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Research helps to understand the dynamics of dune formation

Study carried out at FEM-Unicamp could have several applications, such as pumping oil or missions to Mars

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Barcana-type sand dunes – that is, in the shape of a crescent moon – are structures that appear in the most varied environments: on beaches and deserts, at the bottom of rivers and oceans, inside water and oil pipes, on the surface of Mars and on other planets with the presence of sand and atmosphere. 

Despite differences in scale, which can vary from 10 centimeters in the case of aquatic dunes to kilometers in the case of Martian dunes, the dynamics of formation and displacement of these structures appear to be very similar.

A survey carried out at Unicamp, with support from FAPESP, helped clarify this dynamic in the case of water dunes. And the results obtained could contribute, for example, to a better understanding of the relief of Mars – and therefore to increase the probability of success in missions to the neighboring planet – or to optimize flows and reduce costs in the flow of oil.

“These crescent-shaped or croissant-shaped dunes are called barcanas, and result from the interaction between a granular material (normally sand) and the flow of a fluid (gas or liquid), under predominantly unidirectional flow conditions. Its two ends point in the direction of fluid flow,” he said. Erick de Moraes Franklin, one of the authors of the research, to FAPESP Agency.

The work was done by Franklin and his advisor, doctoral student Carlos Alvarez, and has just been published in the journal Physical Review Letters

The research pointed out a contradiction – at least in the case of water dunes – with the hypothesis that had been adopted to explain the origin and movement of these structures. 

Photo: Scarpa
Erick de Moraes Franklin (left) and Carlos Alvarez in the laboratory at the Faculty of Mechanical Engineering: results were published in the journal “Physical Review Letters”

“Our work showed that the emergence of the two ends of the dunes cannot be explained by the previous model. According to this, the movement of sand would occur mainly in the longitudinal direction and any lateral movement of the grains would be due to a mechanism similar to diffusion. The local speed of displacement of the initial shape would then be inversely proportional to its local height. This would make the lateral, and therefore lower, parts of the pile of sand move faster, thus forming the spikes. But that’s not what we verified experimentally,” said Franklin.

What he and Alvarez observed, in the liquid medium, was that the movement of the grains occurs by rolling and sliding, in a circular fashion.  

“The tips are formed, in large part, by grains that migrate from upstream regions to the tip region. The movement has a large transverse component, which has no diffusive characteristics,” said Franklin.  

Be it a barcan dune at the bottom of a river, which is a few centimeters long and constitutes itself in minutes or even seconds; be it a barcan dune in the desert, which can reach hundreds of meters and takes years to form; be it a barchan dune on Mars, which extends for several kilometers with a formation time of the order of 10 thousand years, these structures obey the same proportions (relationship between length and height) and follow the same laws of movement.  

The height, for example, is always 10 times smaller than the length. Therefore, the results of the study carried out in the Unicamp laboratory, with ultra-fast dunes, can help to understand the dynamics of the Martian relief: how the gigantic dunes were formed and how they are expected to evolve over thousands of years. 

According to Franklin, three factors act, in a complementary or contradictory way, in the process of formation and movement of a dune: the fluid flow, the gravitational force and the inertia of the grains. The fluid flow drags the grains from the lower regions to the higher regions, causing the dune to grow.  

The gravitational force acts in the opposite direction, pulling the grains downwards and tending to cause the dune to flatten. The inertia of the grains – or rather, the difference in inertia between the grains and the fluid – determines the way they interact with the fluid.  

If the inertia of the grains is much greater than the inertia of the fluid, their movement lags behind the movement of the fluid. The grain, which should be deposited on the crest of the dune, is deposited in a lower, downstream region. 

“The complication is this. The fluid is a continuous medium, whose movement can be described by known differential equations. Physicists know how to solve this. However, the grains make up a discontinuous medium. Each dune has billions of grains. The scale is exactly this: on the order of a billion. And each grain is different from the other,” Franklin said.  

“It is impossible, to date, to describe the movements of all of them with a single differential equation. We can describe it grain by grain, but how can we integrate everything afterwards? Therefore, there are several open questions regarding dune dynamics. One of the questions is knowing why a pile of grains, of any shape, evolves to form a barcana-type dune, shaped like a crescent moon. In other words, knowing why spikes form,” he continued.  

Formation dynamics 

Something well known is that there are several types of dunes. And that barcana-type dunes form when the movement of fluid (the wind over the desert or the flow of river water, for example) occurs, on average, in a single direction. There may be occasional variations. But, in statistical terms, there is a largely predominant direction and direction. Seen from above, these dunes are shaped like the letter C. And this means that the fluid moves from the “belly” to the “tips” of the C. So far, nothing new. 

The novelty brought by the study concerns the dynamics of tip formation. The previous model assumed that each grain moved like a projectile, describing a parabola in the vertical plane, in the direction of the fluid. With a unidirectional movement, the lowest parts have greater celerity, as this is inversely proportional to the local height. And this is how the ends would be formed. But experimental research carried out at Unicamp showed that, at least in water, this is not what happens. 

“What we did was set up an experiment, with glass grains under a turbulent flow of water. Using a high-speed camera, capable of recording around a thousand images per second, we filmed the movement of the pile from above, obtaining an enormous amount of images,” said Franklin.  

“The next step was to create a computer program, capable of opening image by image, and identifying each particle that had moved. By monitoring the grains, we determined which ones had formed spikes and which trajectories they had followed. We discovered that the grains did not have a unidirectional movement, as had been assumed. Most of them went around the initial pile, in a circular type movement, forming the spikes,” he said.  

The researcher emphasized that the discovery made by him and his student applies to dunes formed in a liquid environment, but not necessarily for dunes formed in a gaseous environment. The physical explanation for this possible difference is simple and interesting, as Franklin demonstrated. 

“The previous model was based on aeolian dunes, mainly desert dunes. The density of air is one kilogram per cubic meter (1 kg/m3), about. The density of the sand grain is 2500 kilograms per cubic meter (2500 kg/m3). That is, a difference in magnitude of the order of 103. This means that, to move a grain of sand in the desert, the air needs to have a very high speed. So high that, when it displaces the grain, it is launched like a projectile, in a ballistic trajectory,” said Franklin.  

“The grain rises to approximately 1 meter in height and describes a parabolic curve. The direction of flight is the main direction of flow. So the joint motion is actually unidirectional. But water is a thousand times denser than air (1000 kg/m3). Therefore, of the same order of magnitude as the grain of sand. Therefore, it can move the grain at a much slower speed. And in doing so, the grain roughly follows the movement of the water. As it goes around the pile in a circular motion, the grains do the same,” he explained. 

According to the researcher, the experiment showed that the previous model, which had been accepted as an absolute truth, does not apply to all cases.  

“This opens up a whole discussion about the phenomenon. Experiments will need to be carried out with aeolian dunes, to confirm whether, in this case, the previous model really applies. It could be yes, but it could also be no. And there is great interest in the subject due to missions to Mars. A small difference between one Martian dune and the others could possibly signal that the dune region may have had water in the past,” he said.  

In addition to these possible far-reaching applications, the research has a much more immediate application in the case of oil pumping. Due to the fact that much of the oil is extracted together with sand and water, barcana-type dunes form inside the tubes. And they slow down the flow. Which means increased costs. Furthermore, the sand is concentrated in some places. And then it becomes very difficult to remove. Understanding the dynamics of dune formation is essential to solving the problem. 

The article Role of transverse displacements in the formation of subaqueous barchan dunes (doi:10.1103/PhysRevLett.121.164503), by Carlos A. Alvarez and Erick M. Franklin, can be read at https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.164503 www.fem.unicamp.br/~franklin/images/alvarez_franklin(2018).pdf

Follow, in videos produced by the researchers, how the underwater dune forms: www.fem.unicamp.br/~franklin/movies_dunes.html

Other articles associated with barcana dunes are available at: www.fem.unicamp.br/~franklin/publications.html.

 

 

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