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Abstract.

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.

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References

  1. R.A. Bagnold, The physics of blown sand and desert dunes (Chapman and Hall, London, 1941)

  2. B. Andreotti, P. Claudin, S. Douady, Eur. Phys. J. B 38, 341 (2002)

    Google Scholar 

  3. P. Hersen, S. Douady, B. Andreotti, Phys. Rev. Lett. 89, 264301 (2002)

    Article  Google Scholar 

  4. R. Cooke, A. Warren, A. Goudie, Desert Geomorphology (UCL Press, 1993)

  5. K. Pye, H.Tsoar, Aeolian Sand and sand dunes (Unwin Hyman, London, 1990)

  6. H.J. Finkel, J. Geol. 67, 614 (1959)

    Google Scholar 

  7. J.T. Long, R.P. Sharp, Geol. Soc. Am. Bull 75, 149 (1964)

    Google Scholar 

  8. R.M. Norris, J. Geol., 74, 292 (1966)

    Google Scholar 

  9. S.L. Hastenrath, Zeitschrift für Geomorphologie 11, 3003 (1967)

    Google Scholar 

  10. K. Lettau, H.H. Lettau, Zeitschrift für Geomorphologie 13, 182 (1969)

    Google Scholar 

  11. S. Hastenrath, Z. Geomorph. N. F. 31, 167 (1987)

    Google Scholar 

  12. M.C. Slattery, South African Geographical J. 72, 5 (1990)

    Google Scholar 

  13. P.A. Hesp, K. Hastings, Geomorphology 22, 193 (1998)

    Article  Google Scholar 

  14. G. Sauermann, P. Rognon, A. Poliakov, H.J. Herrmann, Geomorphology 36, 47 (2000)

    Article  Google Scholar 

  15. F.K. Wippermann, G. Gross, Boundary-Layer Meteorology 36, 319 (1986)

    Google Scholar 

  16. H. Nishimori, N. Ouchi, Phys. Rev. Lett. 71, 197 (1993)

    Article  Google Scholar 

  17. B.T. Werner, Geology 23, 1107 (1995)

    Article  Google Scholar 

  18. H. Nishimori, M. Yamasaki, K.H. Andersen, J. Mod. Phys. B 12, 256 (1997)

    Google Scholar 

  19. J.M.T. Stam, Sedimentology 44, 127 (1997)

    Google Scholar 

  20. J.H. van Boxel, S.M. Arens, P.M. van Dijk, Earth Surface Processes and Landforms 24, 255 (1999)

    Article  Google Scholar 

  21. G. Sauermann, Modeling of Wind Blown Sand and Desert Dunes, Ph.D. thesis, Universitat Stuttgart (2001)

  22. K. Kroy, Phys. Rev. E 66, 031302 (2002)

    Article  Google Scholar 

  23. B. Andreotti, P. Claudin, S. Douady, Eur. Phys. J. B 28, 321 (2002)

    Article  Google Scholar 

  24. P. Hersen, K.H. Andersen, H. Elbelrhiti, B. Andreotti, P. Claudin, S. Douady, Phys. Rev. E 69, 011304 (2003)

    Article  Google Scholar 

  25. R.S. Anderson, M. Sørensen, B.B. Willetts, Acta Mechanica [suppl] 1, 1 (1991)

    Google Scholar 

  26. M. Sørensen, On the rate of aeolian sand transport, Atelier international: Formation et migration des Dunes, Nouakchott, 2001

  27. B. Andreotti, A two species model of aeolian sand transport, to appear in J. Fluid. Mech. (2004)

  28. P.S. Jackson, J.C.R. Hunt, Quart. J. R. Met. Soc. 101, 929 (1975)

    Article  Google Scholar 

  29. A.C. Fowler, Geomorphological Fluid Mechanics, Chap. 16 (Springer-Verlag, Berlin, 2001), pp. 430-454

  30. V. Schwammle, H.J. Herrmann, A model of barchan dunes including lateral shear stress, cond-mat/0305036 (2003)

  31. V. Schwammle, H.J. Herrmann, Modeling transverse dunes, cond-mat/0301589 (2003)

  32. J. Hardisty, R.J.S. Whitehouse, Nature 332, 532 (1988)

    Article  Google Scholar 

  33. A.D. Howard, Geol. Soc. Am. Bull. 88, 853 (1977)

    Google Scholar 

  34. K.H. Andersen, B. Andreotti, P. Claudin, private communication (2002/2003)

  35. These boundary conditions induces also a weak coupling between slices: the output flux is not homogeneous, so a part of the sand escaping from the horns is transfered to the center of the dune

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Correspondence to P. Hersen.

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Received: 26 January 2004, Published online: 9 April 2004

PACS:

45.70.-n Granular systems - 47.54. + r Pattern selection; pattern formation

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Hersen, P. On the crescentic shape of barchan dunes. Eur. Phys. J. B 37, 507–514 (2004). https://doi.org/10.1140/epjb/e2004-00087-y

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  • DOI: https://doi.org/10.1140/epjb/e2004-00087-y

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