IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v391y2012i20p4606-4614.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843711200413X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2012.05.042?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Veit Schwämmle & Hans J. Herrmann, 2003. "Solitary wave behaviour of sand dunes," Nature, Nature, vol. 426(6967), pages 619-620, December.
    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. Herrmann, H.J & Sauermann, G, 2000. "The shape of dunes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 283(1), pages 24-30.
    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Robson, Dominic T. & Annibale, Alessia & Baas, Andreas C.W., 2022. "Reproducing size distributions of swarms of barchan dunes on Mars and Earth using a mean-field model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    2. Xinchun Liu & Yongde Kang & Hongna Chen & Hui Lu, 2021. "Application of a High-Precision Aeolian Sand Collector in Field Wind and Sand Surveys," IJERPH, MDPI, vol. 18(14), pages 1-19, July.
    3. Herrmann, Hans J. & Kroy, Klaus & Sauermann, Gerd, 2001. "Saturation transients in saltation and their implications on dune shapes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 302(1), pages 244-254.
    4. Amelia Carolina Sparavigna, 2013. "The GNU Image Manipulation Program Applied to Study the Sand Dunes," International Journal of Sciences, Office ijSciences, vol. 2(09), pages 1-8, September.
    5. Zhang, Yong & Sun, HongGuang & Stowell, Harold H. & Zayernouri, Mohsen & Hansen, Samantha E., 2017. "A review of applications of fractional calculus in Earth system dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 29-46.
    6. Lima, A.R & Sauermann, G & Herrmann, H.J & Kroy, K, 2002. "Modelling a dune field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 487-500.
    7. Amelia Carolina Sparavigna, 2013. "A Study of Moving Sand Dunes by Means of Satellite Images," International Journal of Sciences, Office ijSciences, vol. 2(08), pages 33-42, August.
    8. Andrew Gunn & Giampietro Casasanta & Luca Liberto & Federico Falcini & Nicholas Lancaster & Douglas J. Jerolmack, 2022. "What sets aeolian dune height?," Nature Communications, Nature, vol. 13(1), pages 1-8, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:391:y:2012:i:20:p:4606-4614. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.