Granular Matter

, Volume 11, Issue 1, pp 7–11 | Cite as

The dune size distribution and scaling relations of barchan dune fields

  • Orencio Durán
  • Veit Schwämmle
  • Pedro G. Lind
  • Hans J. Herrmann
Open Access


Barchan dunes emerge as a collective phenomena involving the generation of thousands of them in so called barchan dune fields. By measuring the size and position of dunes in Moroccan barchan dune fields, we find that these dunes tend to distribute uniformly in space and follow an unique size distribution function. We introduce an analytical mean-field approach to show that this empirical size distribution emerges from the interplay of dune collisions and sand flux balance, the two simplest mechanisms for size selection. The analytical model also predicts a scaling relation between the fundamental macroscopic properties characterizing a dune field, namely the inter-dune spacing and the first and second moments of the dune size distribution.


Pattern formation Dune fields Dune collisions Master equation Log-normal distributions 


The authors thank Maria Haase for useful discussions. This research was supported in part by the Max-Planck prize.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


  1. 1.
    Kroy K., Sauermann G., Herrmann H.J.: Minimal model for sand dunes. Phys. Rev. Lett. 88, 054301 (2002)CrossRefADSGoogle Scholar
  2. 2.
    Andreotti B., Claudin P., Douady S.: Selection of dune shapes and velocities. Part 1: dynamics of sand, wind and barchans. Eur. Phys. J. B 28, 321 (2002)CrossRefADSGoogle Scholar
  3. 3.
    Andreotti B., Claudin P., Douady S.: Selection of dune shapes and velocities. Part 2: a two-dimensional modeling. Eur. Phys. J. B 28, 341 (2002)CrossRefADSGoogle Scholar
  4. 4.
    Hersen P.: On the crescentic shape of barchan dune. Eur. Phys. J. B 37, 507 (2004)CrossRefADSGoogle Scholar
  5. 5.
    Schwämmle V., Herrmann H.J.: Solitary wave behaviour of dunes. Nature 426, 619 (2003)CrossRefADSGoogle Scholar
  6. 6.
    Durán O., Schwämmle V., Herrmann H.J.: Breeding and solitary wave behavior of dunes. Phys. Rev. E 72, 021308 (2005)CrossRefADSGoogle Scholar
  7. 7.
    Hersen P., Douady S.: Collision of barchan dunes as a mechanism of size regulation. Geophys. Res. Lett. 32, L21403 (2005)CrossRefADSGoogle Scholar
  8. 8.
    Durán O., Herrmann H.J.: Vegetation against dune mobility. Phys. Rev. Lett. 97, 188001 (2006)CrossRefADSGoogle Scholar
  9. 9.
    Schwämmle V., Herrmann H.J.: A model of barchan dunes including lateral shear stress. Eur. Phys. J. E 16, 57 (2005)CrossRefGoogle Scholar
  10. 10.
    Lima A.R., Sauermann G., Herrmann H.J., Kroy K.: A model for dune fields. Phys A 310, 487 (2002)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Hersen P., Andersen K.H., Elbelrhiti H., Andreotti B., Claudin P., Douady S.: Corridors of barchan dunes: stability and size selection. Phys. Rev. E 69, 011304 (2004)CrossRefADSGoogle Scholar
  12. 12.
    Ewing R.C., Kocurek G., Lake L.W.: Pattern analysis of dune-field parameters. Earth Surf. Proc. Landf. 31, 1176–1191 (2006)CrossRefGoogle Scholar
  13. 13.
    Elbelrhiti H., Claudin P., Andreotti B.: Field evidence for surface-wave induced instability of sand dunes. Nature 437, 720 (2005)CrossRefADSGoogle Scholar
  14. 14.
    Elbelrhiti H., Claudin P., Andreotti B.: Barchan dune corridors: field characterization and investigation of control parameters. J. Geophys. Res. 113, F02S15 (2008)CrossRefGoogle Scholar
  15. 15.
    Kocurek G., Townsley M., Yeh E., Havholm K., Sweet M.L.: Dune and dune-field development on Padre Island, Texas, with implications for interdune deposition and water-table-controlled accumulation. J. Sedim. Petrol. 62, 622–635 (1992)Google Scholar
  16. 16.
    Durán, O., Schwämmle, V., Herrmann, H.J.: Barchan dune’s size distribution induced by collisions. cond-mat/0701370v1Google Scholar
  17. 17.
    Durán, O., Herrmann, H.J.: Modelling of saturated sand flux. J. Stat. Mech. P07011 (2006)Google Scholar

Copyright information

© The Author(s) 2008

Authors and Affiliations

  • Orencio Durán
    • 1
  • Veit Schwämmle
    • 2
  • Pedro G. Lind
    • 3
  • Hans J. Herrmann
    • 4
    • 5
  1. 1.Institute for Computational PhysicsStuttgart UniversityStuttgartGermany
  2. 2.Centro Brasileiro de Pesquisas FísicasUrcaBrazil
  3. 3.Centro de Fsica Terica e ComputacionalUniversidade de Lisboa AvenidaLisbonPortugal
  4. 4.Computational Physics, IfB, HIF E12, ETH HönggerbergZurichSwitzerland
  5. 5.Departamento de FísicaUniversidade Federal do CearáFortalezaBrazil

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