.

A lower-than-expected saltation threshold at Martian pressure and below.

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 analogs 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 toward 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 [Formula: see text] 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.

Giant ripples on comet 67P/Churyumov-Gerasimenko sculpted by sunset thermal wind.

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-10 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.

Rheology of dense granular flows for elongated particles.

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 µ is an increasing function of the inertial number I, and we systematically investigate the dependence of µ 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 quasistatic friction coefficient is nonmonotonic with Q: from the spherical case Q=1, it first sharply increases, reaches a maximum around Q≃1.05, and then gently decreases until Q=3, passing its initial value at Q≃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.

Non-local rheology in dense granular flows: Revisiting the concept of fluidity.

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 µ(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.

Direct numerical simulations of aeolian sand ripples.

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 toward 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 midair collisions. Finally, we provide quantitative support for the use of the propagation of these ripples as a proxy for remote measurements of sediment transport.

Aeolian and subaqueous bedforms in shear flows.

A sediment bed sheared by an unbounded flow is unconditionally unstable towards the growth of bedforms called ripples under water and dunes in the aeolian case. We review here the dynamical mechanisms controlling this linear instability, putting the emphasis on testing models against field and laboratory measurements. We then discuss the role of nonlinearities and the influence of finite size effects, namely the depth of the atmospheric boundary layer in the aeolian case and the water depth in the case of rivers.

Nonlocal rheology of granular flows across yield conditions.

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 nonlocal 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.

Aeolian and subaqueous bedforms in shear flows.

A sediment bed sheared by an unbounded flow is unconditionally unstable towards the growth of bedforms called ripples under water and dunes in the aeolian case. We review here the dynamical mechanisms controlling this linear instability, putting the emphasis on testing models against field and laboratory measurements. We then discuss the role of nonlinearities and the influence of finite size effects, namely the depth of the atmospheric boundary layer in the aeolian case and the water depth in the case of rivers.

Transition from the viscous to inertial regime in dense suspensions.

Non-Brownian suspensions present a transition from Newtonian behavior in the zero-shear limit to a shear thickening behavior at a large shear rate, none of which is clearly understood so far. Here, we carry out numerical simulations of such an athermal dense suspension under shear, at an imposed confining pressure. This setup is conceptually identical to recent experiments of Boyer, Guazzelli, and Pouliquen [Phys. Rev. Lett. 107, 188301 (2011)]. Varying the interstitial fluid viscosities, we recover the Newtonian and Bagnoldian regimes and show that they correspond to a dissipation dominated by viscous and contact forces, respectively. We show that the two rheological regimes can be unified as a function of a single dimensionless number, by adding the contributions to the dissipation at a given volume fraction.

Giant aeolian dune size determined by the average depth of the atmospheric boundary layer.

Depending on the wind regime, sand dunes exhibit linear, crescent-shaped or star-like forms resulting from the interaction between dune morphology and sand transport. Small-scale dunes form by destabilization of the sand bed with a wavelength (a few tens of metres) determined by the sand transport saturation length. The mechanisms controlling the formation of giant dunes, and in particular accounting for their typical time and length scales, have remained unknown. Using a combination of field measurements and aerodynamic calculations, we show here that the growth of aeolian giant dunes, ascribed to the nonlinear interaction between small-scale superimposed dunes, is limited by the confinement of the flow within the atmospheric boundary layer. Aeolian giant dunes and river dunes form by similar processes, with the thermal inversion layer that caps the convective boundary layer in the atmosphere acting analogously to the water surface in rivers. In both cases, the bed topography excites surface waves on the interface that in turn modify the near-bed flow velocity. This mechanism is a stabilizing process that prevents the scale of the pattern from coarsening beyond the resonant condition. Our results can explain the mean spacing of aeolian giant dunes ranging from 300 m in coastal terrestrial deserts to 3.5 km. We propose that our findings could serve as a starting point for the modelling of long-term evolution of desert landscapes under specific wind regimes.

Aeolian sand ripples: experimental study of fully developed states.

We report an experimental investigation of aeolian sand ripples, performed both in a wind tunnel and on stoss slopes of dunes. Starting from a flat bed, we can identify three regimes: appearance of an initial wavelength, coarsening of the pattern, and finally saturation of the ripples. We show that both initial and final wavelengths, as well as the propagative speed of the ripples, are linear functions of the wind velocity. Investigating the evolution of an initially corrugated bed, we exhibit nonlinear stable solutions for a finite range of wavelengths, which demonstrates the existence of a saturation in amplitude. These results contradict most of the models.

Field evidence for surface-wave-induced instability of sand dunes.

Field studies of barchans--crescent-shaped dunes that propagate over solid ground under conditions of unidirectional wind--have long focused on the investigation of an equilibrium between sand transport by wind and the control of air flow by dune topography, which are thought to control dune morphology and kinematics. Because of the long timescale involved, however, the underlying dynamic processes responsible for the evolution of dune fields remain poorly understood. Here we combine data from a three-year field study in the Moroccan Sahara with a model study to show that barchans are fundamentally unstable and do not necessarily behave like stable solitary waves, as suggested previously. We find that dune collisions and changes in wind direction destabilize the dunes and generate surface waves on the barchans. Because the resulting surface waves propagate at a higher speed than the dunes themselves, they can produce a series of new barchans of elementary size by breaking the horns of large dunes. The creation of these new dunes provides a mechanism for sand loss that prevents dune fields from merging into a single giant dune and therefore plays a fundamental role in the control of size selection and the development of dune patterns.

Dynamics of granular avalanches caused by local perturbations.

Surface flow of granular material is investigated within a continuum approach in two dimensions. The dynamics is described by the nonlinear coupling between a mobile layer and an erodible bed of static grains. Following previous studies, we use mass and momentum conservation to derive St. Venant-like equations for the evolution of the thickness R of the mobile layer and the profile Z of the bed. This approach allows the rheology in the flowing layer to be specified independently, and we consider in detail the two following models: a constant plug flow and a linear velocity profile. We study and compare these models for nonstationary avalanches triggered by a localized amount of mobile grains on a bed of initially constant slope. We solve analytically the nonlinear dynamical equations by the method of characteristics. This enables us to investigate the temporal evolution of the avalanche size, amplitude, and shape as a function of model parameters and initial conditions. In particular, we can compute their large time behavior as well as the condition for the formation of shocks.

Reorganization of a dense granular assembly: the unjamming response function.

We investigate the mechanical properties of a static dense granular assembly in response to a local forcing. To this end, a small cyclic displacement is applied on a grain in the bulk of a two-dimensional disordered packing under gravity and the displacement fields are monitored. We evidence a dominant long range radial response in the upper half part above the solicitation and after a large number of cycles the response is "quasireversible" with a remanent dissipation field exhibiting long range streams and vortexlike symmetry.