Sand dunes mobility and stability in relation to climate

Sand dunes form an important and unique system that can be mobile or fixed by vegetation. The common mobility indices of sand dunes, which are related to the wind and the amount of precipitation and potential evaporation, do not work in many dune fields around the world. The reasons for that lie in the singular physical characteristics of the sandy soil. Sand has high hydraulic conductivity causing a high rate of infiltration of rain water to the groundwater. Sand particles lack cohesion and that makes wind erosion the main limiting factor for vegetation. Hence, wind power, manifested by the drift potential (DP), is a good index for the limiting factor of plants on sand. The physical–biological interaction is further developed by hysteresis, which shows that a dune can become vegetated when the wind power is sufficiently low. Once vegetated, a much higher wind stress is needed to destroy the vegetation and re-activate the dunes.     

Why do active and stabilized dunes coexist under the same climatic conditions?

Sand dunes can be active (mobile) or stable, mainly as a function of vegetation cover and wind power. However, there exists as yet unexplained evidence for the coexistence of bare mobile dunes and vegetated stabilized dunes under the same climatic conditions. We propose a model for dune vegetation cover driven by wind power that exhibits bistabilty and hysteresis with respect to the wind power. For intermediate wind power, mobile and stabilized dunes can coexist, whereas for low (or high) wind power they can be fixed (or mobile). Climatic change or human intervention can turn active dunes into stable ones and vice versa; our model predicts that prolonged droughts with stronger winds can result in dune reactivation.     

Bifurcation analysis of the transition of dune shapes under a unidirectional wind

A bifurcation analysis of dune shape transition is made. By use of a reduced model of dune morphodynamics, the Dune Skeleton model, we elucidate the transition mechanism between different shapes of dunes under unidirectional wind. It was found that the decrease in the total amount of sand in the system and/or the lateral sand flow shifts the stable state from a straight transverse dune to a wavy transverse dune through a pitchfork bifurcation. A further decrease causes wavy transverse dunes to shift into barchans through a Hopf bifurcation. These bifurcation structures reveal the transition mechanism of dune shapes under unidirectional wind.     

Modeling transverse dunes with vegetation

In the present work, we use dune modeling in order to investigate the evolution of transverse dunes in the presence of vegetation. The vegetation is allowed to grow up to a maximum height with a growth rate R that oscillates in time. We find that the presence of the vegetation establishes a maximum height for the transverse dunes. If the transverse dune is larger than this maximum size, then the vegetation traps a considerable amount of sand, leading to the formation of vegetation marks at the upwind side of the dune. We also investigate the formation of the transverse dune fields from a flat sand beach under saturated sand flux and vegetation growth. We find that the behavior of the field is determined by the maximum height, , of the vegetation cover.     

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     

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.     

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.     

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.     

Vegetation against dune mobility

Vegetation is the most common and most reliable stabilizer of loose soil or sand. This ancient technique is for the first time cast into a set of equations of motion describing the competition between aeolian sand transport and vegetation growth. Our set of equations is then applied to study quantitatively the transition between barchans and parabolic dunes driven by the dimensionless fixation index theta which is the ratio between the dune characteristic erosion rate and vegetation growth velocity. We find a fixation index theta(c) below which the dunes are stabilized, characterized by scaling laws.     

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.     

Selection of dune shapes and velocities Part 2: A two-dimensional modelling

We present in this paper a simplification of the dune model proposed by Sauermann et al. which keeps the basic mechanisms but allows analytical and parametric studies. Two kinds of purely propagative two dimensional solutions are exhibited: dunes and domes. The latter, by contrast to the former, do not present a slip face. Their shape and velocity can be predicted as a function of their size. We recover that dune profiles are not scale invariant (small dunes are flatter than the large ones), and that the inverse of the velocity grows almost linearly with the dune size. We furthermore get the existence of a critical mass below which no dune solution exists. It rises the problem of dune nucleation: how can dunes appear if any bump below this minimal mass gets eroded and disappears? The linear stability analysis of a flat sand bed shows that it is unstable at large wavelengths: dune can in fact nucleate from a small sand mass if the proto-dune is sufficiently long. Received 22 December 2001 / Received in final form 31 May 2002 Published online 31 July 2002     

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.     

Spatial structuring and size selection as collective behaviours in an agent-based model for barchan fields

In order to test parameters of the peculiar dynamics occurring in barchan fields, and compute statistical analysis over large numbers of dunes, we build and study an agent-based model, which includes the well-known physics of an isolated barchan, and observations of interactions between dunes. We showed in a previous study that such a model, where barchans interact through short-range sand recapture and collisions, reproduces the peculiar behaviours of real fields, namely its spatial structuring along the wind direction, and the size selection by the local density. In this paper we focus on the mechanisms that drives these features. In particular, we show that eolian remote sand transfer between dunes ensures that a dense field structures itself into a very heterogeneous pattern, which alternates dense and diluted stripes in the wind direction. In these very dense clusters of dunes, the accumulation of collisions leads to the local emergence of a new size for the dunes.     

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.     

Saltation transport on Mars

We present the first calculation of saltation transport and dune formation on Mars and compare it to real dunes. We find that the rate at which grains are entrained into saltation on Mars is 1 order of magnitude higher than on Earth. With this fundamental novel ingredient, we reproduce the size and different shapes of Mars dunes, and give an estimate for the wind velocity on Mars.     

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.