Dunes

Dunes are beautiful and also a technological problem. They appear in deserts, along coasts on the ocean floor and even on mars .

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The figure shows Barchan dunes close to Laayounne in Southern Marocco. You can find more details about our measurements of the form and the scaling with size in our paper published in Geomorphology Vol 36, p.47-62 (2000).

We did some studies of a huge Barchan close to the beach of Jericoacoara in Brazil measuring air velocity and sand flux as described in the following paper that was published in Geomorphology Vol.1325, p.1-11 (2003). There the transport mechanism by saltation can be very violent as seen in the following movie .

With Murilo de Almeida and Jose Soares Andrade we simulated the saltation process in a virtual wind channel as published in Physical Review Letters Vol.96, 018001 (2006). There we show that only above a certain wind strength one finds granular transport and that the saturated sand flux increases quadratically with the extra wind strength. Using the same technique we also studied what happens under Mars conditions as published in PNAS Vol.105, 6222 (2008) finding giant saltation trajectories and a rather low threshold wind strength to sustain the saturated flux. This paper found large resonance in the media with a list of 60 sites that include journals like Der Spiegel , National Geographic , Science News , Ciencia Hoje , New Scientist , O Povo , wissenschaft.de , space.com , Folha de Sao Paulo , Wikipedia and even a blog was created.

With Marcus Vinicius Carneiro we did a full three dimensional simulation of the particle trajectories in saltation published in Physical Review Letters Vol. 107, 098001 (2011) finding that the onset of saltation exhibits a jump in the sand flux. With the same technique we discovered that mid-air collisions enhance the flux substantially as shown in the paper in Physical Review Letters Vol. 111, 058001 (2013), which was commented among others in Research Highlights of Nature, Physics World , Physics and insidescience .

A striking phenomenon observed during saltation is that the sand can charge up electrically. This is not easy to understand because all grains are made of the same material and have about the same size. With Thomas Paehtz and Troy Shinbrot we studied this phenomenon numerically and experimentally with glass beads and found that polarization at collisions where charge annihilation only occurs locally at the contact point can explain the phenomenon as described in a recent paper which has been commented in Science News , News and Views , Online FAPESP and Wired Science .

With Gerd Sauermann and Klaus Kroy we developped a model consisting of three coupled equations for the motion of the free sand surface under the action of the wind. The model is described in a paper in Phys. Rev. Lett. Vol. 88, p. 54301 (2002) and derived in a paper published in Phys.Rev. E Vol.64, p.31305 (2001) and a later paper published in Phys. Rev. E Vol.66, p.31302 (2002). At the meeting on dunes in Nouakchott in february of 2001 we presented the following contribution that gives a brief review of the model and an even simpler version of the model is described in an older paper published in Physica A, Vol 283, p. 24-30 (2000). The most recent version of our full computer program can be downloaded here . One particularly subtle problem is the correct modelization of the "separation bubble" behind the crest of a dune inside which the wind is so strongly screened that aeolian grain transport is virtually suppressed. The shape of this separation bubble can be obtained on given topographies using the commercial code FLUENT and in a paper published in Physica A, Vol.357, p.44-49 (2005) we present with Soares Andrade, Eric Parteli and Volker Schatz some results. In a contribution to the proceedings of Powders and Grains we propose a closed expression for the size of the separation bubble as function of the distance between crest and brink.

I also wrote with Pierre Rognon a small article for the Bulletin of the SFP in french destined to a broader public. An overview over the mechanisms of wind-blown sand and derivations of the equations are also given in my review which was published in a book edited by H. Hinrichsen and D. Wolf. I also wrote the chapter on dunes in the Encyclopedia of Nonlinear Science. You can also download a talk that I gave in several occasions on the subject.

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In the figure to the left we see the result of the numerical solution of these equations for a given initial configuration consisting of several Gaussian heaps resulting after the wind has blown from the same direction during some time. More detailed numerical studies on Barchans were performed with Veit Schwämmle and are written up in the following paper published in EPJE Vol.16, p.57-65 (2005). There exists a minimal size for Barchans below which they are not stable anymore. This was systematically investigated in a paper with Eric Parteli and Orencio Duran published in Phys. Rev. E, Vol.75, 011301 (2007).

With Veit Schwämmle we also simulated transverse dunes as published in Earth Surface Processes and Landforms, Vol.29, p.769-784 (2004) and found that their evolution from a flat surface is like a dilatation, i.e. that with time they increase and separate from each other.

A particularly beautiful realization of transverse dunes are the Lençóis Maranhenses in the northeast of Brazil. As seen on the photo below the dunes in this natural park are separated by lagoons. With Eric Parteli , Veit Schwämmle and Luis Parente Maia we studied in a field trip during september 2003 these dunes and reproduced the measured profiles with our model as can be read about in our paper published in Geomorphology Vol.81, p. 29-42 (2006). There the transport mechanism by saltation can even occur on wet sand as seen in the following movie . The velocity of the dunes can monitored there also by studying the residual ridges they leave behind as we did with Noam Levin and Haim Tsoar as published in Sedimentology Vol.56, p.1623 (2009) where is even became the cover . In 2006 we went there again to study quicksand .

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When the wind is not constant but periodically switches directions other shapes of duenes appear like longitudinal or seif dunes. With Eric Parteli, Orencio Durán and Haim Tsoar we studied this case as presented in our recent PNAS Vol. 106, 22085 2009).

In a paper in Nature Vol.426, p.619-620 (2003) we showed with Veit Schwämmle that when a smaller Barchan dune hits a larger one from the back it can either coalesce completely, join and eject two babies from the horns (see this movie ) or exchange so much mass that finally the one in front escapes and in such a way they behave like solitary waves as seen in the following movie . An article with more details was published with Orencio Duran in Phys.Rev.E. Vol.72, 021308 (2005).

An entire field of barchan dunes was modelled in a paper printed in Physica A, Vol.310, 487-500 (2002) and shown that the field stays confined within a stripe. With Eric Parteli we developped a simple one-dimensional model for a field of transverse dunes with flux between the dunes which reproduced the selection of a characteristic dune height. as shown in the paper printed in Physica A, Vol.327, p.554-562 (2003). This model has been made more realistic and compared to the fields in Lençóis Maranhenses with Jae Hwan Lee in a paper Int.J.Mod.Phys.C Vol.16, p.1879-1892 (2005). A beautiful simulation of the genesis of a dune field using our equations of motion can be seen in a movie made by Orencio Duran .

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With Orencio Duran we extended the model to also include the growth of vegetation by including a further equation. Vegetation can stop sand motion but sand motion can also kill vegetation. The two effects therefore compete against each other. In a paper published in Physical Review Letters Vol. 97, 188001 (2006) we showed that vegetation can tranform Barchans into parabolic dunes. In the image on the left side we see different such parabolic dunes depending on the ratio between dune velocity and vegetation growth velocity. These shapes compare very well with aeral photos from real dunes. We also did a field study of parabolic dunes along the Northeastern coast of Brazil and compared them to our calculations as discussed in a paper published in Geomorphology Vol.102, p.460 (2008). Our work on vegetation was commented in the Physics Web and on Plus magazine .

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On Mars there are also dunes as the "cockroach" Barchans seen in the image at right. Some Mars dunes have shapes never seen on Earth. With Eric Parteli we applied our equations using Mars parameters to reproduce some of these shapes as described in a paper published in Physical Review Letters Vol.98, 198001 (2007) and in more detail in a paper published in Phys. Rev.E, Vol.76, 041307 (2007). This work was commented in Physics Web , Physics Update , wissenschaft.de , SPACE.com , Sonntag (Aarau) and in over 100 other journals and sites like, in softpedia , in the Dutch Kennislink , in the Mars Society , in the Russian magazines lenta , grani , our Texas and podrobnosti , in sci.astro.amateur , in French , in Farsi and in the Brazilian Pesquisa Fapesp and Funcap Ciencia . See a list of all the sites which comment this paper. A longer article also appeared in SIAM News . We see a "cockroach" Barchan calculated in this way below.

We also studied with Eric Parteli and Haim Tsoar dunes under periodically varying wind directions as for instance linear or seif dunes on Earth and on Mars conditions as described in an article published in PNAS, Vol.106, p.22085 (2009) and discussed in Ciencia Hoje .

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Many popular articles have been published about our dune modelization including in french one in Pour la Science and one in Ca m'interesse , in portuguese in Pesquisa FapPesquisa Fapesp esp and in german one in Physik Journal , one in Rheinpfalz , one in the GDNÄ-Aktuell , one in Neue Züricher Zeitung , one in the Sonntagszeitung , one in the Tages-Anzeiger , one in GEO and another in the Stuttgarter Zeitung . Also the German radio aired some interviews .

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My fascination with dunes in fact is quite old. In the picture left you see me 30 years ago on the highest dune of South America which is called "El Purpur" and lies in Peru according to the legend stuck on an ancient Chan-Chan ruin.