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Linear stability analysis of transverse dunes

Author

Listed:
  • Melo, Hygor P.M.
  • Parteli, Eric J.R.
  • Andrade, José S.
  • Herrmann, Hans J.

Abstract

Sand-moving winds blowing from a constant direction in an area of high sand availability form transverse dunes, which have a fixed profile in the direction orthogonal to the wind. Here we show, by means of a linear stability analysis, that transverse dunes are intrinsically unstable. Any perturbation in the cross-wind profile of a transverse dune amplifies in the course of dune migration due to the combined effect of two main factors, namely: the lateral transport through avalanches along the dune’s slip-face, and the scaling of dune migration velocity with the inverse of the dune height. Our calculations provide a quantitative explanation for recent observations from experiments and numerical simulations, which showed that transverse dunes moving on the bedrock (or “transverse sand ridges”) cannot exist in a stable form and decay into a chain of crescent-shaped barchans.

Suggested Citation

  • Melo, Hygor P.M. & Parteli, Eric J.R. & Andrade, José S. & Herrmann, Hans J., 2012. "Linear stability analysis of transverse dunes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4606-4614.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:20:p:4606-4614
    DOI: 10.1016/j.physa.2012.05.042
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    References listed on IDEAS

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    1. Herrmann, H.J & Sauermann, G, 2000. "The shape of dunes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 283(1), pages 24-30.
    2. Herrmann, H.J. & Andrade, J.S. & Schatz, V. & Sauermann, G. & Parteli, E.J.R., 2005. "Calculation of the separation streamlines of barchans and transverse dunes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 357(1), pages 44-49.
    3. Veit Schwämmle & Hans J. Herrmann, 2003. "Solitary wave behaviour of sand dunes," Nature, Nature, vol. 426(6967), pages 619-620, December.
    4. Bruno Andreotti & Antoine Fourrière & Fouzia Ould-Kaddour & Brad Murray & Philippe Claudin, 2009. "Giant aeolian dune size determined by the average depth of the atmospheric boundary layer," Nature, Nature, vol. 457(7233), pages 1120-1123, February.
    5. Hicham Elbelrhiti & Philippe Claudin & Bruno Andreotti, 2005. "Field evidence for surface-wave-induced instability of sand dunes," Nature, Nature, vol. 437(7059), pages 720-723, September.
    Full references (including those not matched with items on IDEAS)

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