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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
Article

Abstract

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.

Keywords

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

Notes

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.

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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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