arXiv subjects

Philippe Claudin

Publications and source records attributed to Philippe Claudin.

At least 19 recordsLinked to original sources

arXiv2025

Transverse vortices induced by modulated granular shear flows of elongated particles

We perform discrete element method (DEM) simulations of elongated grains in a shear cell for various particle aspect ratios and contact frictions, with an additional heterogeneous force perturbation in the flow direction. For a perturbation in the form of a single Fourier mode, we show that the response of the system consists of transverse secondary flows that average onto a pattern of four vortices. We also theoretically studied this phenomenon by generalizing the granular rheology $\mu(I)$ to the case of elongated grains and computing the linear response to such a perturbation. Even if the agreement between theory and simulations remains qualitative only, we can reproduce and understand the inversion of the vortex pattern when the cell aspect ratio is increased from a vertically to a horizontally elongated cell shape, emphasizing the key role of the second normal stress difference as well as the cell geometry.

cond-mat.soft↗

arXiv2024

Exploring noisy Jeffery orbits: A combined Fokker-Planck and Langevin analysis in 2D and 3D

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 ($β=1$) obtained by Doi and Edwards to particles with arbitrary shape factor ($0\le β\le 1$) 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 Péclet 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 Péclet 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.

cond-mat.soft↗

arXiv2023

Hydrodynamic roughness induced by a multiscale topography

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.

physics.flu-dyn↗

arXiv2023

Sedimentation of a single soluble particle at low Reynolds and high Péclet numbers

We investigate experimentally the dissolution of an almost spherical butyramide particle during its sedimentation, in the low Reynolds high Péclet 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 Péclet 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 Péclet number.

physics.flu-dyn↗

arXiv2022

Local Wind Regime Induced by Giant Linear Dunes: Comparison of ERA5-Land Reanalysis with Surface Measurements

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.

physics.geo-ph↗

arXiv2022

Coexistence of two dune growth mechanisms in a landscape-scale experiment

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.

physics.geo-ph↗

arXiv2021

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~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.

physics.geo-ph↗

arXiv2020

Flow and rheology of frictional elongated grains

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 $μ(I)$ rheology, the effective friction was found to be a non-monotonic function of the aspect ratio for interparticle friction coefficient $μ_p \lesssim 0.4$, while it was an increasing function for larger $μ_p$. 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.

cond-mat.soft↗

arXiv2020

Dune initiation in a bimodal wind regime

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.

physics.geo-ph↗

arXiv2020

Incipient bedforms in a bidirectional wind regime

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.

physics.flu-dyn↗

arXiv2020

Spatial and temporal development of incipient dunes

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.

physics.geo-ph↗

arXiv2020

Periodicity in fields of elongating dunes

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.

physics.geo-ph↗

arXiv2019

A unified model of ripples and dunes in water and planetary environments

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.

physics.geo-ph↗

arXiv2017

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 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.

cond-mat.soft↗

arXiv2016

Active dry granular flows: rheology and rigidity transitions

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 $μ$ and the volume fraction $ϕ$ 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 $μ$ and $ϕ$ 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'.

cond-mat.soft↗

arXiv2015

Paper waves in the wind

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.

physics.flu-dyn↗

arXiv2015

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.

cond-mat.soft↗

arXiv2014

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 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.

cond-mat.soft↗