On the crescentic shape of barchan dunes

Aeolian sand dunes originate from wind flow and sand bed interactions. According to wind properties and sand availability, they can adopt different shapes, ranging from huge motion-less star dunes to small and mobile barchan dunes. The latter are crescentic and emerge under a unidirectional wind, with a low sand supply. Here, a 3d model for barchan based on existing 2d model is proposed. After describing the intrinsic issues of 3d modeling, we show that the deflection of particules in reptation due to the shape of the dune leads to a lateral sand flux deflection, which takes the mathematical form of a non-linear diffusive process. This simple and physically meaningful coupling method is used to understand the shape of barchan dunes.Received: 26 January 2004, Published online: 9 April 2004PACS: 45.70.-n Granular systems - 47.54. + r Pattern selection; pattern formation     

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 characteristic quantities 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. Received 22 December 2001 / Received in final form 31 May 2002 Published online 31 July 2002     

A model of Barchan dunes including lateral shear stress

Barchan dunes are found where sand availability is low and wind direction quite constant. The two dimensional shear stress of the wind field and the sand movement by saltation and avalanches over a barchan dune are simulated. The model with one dimensional shear stress is extended including surface diffusion and lateral shear stress. The resulting final shape is compared to the results of the model with a one dimensional shear stress and confirmed by comparison to measurements. We found agreement and improvements with respect to the model with one dimensional shear stress. Additionally, a characteristic edge at the center of the windward side is discovered which is also observed for big barchans. Diffusion effects reduce this effect for small dunes.     

The morphology of dunes

The motion of dunes and their morphology is a fascinating, largely unexplored subject. Already the barchan, the simplest moving dune, poses many questions. We will present some results of field measurements on desert and costal dunes. Then we will present a model which consists of three coupled equations of motion for the topography, the shear stress of the wind and the sand flux. These evolution equations are verified on the experimental data and new possibilities of simulations of dunes are put in perspective.     

Relevant length scale of barchan dunes

A new experiment can create small scale barchan dunes under water: some sand is put on a tray moving periodically and asymmetrically in a water tank, and barchans rapidly form. We measure basic morphological and dynamical properties of these dunes and compare them to field data. These favorable results demonstrate experimentally the relevance of the so-called "saturation length" for the control of the dunes physics.     

Laboratory singing sand avalanches

Some desert sand dunes have the peculiar ability to emit a loud sound up to 110 dB, with a well-defined frequency: this phenomenon, known since early travelers (Darwin, Marco Polo, etc.), has been called the song of dunes. But only in late 19th century scientific observations were made, showing three important characteristics of singing dunes: first, not all dunes sing, but all the singing dunes are composed of dry and well-sorted sand; second, this sound occurs spontaneously during avalanches on a slip face; third this is not the only way to produce sound with this sand.More recent field observations have shown that during avalanches, the sound frequency does not depend on the dune size or shape, but on the grain diameter only, and scales as the square root of g/d - with g the gravity and d the diameter of the grains - explaining why all the singing dunes in the same vicinity sing at the same frequency.We have been able to reproduce these singing avalanches in laboratory on a hard plate, which made possible to study them more accurately than on the field. Signals of accelerometers at the flowing surface of the avalanche are compared to signals of microphones placed above, and it evidences a very strong vibration of the flowing layer at the same frequency as on the field, responsible for the emission of sound.Moreover, other characteristics of the booming dunes are reproduced and analyzed, such as a threshold under which no sound is produced, or beats in the sound that appears when the flow is too large. Finally, the size of the coherence zones emitting sound has been measured and discussed.     

Transverse instability of dunes

The simplest type of dune is the transverse one, which propagates with invariant profile orthogonally to a fixed wind direction. Here we show, by means of numerical simulations, that transverse dunes are unstable with respect to along-axis perturbations in their profile and decay on the bedrock into barchan dunes. Any forcing modulation amplifies exponentially with growth rate determined by the dune turnover time. We estimate the distance covered by a transverse dune before fully decaying into barchans and identify the patterns produced by different types of perturbation.     

Spatiotemporal model for the progression of transgressive dunes

Transgressive dune fields, which are active sand areas surrounded by vegetation, exist on many coasts. In some regions like in Fraser Island in Australia, small dunes shrink while large ones grow, although both experience the same climatic conditions. We propose a general mathematical model for the spatiotemporal dynamics of vegetation cover on sand dunes and focus on the dynamics of transgressive dunes. Among other possibilities, the model predicts growth parallel to the wind with shrinkage perpendicular to the wind, where, depending on geometry and size, a transgressive dune can initially grow although eventually shrink. The larger is the initial area the slower its stabilization process. The model’s predictions are supported by field observations from Fraser Island in Australia.     

Modelling a dune field

We present a model to describe the collective motion of barchan dunes in a field. Our model is able to reproduce the observation that a typical dune stays confined within a stripe. We also obtain some of the pattern structures which resemble those observed from aerial photos which we do analyse and compare with the specific field of Laâyounne.     

Evolution and shapes of dunes

The motion of dunes and their morphology is a fascinating, largely unexplored subject. Already the barchan, the simplest moving dune, poses many questions. I will present some results of field-measurements on desert and coastal dunes. Then I will present a model which consists of three coupled equations of motion for the topography, the shear stress of the wind and the sand flux. These evolution equations are verified on the experimental data and new possibilities of simulations of dunes are put in perspective. To cite this article: H.J. Herrmann, C. R. Physique 3 (2002) 197–206.     

Dune morphodynamics

The physics of dunes relies on the interaction between a wind flow and an erodible topography. Thus, if strong enough to transport grains, the wind shapes sandy areas into dune fields. These dunes are reminiscent of a wavy sea so that sandy deserts are called sand seas. However, the comparison stops there. Contrary to water waves, dunes propagate only under wind action and when the wind stops, they do not vanish but stand. Consequently, dunes are not only the result of the present winds, but can integrate the wind regimes over long periods. Thus, they exhibit a range of shapes and sizes with superimposed patterns. They are witnesses of past wind regimes and their shape and orientation are used to constraint climatic models on other planetary bodies where they are observed as well (e.g., Mars, Titan and Venus). Here, we discuss the morphodynamics of dunes and endeavor to identify and to explain the physical mechanisms at play in the selection of their shape, size and orientation, whilst focusing on Earth desert sand dunes.     

沙丘粗糙面的二次极化电磁散射

研究了新月形沙丘粗糙面的二次极化电磁散射. 结合射线追踪理论, 由一次散射面元的反射场照射到二次散射面元, 采用基尔霍夫近似推导了二次散射面元的二次极化散射场. 计算结果表明二次极化散射结果在特定的角度和类型范围内有显著影响. 在电磁波射向背风坡时可以发现其同极化散射截面在入射角较大时大于其他入射方向的结果, 入射角在休止角附近时的交叉极化散射截面出现峰值, 以及前后狭长沙丘之间的二次极化散射特别突出. 本文结果可用于反演分析沙漠地区的风场信息. 关键词： 新月形沙丘 二次极化散射 射线追踪 休止角     

Song of the dunes as a self-synchronized instrument

Since Marco Polo it has been known that some sand dunes have the peculiar ability to emit a loud sound with a well-defined frequency, sometimes for several minutes. The origin of this sustained sound has remained mysterious, partly because of its rarity in nature. It has been recognized that the sound is not due to the air flow around the dunes but to the motion of an avalanche, and not to an acoustic excitation of the grains but to their relative motion. By comparing singing dunes around the world and two controlled experiments, in the laboratory and the field, we prove that the frequency of the sound is the frequency of the relative motion of the sand grains. Sound is produced because moving grains synchronize their motions. The laboratory experiment shows that the dune is not needed for sound emission. A velocity threshold for sound emission is found in both experiments, and an interpretation is proposed.     

The song of dunes as a wave-particle mode locking

Singing dunes, which emit a loud sound as they avalanche, constitute a striking and poorly understood natural phenomenon. We show that, on the one hand, avalanches excite elastic waves at the surface of the dune, whose vibration produces the coherent acoustic emission in the air. The amplitude of the sound (approximately 105 dB) saturates exactly when the vibration makes the grains take off the flowing layer. On the other hand, we show that the sound frequency (approximately 100 Hz) is controlled by the shear rate inside the sand avalanche, which for granular matter is equivalent to the mean rate at which grains make collisions. This proves the existence of a feedback of elastic waves on particle motion, leading to a partial synchronization of the avalanching sand grains. It suggests that the song of dunes results from a wave-particle mode locking.     

Linear stability analysis of transverse dunes

Sand-moving winds blowing from a constant direction in an area of high sand availability form transverse dunes, which have a fixed profile in the direction orthogonal to the wind. Here we show, by means of a linear stability analysis, that transverse dunes are intrinsically unstable. Any perturbation in the cross-wind profile of a transverse dune amplifies in the course of dune migration due to the combined effect of two main factors, namely: the lateral transport through avalanches along the dune’s slip-face, and the scaling of dune migration velocity with the inverse of the dune height. Our calculations provide a quantitative explanation for recent observations from experiments and numerical simulations, which showed that transverse dunes moving on the bedrock (or “transverse sand ridges”) cannot exist in a stable form and decay into a chain of crescent-shaped barchans.     

Quantitative visualization of flow fields associated with alluvial sand dunes: Results from the laboratory and field using ultrasonic and acoustic doppler anemometry

This paper presents results detailing the quantitative visualization of flow fields associated with natural sand dunes, Fraser River Estuary, Canada, using the complementary approaches of laboratory modelling and field instrumentation. Ultrasonic Doppler velocity profiling is used in the laboratory to elucidate the mean flow fields of low-angle dunes (leeside slope angle ≈14°) that are typical of many large natural rivers. These dunes do not possess a zone of permanent flow separation in the dune leeside and have a velocity structure that is dominated by the effects of flow acceleration and deceleration generated by topographic forcing of flow over the dune form. Turbulence associated with these dunes appears linked to both longer-period shear layer flapping and eddy generation along the shear layer. The field study uses acoustic Doppler profiling to reveal similar mean flow patterns and shows that flow is dominated by deceleration in the leeside without the presence of a region of permanent separated flow.     

三维混合沙输运数值模拟

采用计算流体力学和颗粒离散元耦合的方法模拟了三维混合沙输运过程。采用体平均的Navier-stokes方程来描述气相运动,考虑了气相和颗粒相的相互作用。颗粒运动通过求解牛顿运动方程来求解,采用硬球模型描述颗粒和颗粒及颗粒和壁面的碰撞。本模型中,颗粒运动是三维的而气相运动是二维的。计算结果表明:总输沙率沿高度方向在大于2cm以上按照指数衰减,在2 cm以下则偏大;各粒径颗粒具有不同的输沙率分布,粗粒径颗粒按指数规律衰减,其它粒径颗粒输沙率随高度先指数增加后减少;各粒径颗粒平均水平速度随高度对数函数增加且同高度时随粒径增大而减小,1 cm高度以下则相反;沙粒平均粒径沿高度线性递减,2 cm以下粒径偏大。     

Simulating self-organized molecular patterns using interaction-site models

The triboelectric charging of collision particles is essential to understand sand electrification in wind-blown sand fluxes. The physical model of electron trapped in high-energy states has been proposed to explain the triboelectric charging between identical insulating granular materials. In this study we propose an improved triboelectric charging model which combines the soft sphere model and the trapped electron model to calculate the net charge transfer during particles' collisions. Based on our charging model, we investigate the sand electrification of wind-blown sand, such as the charge flux varying with height, the charge-to-mass ratio of wind-blown sand, and the equilibrium time that the charge takes to approach a stable state. Numerical simulation results of the averaged charge-to-mass ratio in wind-blown sand fluxes are in good agreement with the experimental data.     

Calculation of the separation streamlines of barchans and transverse dunes

We use FLUENT to calculate the wind profile over barchans and transverse dunes. The form of the streamlines of flow separation at the lee side of the dunes is determined for a symmetric barchan dune in three dimensions, and for the height profile of a measured transverse dune field in the Lençóis Maranhenses.