arXiv subjects

P. Claudin

Publications and source records attributed to P. Claudin.

At least 37 records · Page 2Linked to original sources

arXiv2013

Field evidence for the upwind velocity shift at the crest of low dunes

Wind topographically forced by hills and sand dunes accelerates on the upwind (stoss) slopes and reduces on the downwind (lee) slopes. This secondary wind regime, however, possesses a subtle effect, reported here for the first time from field measurements of near-surface wind velocity over a low dune: the wind velocity close to the surface reaches its maximum upwind of the crest. Our field-measured data show that this upwind phase shift of velocity with respect to topography is found to be in quantitative agreement with the prediction of hydrodynamical linear analysis for turbulent flows with first order closures. This effect, together with sand transport spatial relaxation, is at the origin of the mechanisms of dune initiation, instability and growth.

cond-mat.soft↗

arXiv2013

Mechanical response of an inclined frictional granular layer approaching unjamming

We present an orthotropic elastic analysis of frictional granular layers under gravity by studying their 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 α with respect to the critical angle α_c. We find that the shear modulus of the system decreases with α, but reaches a finite value as αtends to α_c. We also analyze the vibration modes of the system and show that the soft modes play an increasing, though not crucial, role approaching the transition.

cond-mat.soft↗

arXiv2010

Transport relaxation time and length scales in turbulent suspensions

We show that in a turbulent flow transporting suspended sediment, the unsaturated sediment flux $q(x,t)$ can be described by a first-order relaxation equation. From a mode analysis of the advection-diffusion equation for the particle concentration, the relaxation length and time scales of the dominant mode are shown to be the deposition length $H U/V_{\rm fall}$ and deposition time $H/V_{\rm fall}$, where $H$ is the flow depth, $U$ the mean flow velocity and $V_{\rm fall}$ the sediment settling velocity. This result is expected to be particularly relevant for the case of sediment transport in slowly varying flows, where the flux is never far from saturation. Predictions are shown to be in quantitative agreement with flume experiments, for both net erosion and net deposition situations.

cond-mat.soft↗

arXiv2009

On the different regimes of subaqueous transport

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.

cond-mat.soft↗

arXiv2008

Bedforms in a turbulent stream.Part 1: Turbulent flow over topography

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 gradients balance. We study the sensitivity of the calculation with respect to (i) the choice of the turbulence closure, (ii) the motion of the bottom (growth or propagation), (iii) the physics at work in the surface layer, responsible for the hydrodynamic roughness of the bottom, (iv) the aspect ratio of the bedform and (v) the effect of the free surface, which can be interpreted in terms of standing gravity waves excited by topography. The most important effects are those of points (iii) to (v). We show that the dynamical mechanisms controlling the hydrodynamical roughness (mixing due to roughness elements, viscosity, sediment transport, etc) have an influence on the basal shear stress when the thickness of the surface layer is comparable to that of the inner layer. We evidence that non-linear effects tend to oppose linear ones and are of the same order for bedform aspect ratios of the order of 1/10. We show that the influence of the free surface on the basal shear stress is dominant when the wavelength is large compared to the flow depth, so that the inner layer extends throughout the flow and in the resonant conditions, and when the downstream material velocity balances the upstream wave propagation.

cond-mat.soft↗

arXiv2008

Bedforms in a turbulent stream.Part 2: Formation of ripples by primary linear instability and of dunes by non-linear pattern coarsening

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 framework allows to give a clear picture of the instability in terms of dynamical mechanisms. The relation between the wavelength at which ripples form and the flux saturation length is quantitatively derived. Inverting the problem, experimental data is used to determine the saturation length as a function of grain size and shear velocity. Finally, using the systematic expansion of the flow field with respect to the corrugation amplitude, we discuss the non-linear selection of ripple aspect ratio. Investingating the effect of a free surface on the linear instability, we show that the excitation of standing waves at the surface has a stabilising effect, independently of the details of the flow and sediment transport models. Consequently, the shape of the dispersion relation is such that dunes can not result from a primary linear instability. We present the results of field experiments performed in the natural sandy Leyre river, which evidence the formation of ripples by a linear instability and the formation of dunes by a non-linear pattern coarsening limited by the free surface. We show that mega-dunes form when the sand bed presents heterogeneities such as a wide distribution of grain sizes.

cond-mat.soft↗

arXiv2008

Measurements of the aeolian sand transport saturation length

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 stability analysis of dune formation, it is then possible to deduce the saturation length from field data. Both direct and indirect measurements agree that the saturation length is almost independent of the wind strength. This demonstrates that, in contrast with erosion, grain inertia is the dominant dynamical mechanism limiting sediment transport saturation.

cond-mat.soft↗

arXiv2007

Comment on "Minimal size of a barchan dune"

It is now an accepted fact that the size at which dunes form from a flat sand bed as well as their `minimal size' scales on the flux saturation length. This length is by definition the relaxation length of the slowest mode toward equilibrium transport. The model presented by Parteli, Duran and Herrmann [Phys. Rev. E 75, 011301 (2007)] predicts that the saturation length decreases to zero as the inverse of the wind shear stress far from the threshold. We first show that their model is not self-consistent: even under large wind, the relaxation rate is limited by grain inertia and thus can not decrease to zero. A key argument presented by these authors comes from the discussion of the typical dune wavelength on Mars (650 m) on the basis of which they refute the scaling of the dune size with the drag length evidenced by Claudin and Andreotti [Earth Pla. Sci. Lett. 252, 30 (2006)]. They instead propose that Martian dunes, composed of large grains (500 micrometers), were formed in the past under very strong winds. We show that this saltating grain size, estimated from thermal diffusion measurements, is not reliable. Moreover, the microscopic photographs taken by the rovers on Martian aeolian bedforms show a grain size of 87 plus or minus 25 micrometers together with hematite spherules at millimetre scale. As those so-called ``blueberries'' can not be entrained by reasonable winds, we conclude that the saltating grains on Mars are the small ones, which gives a second strong argument against the model of Parteli et al.

cond-mat.soft↗

arXiv2007

Integral method for flows down an incline: viscous, turbulent and granular cases

The integral method can be used to model accurately flows down an inclined plane. Such a method consists in projecting the full 3D equations on a lower dimensional representation. The vertical velocity profiles have their functional form fixed, based from the exact solution of homogeneous steady flows. This projection is achieved by integration of the momentum equation over the flow depth -- Saint-Venant approach. Here we generalize the viscous case to two non-newtonian constitutive relations: a Prandtl-like turbulent closure and a local granular rheology. We discuss one application in each case: the formation of anti-dunes in viscous streams, the transverse velocity profile in turbulent channels and the Kapitza instability in dense granular flows. They demonstrate the usefulness of this approach to get a model qualitatively correct, quantitatively reasonable and in which the dynamical mechanisms at work can be easily identified.

cond-mat.soft↗

arXiv2006

Scale separation in granular packings: stress plateaus and fluctuations

It is demonstrated, by numerical simulations of a 2D assembly of polydisperse disks, that there exists a range (plateau) of coarse graining scales for which the stress tensor field in a granular solid is nearly resolution independent, thereby enabling an `objective' definition of this field. Expectedly, it is not the mere size of the the system but the (related) magnitudes of the gradients that determine the widths of the plateaus. Ensemble averaging (even over `small' ensembles) extends the widths of the plateaus to sub-particle scales. The fluctuations within the ensemble are studied as well. Both the response to homogeneous forcing and to an external compressive localized load (and gravity) are studied. Implications to small solid systems and constitutive relations are briefly discussed.

cond-mat.stat-mech↗

arXiv2005

Sensitivity of the stress response function to packing preparation

A granular assembly composed of a collection of identical grains may pack under different microscopic configurations with microscopic features that are sensitive to the preparation history. A given configuration may also change in response to external actions such as compression, shearing etc. We show using a mechanical response function method developed experimentally and numerically, that the macroscopic stress profiles are strongly dependent on these preparation procedures. These results were obtained for both two and three dimensions. The method reveals that, under a given preparation history, the macroscopic symmetries of the granular material is affected and in most cases significant departures from isotropy should be observed. This suggests a new path toward a non-intrusive test of granular material constitutive properties.

cond-mat.soft↗

arXiv2005

From the stress response function (back) to the sandpile `dip'

We relate the pressure `dip' observed at the bottom of a sandpile prepared by successive avalanches to the stress profile obtained on sheared granular layers in response to a localized vertical overload. We show that, within a simple anisotropic elastic analysis, the skewness and the tilt of the response profile caused by shearing provide a qualitative agreement with the sandpile dip effect. We conclude that the texture anisotropy produced by the avalanches is in essence similar to that induced by a simple shearing -- albeit tilted by the angle of repose of the pile. This work also shows that this response function technique could be very well adapted to probe the texture of static granular packing.

cond-mat.soft↗

arXiv2004

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 2D 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 sollicitation and after a large number of cycles the response is `quasi-reversible' with a remanent dissipation field exhibiting long range streams and vortex-like symmetry.

cond-mat.soft↗

arXiv2003

Numerical stress response functions of static granular layers

We investigate the stress response function of a layer of grains, i.e. the stress profile in response to a localized overload. The shape of the profile is very sensitive to the packing arrangement, and is thus a good signature of the preparation procedure of the layer. This study has been done by the use of molecular dynamics numerical simulations. Here, for a given rain-like preparation, we present the scaling properties of the response function, and in particular the influence of the thickness of the layer, and the importance of the location of the overload and measurement points (at the boundaries, in the bulk).

cond-mat.soft↗

arXiv2003

Corridors of barchan dunes: stability and size selection

Barchans are crescentic dunes propagating on a solid ground. They form dune fields in the shape of elongated corridors in which the size and spacing between dunes are rather well selected. We show that even very realistic models for solitary dunes do not reproduce these corridors. Instead, two instabilities take place. First, barchans receive a sand flux at their back proportional to their width while the sand escapes only from their horns. Large dunes proportionally capture more than they loose sand, while the situation is reversed for small ones: therefore, solitary dunes cannot remain in a steady state. Second, the propagation speed of dunes decreases with the size of the dune: this leads -- through the collision process -- to a coarsening of barchan fields. We show that these phenomena are not specific to the model, but result from general and robust mechanisms. The length scales needed for these instabilities to develop are derived and discussed. They turn out to be much smaller than the dune field length. As a conclusion, there should exist further - yet unknown - mechanisms regulating and selecting the size of dunes.

cond-mat↗

arXiv2003

Anisotropy in granular media: classical elasticity and directed force chain network

A general approach is presented for understanding the stress response function in anisotropic granular layers in two dimensions. The formalism accommodates both classical anisotropic elasticity theory and linear theories of anisotropic directed force chain networks. Perhaps surprisingly, two-peak response functions can occur even for classical, anisotropic elastic materials, such as triangular networks of springs with different stiffnesses. In such cases, the peak widths grow linearly with the height of the layer, contrary to the diffusive spreading found in `stress-only' hyperbolic models. In principle, directed force chain networks can exhibit the two-peak, diffusively spreading response function of hyperbolic models, but all models in a particular class studied here are found to be in the elliptic regime.

cond-mat.stat-mech↗

arXiv2002

Directed force chain networks and stress response in static granular materials

A theory of stress fields in two-dimensional granular materials based on directed force chain networks is presented. A general equation for the densities of force chains in different directions is proposed and a complete solution is obtained for a special case in which chains lie along a discrete set of directions. The analysis and results demonstrate the necessity of including nonlinear terms in the equation. A line of nontrivial fixed point solutions is shown to govern the properties of large systems. In the vicinity of a generic fixed point, the response to a localized load shows a crossover from a single, centered peak at intermediate depths to two propagating peaks at large depths that broaden diffusively.

cond-mat↗

arXiv2001

Stress response function of a granular layer: quantitative comparison between experiments and isotropic elasticity

We measured the vertical pressure response function of a layer of sand submitted to a localized normal force at its surface. We found that this response profile depends on the way the layer has been prepared: all profiles show a single centered peak whose width scales with the thickness of the layer, but a dense packing gives a wider peak than a loose one. We calculate the prediction of isotropic elastic theory in presence of a bottom boundary and compare it to the data. We found that the theory gives the right scaling and the correct qualitative shape, but fails to really fit the data.

cond-mat↗