A model for ripple instabilities in granular media

Terzidis, O.; Claudin, Philippe; Bouchaud, Jean‐Philippe

doi:10.1007/s100510050441

Cited by 39 publications

(60 citation statements)

References 8 publications

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“…Their wavelength ranges from the centimeter to the meter with a constant aspect ratio (≃ 4%) [2]. Although many different models have been proposed to explain the formation and evolution of aeolian ripples [3,4,5,6,7,8,9,10,11], few field observations [1,2,12] and controlled experiments [4,13,14] have been performed so far. By contrast with subaqueous dunes or ripples which result from a hydrodynamic instability induced by the interaction between shape and flow [1], aeolian ripples are of different nature and result from a screening instability.…”

Section: Olivier Pouliquenmentioning

confidence: 99%

Aeolian Sand Ripples: Experimental Study of Fully Developed States

2006

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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. The surface of aeolian sand dunes is not smooth but is usually formed into regular patterns of ripples, transverse to the wind [1]. Their wavelength ranges from the centimeter to the meter with a constant aspect ratio (≃ 4%) [2]. Although many different models have been proposed to explain the formation and evolution of aeolian ripples [3,4,5,6,7,8,9,10,11], few field observations [1, 2, 12] and controlled experiments [4,13,14] have been performed so far. By contrast with subaqueous dunes or ripples which result from a hydrodynamic instability induced by the interaction between shape and flow [1], aeolian ripples are of different nature and result from a screening instability. When the 'saltons' -high energy grains -collide the bed, they eject grains of smaller energy, 'reptons'. The windward slope of a small bump is submitted to more impacts than the lee slope, so that the flux of reptons is higher uphill than downhill and makes the bump amplify.Most of the models agree for the linear stage of the instability -see [5] for a pedagogical review. They assume that the reptons remain trapped by the bed after a single hop of length a, distributed according to a distribution P (a). The saltons are considered as an external reservoir which brings energy into the system. On this basis, the most unstable wavelength λ 0 is found to scale on the reptation lengthā = da a P (a). Besides, the most recent investigations of sand transport, both experimental [15,16] and theoretical [17,18], indicate that P (a) is independent of the wind shear velocity u * , which implies thatā scales on the grain diameter d. The initial wavelength of the ripples λ 0 is thus expected to be independent of the wind strength.

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Section: Olivier Pouliquenmentioning

confidence: 99%

Aeolian Sand Ripples: Experimental Study of Fully Developed States

2006

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“…Note that, for φ = 0, the set of equations (7)- (8) conserves the total amount of material. This is actually the relevant physical situation in the context of pattern (ripple) formation on aeolian sand dunes, where so-called "hydrodynamic" models like the above have recently proved successful [55]. In our present context, the smallness of the typical erosion rate ( 1s −1 ) as compared with the adatom diffusion rate ( 1ps −1 ) allows to eliminate the R field adiabatically near threshold of the morphological instability and obtain perturbatively the following interface equation at normal incidence [7] …”

Section: Pattern Formation: Ion-beam Sputteringmentioning

confidence: 99%

“…the λ (1) = 0 case of equation (9), and has been derived in other physical contexts, such as ripple formation on aeolian sand dunes [55] (c), or amorphous thin film growth [60].…”

Section: Domain Coarsening: Epitaxial Growth Of Vicinal Surfacesmentioning

confidence: 99%

Universal non-equilibrium phenomena at submicrometric surfaces and interfaces

Cuerno

Castro

Muñoz-García

et al. 2007

Eur. Phys. J. Spec. Top.

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Abstract. The recent widespread interest in processes occurring at micro and nanometric scales has increased the physical relevance of the surfaces and interfaces constituting system boundaries, both at and far from equilibrium. In the latter case, universal properties occur, such as scale invariance (surface kinetic roughening), surface pattern formation or domain coarsening. However, descriptions of these systems feature limited predictive power when based merely on universality principles. We review examples from Materials Science at nano and submicrometric scales, that underlie the importance of describing growing surfaces by means of (phenomenological) constitutive laws, in order to correctly describe the rich behaviors experimentally found across many different systems. Additionally, this approach provides new generic models that are also of interest in the wider contexts of Pattern Formation and Non-Linear Science.

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“…However, Anderson and Bunas [13] found using a cellular automaton model that inverse-graded ripple lamination is due to different hopping lengths of small and large grains. These models do not include the interactions between the moving grains and the static surface [20]-i.e., grains are assumed to stop as soon as they reach the sand surface-which are expected to be relevant for the dynamics in the rolling face of the ripples [21,22]. Recent studies by Terzidis et al [22] have reproduced the ripple instability using the theory of surface flows of grains proposed by Bouchaud and collaborators [23].…”

Section: Figmentioning

confidence: 99%

Grain segregation mechanism in aeolian sand ripples

Makse

2000

Eur. Phys. J. E

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Many sedimentary rocks are formed by migration of sand ripples. Thin layers of coarse and fine sand are present in these rocks, and understanding how layers in sandstone are created has been a longstanding question. Here, we propose a mechanism for the origin of the most common layered sedimentary structures such as inverse graded climbing ripple lamination and cross-stratification patterns. The mechanism involves a competition between three segregation processes: (i) sizesegregation and (ii) shape-segregation during transport and rolling, and (iii) size segregation due to different hopping lengths of the small and large grains. We develop a discrete model of grain dynamics which incorporates the coupling between moving grains and the static sand surface, as well as the different properties of grains, such as size and roughness, in order to test the plausibility of this physical mechanism. PACS: 81.05.Rm, 91.65.Ti

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A model for ripple instabilities in granular media

Cited by 39 publications

References 8 publications

Aeolian Sand Ripples: Experimental Study of Fully Developed States

Aeolian Sand Ripples: Experimental Study of Fully Developed States

Universal non-equilibrium phenomena at submicrometric surfaces and interfaces

Grain segregation mechanism in aeolian sand ripples

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