arXiv subjects

Philippe Claudin

Publications and source records attributed to Philippe Claudin.

34 records · Page 2Linked to original sources

arXiv2014

A two-phase flow model of sediment transport: transition from bedload to suspended load

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.

cond-mat.soft↗

arXiv2013

A non-local rheology for 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 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.

cond-mat.soft↗

arXiv2012

Dynamical compressibility of dense granular shear flows

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.

cond-mat.stat-mech↗

arXiv2012

The bar instability revisited

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 β. We have investigated the characteristics of the most unstable mode as a function of the main parameters, Lsat/H, β 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 β. By contrast, in the alternate bar regime (large Lsat/H), the selected wavelength does not depend much on β and approximately scales as H^(2/3)L^(1/3)/C, where C is the Chézy number.

physics.flu-dyn↗

arXiv2012

Transition from 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 behaviour 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 set-up is conceptually identical to the recent experiments of Boyer and co-workers [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.

cond-mat.soft↗

arXiv2012

Numerical simulation of turbulent sediment transport, from bed load to saltation

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.

cond-mat.soft↗

arXiv2007

Barchan dune corridors: field characterization and investigation of control parameters

The structure of the barchan field located between Tarfaya and Laayoune (Atlantic Sahara, Morocco) is quantitatively investigated and compared to that in La Pampa de la Joya (Arequipa, Peru). On the basis of field measurements, we show how the volume, the velocity and the output sand flux of a dune can be computed from the value of its body and horn widths. The dune size distribution is obtained from the analysis of aerial photographs. It shows that these fields are in a statistically homogeneous state along the wind direction and present a `corridor' structure in the transverse direction, in which the dunes have a rather well selected size. Investigating the possible external parameters controlling these corridors, we demonstrate that none among topography, granulometry, wind and sand flux is relevant. We finally discuss the dynamical processes at work in these fields (collisions and wind fluctuations), and investigate the way they could regulate the size of the dunes. Furthermore we show that the overall sand flux transported by a dune field is smaller than the maximum transport that could be reached in the absence of dunes, i.e. in saltation over the solid ground.

cond-mat.soft↗

arXiv2006

A scaling law for aeolian dunes on Mars, Venus, Earth, and for subaqueous ripples

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 determine the diameter of saltating grains on Mars. A first estimate comes from photographs of aeolian ripples taken by the rovers Opportunity and Spirit, showing grains whose diameters are smaller than on Earth dunes. In addition we calculate the effect of cohesion and viscosity on the dynamic and static transport thresholds. It confirms that the small grains visualised by the rovers should be grains experiencing saltation. Finally, we show that, within error bars, the scaling of $λ$ with $L_{\rm drag}$ holds over almost five decades. We conclude with a discussion on the time scales and velocities at which these bed instabilities develop and propagate on Mars.

cond-mat.soft↗

arXiv2005

Aeolian sans ripples: experimental study of saturated 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 non-linear stable solutions for a finite range of wavelengths, which demonstrates the existence of a saturation in amplitude. These results contradict most of the models.

cond-mat.soft↗

arXiv2004

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 a non-linear coupling between the two `states' of the granular material: a mobile layer and a static bed. 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 static bed. This approach allows the rheology in the flowing layer to be specified independently, and we consider in details the two following models: a constant plug flow and a linear velocity profile. We study and compare these models for non-stationary avalanches triggered by a localized amount of mobile grains on a static bed of constant slope. We solve analytically the non-linear 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.

cond-mat.stat-mech↗

arXiv2002

Stress response function of a two-dimensional ordered packing of frictional beads

We study the stress profile of an ordered two-dimensional packing of beads in response to the application of a vertical overload localized at its top surface. Disorder is introduced through the Coulombic friction between the grains which gives some indeterminacy and allows the choice of one constrained random number per grain in the calculation of the contact forces. The so-called `multi-agent' technique we use, lets us deal with systems as large as $1000\times1000$ grains. We show that the average response profile has a double peaked structure. At large depth $z$, the position of these peaks grows with $cz$, while their widths scales like $\sqrt{Dz}$. $c$ and $D$ are analogous to `propagation' and `diffusion' coefficients. Their values depend on that of the friction coefficient $μ$. At small $μ$, we get $c_0-c \propto μ$ and $D \propto μ^β$, with $β\sim 2.5$, which means that the peaks get closer and wider as the disorder gets larger. This behavior is qualitatively what was predicted in a model where a stochastic relation between the stress components is assumed.

cond-mat↗

arXiv2002

Selection of dune shapes and velocities. Part 1: Dynamics of sand, wind and barchans

Almost fifty years of investigations of barchan dunes morphology and dynamics is reviewed, with emphasis on the physical understanding of these objects. The characteristics measured on the field (shape, size, velocity) and the physical problems they rise are presented. Then, we review the dynamical mechanisms explaining the formation and the propagation of dunes. In particular a complete and original approach of the sand transport over a flat sand bed is proposed and discussed. We conclude on open problems by outlining future research directions.

cond-mat↗

arXiv2002

Selection of dune shapes and velocities. Part 2: A two-dimensional modelling

We present in this paper a simplification of the dune model proposed by Sauermann et al. which keeps the basic mechanisms but allows analytical and parametric studies. Two kinds of purely propagative two dimensional solutions are exhibited: dunes and domes, which, by contrast to the former, do not show avalanche slip face. Their shape and velocity can be predicted as a function of their size. We recover in particular that dune profiles are not scale invariant (small dunes are flatter than the large ones), and that the inverse of the velocity grows almost linearly with the dune size. We furthermore get the existence of a critical mass below which no stable dune exists. However, the linear stability analysis of a flat sand sheet shows that it is unstable at large wavelengths and suggests a mechanism of dune initiation.

cond-mat↗

arXiv1999

Exact Solutions of a Model for Granular Avalanches

We present exact solutions of the non-linear {\sc bcre} model for granular avalanches without diffusion. We assume a generic sandpile profile consisting of two regions of constant but different slope. Our solution is constructed in terms of characteristic curves from which several novel predictions for experiments on avalanches are deduced: Analytical results are given for the shock condition, shock coordinates, universal quantities at the shock, slope relaxation at large times, velocities of the active region and of the sandpile profile.

cond-mat.stat-mech↗

arXiv1998

A model for ripple instabilities in granular media

We extend the model of surface granular flow proposed in \cite{bcre} to account for the effect of an external `wind', which acts as to dislodge particles from the static bed, such that a stationary state of flowing grains is reached. We discuss in detail how this mechanism can be described in a phenomenological way, and show that a flat bed is linearly unstable against ripple formation in a certain region of parameter space. We focus in particular on the (realistic) case where the migration velocity of the instability is much smaller than the grains' velocity. In this limit, the full dispersion relation can be established. We find that the critical wave vector is of the order of the saltation length. We provide an intuitive interpretation of the instability.

cond-mat↗

arXiv1998

Stick-slip Transition in the Scalar Arching Model

When some granular material contained into a silo is pushed upwards with a piston, an irregular stick-slip motion of the system of grains is observed. We show how one can adapt the `Scalar Arching Model' -- proposed as a model for giant stress fluctuations in silos -- in order to describe this stick-slip phenomenon. As a function of the sensitivity of the system to mechanical noise, the system exhibit two different phases: a `jammed' phase, and a `sliding' phase where irregular stick-slip is observed. We analyze the transition, which is found to be of mean-field type, and study the statistical properties of the intermittent stick-slip motion.

cond-mat↗