DPTM simulation of aeolian sand ripple

Aeolian sand ripple and its time evolution are simulated by the discrete particle tracing method (DPTM) presented in this paper. The difference between this method and the current methods is that the former can consider the three main factors relevant to the formation of natural aeolian sand ripples, which are the wind-blown sand flux above the sand bed formed by lots of sand particles with different diameters, the particle-bed collision and after it the rebound and ejection of sand particles in the sand bed, the saltation of high-speed sand particles and the creep of low-speed sand particles, respectively. The simulated aeolian sand ripple is close to the natural sand ripple not only in basic shape and characteristic, particle size segregation and stratigraphy, but also in formation stages. In addition, three important speeds can be obtained by this method, which are the propagation speed of the saturated aeolian sand ripple and the critical frictional wind speeds of emergence and disappearance of sand ripple. Supported by the Key Project of the National Natural Science Foundation of China (Grant No. 10532040)     

Sand ripple dynamics in the case of out-of-equilibrium aeolian regimes

From a phenomenological hydrodynamical model, we analyze the aeolian sand ripple evolution in an out-of-equilibrium aeolian regime where erosion exceeds accretion (and vice versa). We find, in particular, that the ripple structure can be destroyed in favor of a flat sand bed. In the ripple regime we report on a new class of generic dynamics described by the Benney equation. This equation reveals either order or disorder depending on whether wave dispersion is strong or weak. In both cases, the average wavelength of the pattern is fixed in time. This markedly contrasts with the regime of equilibrium aeolian regime -reached when erosion balances deposition- where ripples undergo a coarsening process at long time (i.e., the wavelength increases indefinitely with time).Received: 4 August 2003, Published online: 5 February 2004PACS: 81.05.Rm Porous materials; granular materials     

A nonlinear model for aeolian sand ripples

Starting from the phenomenological model for sand ripple formation developed in [#!Bouchaud98!#], we proposed a new interpretation in the light of recent experiments. Furthermore, we derive, close to the threshold of ripple instability, a nonlinear equation for the spatio-temporal evolution of the sand bed profile, which to leading order has a quadratic nonlinearity. This equation is identical to that derived recently on the basis of geometry and conservation law [#!Csahok98!#]. Our derivation connects the coefficients of the nonlinear equation to the underlying physical mechanisms (reptation length...). This equation reveals ripple structures which then undergo a coarsening process, as observed in wind tunnel experiment. Small, fast moving ripples are absorbed by larger, slower forms resulting in a growth of the mean wavelength. Received 5 January 1999     

Stability characteristics of the open channel flow above the asymmetrical irregular sand ripples

Sandy bed cannot keep its original smoothness as the flows pass. With the increase of the flow intensity, the bed forms will appear as sand ripples and dune in turn. Among these morphologies, the sand ripple scale is the smallest, which is generally symmetrical when it just appears, but as time goes on, the asymmetrical form gradually develops. Just because of this sand ripples asymmetry, it manifests the influence of the flow on the bed morphology and also the impact on the laminar flow dynamical process, especially the stability characteristics. The stability features of laminar flow on open channels with the asymmetrical sand ripples are discussed, and also the results on the symmetrical sand ripples are compared in detail.     

Long-time behavior of sand ripples induced by water shear flow

The European Physical Journal E - The formation of sand ripples under water shear flow in a narrow annular channel and the approach of the ripple pattern towards a steady state were studied...     

Use of forecasting signatures to help distinguish periodicity,randomness, and chaos in ripples and other spatial patterns

Forecasting of one-dimensional time series previously has been used to help distinguish periodicity, chaos, and noise. This paper presents two-dimensional generalizations for making such distinctions for spatial patterns. The techniques are evaluated using synthetic spatial patterns and then are applied to a natural example: ripples formed in sand by blowing wind. Tests with the synthetic patterns demonstrate that the forecasting techniques can be applied to two-dimensional spatial patterns, with the same utility and limitations as when applied to one-dimensional time series. One limitation is that some combinations of periodicity and randomness exhibit forecasting signatures that mimic those of chaos. For example, sine waves distorted with correlated phase noise have forecasting errors that increase with forecasting distance, errors that are minimized using nonlinear models at moderate embedding dimensions, and forecasting properties that differ significantly between the original and surrogates. Ripples formed in sand by flowing air or water typically vary in geometry from one to another, even when formed in a flow that is uniform on a large scale; each ripple modifies the local flow or sand-transport field, thereby influencing the geometry of the next ripple downcurrent. Spatial forecasting was used to evaluate the hypothesis that such a deterministic process-rather than randomness or quasiperiodicity-is responsible for the variation between successive ripples. This hypothesis is supported by a forecasting error that increases with forecasting distance, a greater accuracy of nonlinear relative to linear models, and significant differences between forecasts made with the original ripples and those made with surrogate patterns. Forecasting signatures cannot be used to distinguish ripple geometry from sine waves with correlated phase noise, but this kind of structure can be ruled out by two geometric properties of the ripples: Successive ripples are highly correlated in wavelength, and ripple crests display dislocations such as branchings and mergers.     

Formation of subwavelength periodic structures on tungsten induced by ultrashort laser pulses

The evolution of surface morphology of tungsten irradiated by single-beam femtosecond laser pulses is investigated. Ripplelike periodic structures have been observed. The period of these ripples does not show a simple relation to the wavelength and angle of incidence. The orientation of ripples is aligned perpendicularly to the direction of polarization for linearly polarized light. Surprisingly, we find that the alignment of the ripple structure turned left or right by 45 degrees with respect to the incident plane when using right and left circularly polarized light, respectively. The period of the ripple can be controlled by the pulse energy, the number of pulses, and the incident angle. We find a clear threshold for the formation as a function of pulse energy and number of pulses. The mechanism for the ripple formation is discussed, as well as potential applications in large-area structuring of metals.     

Self-organization of ripples on Ti irradiated with focused ion beam

30 keV focused Ga⁺ ions were used to raster the metallographically polished surface of commercially pure Ti (CP Ti) at various FIB incidence angles over a wide range of doses (10¹⁶-10¹⁸ ions/cm²) at room temperature. The sputtered surfaces were observed in situ using FIB imaging and later carefully characterized ex situ under scanning electron microscope (SEM) and atomic force microscope (AFM). Ripples were observed on the irradiated surfaces even at the normal FIB incidence angle. The ripple evolution is analyzed as functions of surface diffusion, surface crystallographic orientation, ion dose and incidence angle. It is found that the ripple orientation was progressively influenced by the ion beam direction with incidence angle increasing and in some cases curved ripples or fragmented rods viewed from different angles occurred at high ion doses. The morphological evolution from the well-developed straight ripples to the curved ones is never observed. The formation of ripples is attributed to the competition between the formation of ripples due to anisotropic surface diffusion and the formation of incidence-angle dependent ripples determined by Bradley-Harper (BH) model.     

From quantum fluctuations to large-scale structures

An acceleration phase in the early universe allows microscopic quantum fluctuations inside a causal domain to expand into macroscopic ripples in the spacetime metric. These, in turn, can evolve into large-scale structures in the universe. After its generation from quantum fluctuations, a ripple in the metric spends a long period outside the causal domain where its evolution is characterized by a conserved amplitude, a fact closely related to the large-scale Friedmann-like evolution of the perturbed Friedmann universe. We show that, under the assumption of linear processes, the generation and evolution of large-scale structures can be described quite simply.     

Grain segregation mechanism in aeolian sand ripples

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) size-segregation 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. Received 19 July 1999 and Received in final form 4 August 1999     

时间整形飞秒激光诱导熔融硅表面纳米周期条纹的电子动力学研究

研究了时间整形飞秒激光在熔融硅表面诱导纳米周期条纹结构的电子动力学过程.通过引入非线性电离机制和表面等离子激元的瞬态作用机理,建立了关于时间整形飞秒激光诱导和调控熔融硅表面纳米周期条纹结构的电子动力学模型,并应用该模型研究获得了纳米条纹周期与时间整形脉冲时间间隔的定量关系.理论研究结果表明,通过调节时间整形脉冲的时间间隔可以实现操控表面等离子激元与激光瞬态干涉过程中的波矢配对,最终可实现对诱导的纳米条纹周期的调控.此模型预测得到的纳米条纹周期与实验结果符合得很好.该研究对于深刻理解整形脉冲链诱导材料表面纳米周期结构的电子动力学操纵机制以及对条纹周期的调控都具有重要的理论价值.     

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.     

The laser polarization as control parameter in the formation of laser-induced periodic surface structures: Comparison of numerical and experimental results

Considering self-organized surface pattering upon multi-pulse femtosecond laser irradiation, in particularly the strong dependence of ripples orientation on the laser polarization, we present numerical simulations from an adopted surface erosion model and compare the result to our experimental data on laser-induced nanostructures formation. We present the surface morphologies obtained by this model for different polarizations of the incident laser electric field and show good agreement with ripple formation produced by laser ablation experiments. The correlation of ripples orientation with laser polarization can be described within a model where the polarization causes a breaking of symmetry at the surface. Further we discuss a time evolution of pattern formation. Our results support the non-linear self-organization mechanism of pattern formation on the surface of solids.     

Long-time behavior of sand ripples induced by water shear flow

The formation of sand ripples under water shear flow in a narrow annular channel and the approach of the ripple pattern towards a steady state were studied experimentally. Four results are obtained: i) The mean amplitude, the average drift velocity and the mean sediment transport rate of the evolving bed shape are strongly related. A quantitative characterization of this relation is given. ii) The ripple pattern reaches a stationary state with a finite ripple amplitude and wavelength. The time needed to reach the state depends on the shear stress and may be several days. iii) The onset of ripple formation is determined by the bed shear stress, but it seems neither to depend on the grain diameter nor on the depth of the water layer. iv) The ripple amplitude, drift velocity and sediment transport in this stationary state depend on the grain size. This dependency is neither captured by the particle Reynolds number nor by the Shields parameter: an empirical scaling law is presented instead.     

Large-eddy simulation of formation of three-dimensional aeolian sand ripples in a turbulent field

With the method of large-eddy simulation, the equation of spherule motion and the method of immersed boundary condition, numerical simulations of three-dimensional turbulent aeolian motion and the formation of sand ripples under three-dimensional turbulent wind and the mutual actions of saltation and creeping motion were carried out. The resulting sand ripples have the form that is flat on the upwind side and steep on the leeward, which is identical to the sand ripples in nature. We also realized the self-restoration process of three-dimensional sand ripples, which shows the correctness of the method of numerical simulation and the models of saltation and creeping. Finally, We analyzed the influence of sand ripples on the three-dimensional turbulent wind field, and found that due to the appearance and development of sand ripples, in the normal direction of ground there exists stronger energy exchange, and moreover, there is close correspondence between the forms of sand ripples and the vorticity close to the ground surface. Supported by the Key Project of National Natural Science Foundation of China (Grant No. 10532040)     

Formation of ripples over a sand bed submitted to a turbulent shear flow

We investigate the process of ripple formation when a sand bed is submitted to a steady and turbulent liquid flow. The sand transport dynamics is described in terms of a simple relaxation law which accounts for the fact that the transport rate does not adapt instantaneously to its equilibrium value. The equilibrium sand flux is evaluated using a standard law based on the estimation of the flow shear stress calculated at the sand bed surface. The latter is estimated from an analytical resolution of the flow over a deformed sand bed which is based on the Jackson and Hunt calculation [J.C.R. Hunt, Quart. J. R. Met. Soc. 101, 929 (1975)]. Within this model, we investigate the stability of the sand bed and are able to derive analytical scaling laws for the wavelength and phase velocity of the most dangerous mode. In the deep flow limit, the model predicts the occurrence of a single mode of instability corresponding to the formation of ripples. Predictions of our model are compared with previous models and available experimental data.     

Ultrafast time-resolved imaging of femtosecond laser-induced periodic surface structures on GaAs

We report the formation dynamics of periodic ripples on Ga As induced by femtosecond laser pulses（800 nm, 50 fs） via a collinear time-resolved imaging technique with a temporal resolution of 1 ps and a spatial resolution of 440 nm. The onset of periodic ripples emerges in the initial tens of picoseconds in the timescale of material ejection. The periodic ripples appear after irradiation of at least two pump pulses at surface defects produced by the first pulse and the ripple positions kept stable until the formation processes complete. The formation mechanisms of laser-induced periodic ripples are also discussed.     

Ripple formation in various metals and super-hard tetrahedral amorphous carbon films in consequence of femtosecond laser irradiation

Ripple formation in consequence of ultrashort laser pulse irradiation of materials is a well-known phenomenon. We have investigated the formation of ripples in various metals, i.e. steel, tungsten carbide hard metal, as well as in superhard ta-C films, where we used femtosecond laser pulses of 775 nm and 387 nm mean wavelength and 150 fs pulse duration. The aim was to investigate how the ripple parameters depend on irradiation parameters, and if such ripples have a potentiality for applications. In the paper, we will show that on smooth surfaces the ripple orientation is perpendicular to the electric field vector of the linearly polarized laser beam, as is well-known. Moreover, it will be shown that the ripple period decreases with decreasing laser wavelength and/or increasing angle of incidence of the laser beam on the substrate. By using optimum parameters large areas of the materials and films can be rippled swiftly, which would be important for applications. For instance, the improvement of frictional and wear behavior of tribologically stressed surfaces by ripples was investigated on ta-C coated steel surfaces.     

Dynamics of aeolian sand ripples

We analyze theoretically the dynamics of aeolian sand ripples. In order to put the study in the context, we first review existing models. This paper is a continuation of two previous papers (Z. Csahók et al., Physica D 128, 87 (1999); A. Valance et al., Eur. Phys. J. B 10, 543 (1999)), the first one is based on symmetries and the second on a hydrodynamical model. We show how the hydrodynamical model may be modified to recover the missing terms that are dictated by symmetries. The symmetry and conservation arguments are powerful in that the form of the equation is model-independent. We then present an extensive numerical and analytical analysis of the generic sand ripple equation. We find that at the initial stage the wavelength of the ripple is that corresponding to the linearly most dangerous mode. At later stages the profile undergoes a coarsening process leading to a significant increase of the wavelength. We find that including the next higher-order nonlinear term in the equation leads naturally to a saturation of the local slope. We analyze both analytically and numerically the coarsening stage, in terms of a dynamical exponent for the mean wavelength increase. We discuss some future lines of investigations. Received 20 January 2000     

Uniaxial magnetic anisotropy in nanostructured Co/Cu(001): from surface ripples to nanowires

We have investigated the correlation between morphology and magnetic anisotropy in nanostructured Co films on Cu(001). The formation of nanoscale ripples by ion erosion is found to deeply affect the magnetic properties of the Co film. A surface-type uniaxial magnetic anisotropy with easy axis parallel to the ripples is observed. The origin of the magnetic anisotropy has been identified with the modification of thermodynamic-step distribution induced by ripple formation. At higher ion doses, when Co ripples detach and crystalline nanowires form, a strong enhancement of the magnetic anisotropy due to magnetostatic contributions is observed.