Giant aeolian dune size determined by the average depth of the atmospheric boundary layer

Abstract

Depending on the wind regime1,2, sand dunes exhibit linear3,4, crescent-shaped or star-like forms5 resulting from the interaction between dune morphology and sand transport6,7,8. Small-scale dunes form by destabilization of the sand bed9,10,11 with a wavelength (a few tens of metres) determined by the sand transport saturation length11,12,13. The mechanisms controlling the formation of giant dunes, and in particular accounting for their typical time and length scales, have remained unknown. Using a combination of field measurements and aerodynamic calculations, we show here that the growth of aeolian giant dunes, ascribed to the nonlinear interaction between small-scale superimposed dunes4,10,14,15, is limited by the confinement of the flow within the atmospheric boundary layer16,17. Aeolian giant dunes and river dunes form by similar processes, with the thermal inversion layer that caps the convective boundary layer in the atmosphere18 acting analogously to the water surface in rivers. In both cases, the bed topography excites surface waves on the interface that in turn modify the near-bed flow velocity. This mechanism is a stabilizing process that prevents the scale of the pattern from coarsening beyond the resonant condition. Our results can explain the mean spacing of aeolian giant dunes ranging from 300 m in coastal terrestrial deserts to 3.5 km. We propose that our findings could serve as a starting point for the modelling of long-term evolution of desert landscapes under specific wind regimes.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Separation of length scales between small and giant dunes for the different wind regimes.
Figure 2: Selection of the wavelength of giant dunes by the depth of the atmospheric boundary layer.
Figure 3: Linear stability analysis of the dune formation process.
Figure 4: Pattern coarsening and nonlinear wavelength selection.

References

  1. 1

    Fryberger, S. G. & Dean, G. in A Study of Global Sand Seas (ed. McKee, E. D.) 137–169 (Geological Survey Professional Paper 1052, 1979)

    Google Scholar 

  2. 2

    Werner, B. T. Eolian dunes; computer simulations and attractor interpretation. Geology 23, 1107–1110 (1995)

    ADS  Article  Google Scholar 

  3. 3

    Tsoar, H. Dynamic processes acting on a longitudinal (seif) sand dune. Sedimentology 30, 567–578 (1983)

    ADS  Article  Google Scholar 

  4. 4

    Bristow, C. S., Bailey, S. D. & Lancaster, N. The sedimentary structure of linear sand dunes. Nature 406, 56–59 (2000)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Lancaster, N. The dynamics of star dunes: an example from Gran Desierto, Mexico. Sedimentology 36, 273–289 (1989)

    ADS  Article  Google Scholar 

  6. 6

    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, 321–339 (2002)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Wiggs, G. F. S., Livingstone, I. & Warren, A. The role of streamline curvature in sand dune dynamics: evidence from field and wind tunnel measurements. Geomorphology 17, 29–46 (1996)

    ADS  Article  Google Scholar 

  8. 8

    Lancaster, N., Nickling, W. G., McKenna-Neuman, C. K. & Wyatt, V. E. Sediment flux and airflow on the stoss slope of a barchan dune. Geomorphology 17, 55–62 (1996)

    ADS  Article  Google Scholar 

  9. 9

    Andreotti, B., Claudin, P. & Douady, S. Selection of dune shapes and velocities. Part 2. Eur. Phys. J. B 28, 341–352 (2002)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Elbelrhiti, H., Claudin, P. & Andreotti, B. Field evidence for surface-wave-induced instability of sand dunes. Nature 437, 720–723 (2005)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Claudin, P. & Andreotti, B. A scaling law for aeolian dunes on Mars, Venus, Earth, and for subaqueous ripples. Earth Planet. Sci. Lett. 252, 30–44 (2006)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Kroy, K., Sauermann, G. & Herrmann, H. Minimal model for sand dunes. Phys. Rev. Lett. 88, 054301 (2002)

    ADS  Article  Google Scholar 

  13. 13

    Hersen, P., Douady, S. & Andreotti, B. Relevant length scale of barchan dunes. Phys. Rev. Lett. 89, 264301 (2002)

    ADS  Article  Google Scholar 

  14. 14

    Bristow, C. S., Duller, G. A. T. & Lancaster, N. Age and dynamics of linear dunes in the Namib desert. Geology 35, 555–558 (2007)

    ADS  Article  Google Scholar 

  15. 15

    Kocurek, G., Havholm, K. G., Deynoux, M. & Blakey, R. C. Amalgamated accumulations resulting from climatic and eustatic changes, Akchar Erg, Mauritania. Sedimentology 38, 751–772 (1991)

    ADS  Article  Google Scholar 

  16. 16

    Wilson, I. G. Aeolian bedforms—their development and origins. Sedimentology 19, 173–210 (1972)

    ADS  Article  Google Scholar 

  17. 17

    Hanna, S. R. The formation of longitudinal sand dunes by large helical eddies in the atmosphere. J. Appl. Meteorol. 8, 874–883 (1969)

    ADS  Article  Google Scholar 

  18. 18

    Stull, R. B. An Introduction to Boundary Layer Meteorology Ch. 1, 11 (Kluwer Academic, 1988)

    Google Scholar 

  19. 19

    Lancaster, N. The development of large aeolian bedforms. Sedim. Geol. 55, 69–89 (1988)

    ADS  Article  Google Scholar 

  20. 20

    Ewing, R. C., Kocurek, G. & Lake, L. W. Pattern analysis of dune-field parameters. Earth Surf. Processes Landforms 31, 1176–1191 (2006)

    ADS  Article  Google Scholar 

  21. 21

    Wurtele, M. G., Sharman, R. D. & Datta, A. Atmospheric lee waves. Annu. Rev. Fluid Mech. 28, 429–476 (1996)

    ADS  MathSciNet  Article  Google Scholar 

  22. 22

    Baddock, M. C., Livingstone, I. & Wiggs, G. F. S. The geomorphological significance of airflow patterns in transverse dune interdunes. Geomorphology 87, 322–336 (2007)

    ADS  Article  Google Scholar 

  23. 23

    Parteli, E. J. R., Schwämmle, V., Herrmann, H. J., Monteiro, L. H. U. & Maia, L. P. Profile measurement and simulation of a transverse dune field in the Lençóis Maranhenses. Geomorphology 81, 29–42 (2006)

    ADS  Article  Google Scholar 

  24. 24

    Andersen, K. H., Chabanol, M.-L. & van Hecke, M. Dynamical models for sand ripples beneath surface waves. Phys. Rev. E 63, 066308 (2001)

    ADS  CAS  Article  Google Scholar 

  25. 25

    Politi, P. & Misbah, C. When does coarsening occur in the dynamics of one-dimensional fronts? Phys. Rev. Lett. 92, 090601 (2004)

    ADS  Article  Google Scholar 

  26. 26

    Best, J. The fluid dynamics of river dunes: a review and some future directions. J. Geophys. Res. 100, F04S02 (2005)

    Google Scholar 

  27. 27

    Raudkivi, A. J. Transition from ripples to dunes. J. Hydraul. Eng. 132, 1316–1320 (2006)

    Article  Google Scholar 

  28. 28

    Tokano, T., Ferri, F., Colombatti, G., Mäkinen, T. & Fulchignoni, M. Titan's planetary boundary layer structure at the Huygens landing site. J. Geophys. Res. 111, E08007 (2006)

    ADS  Article  Google Scholar 

  29. 29

    Savijärvi, H., Määttänen, A., Kauhanen, J. & Harri, A. M. Mars Pathfinder: New data and new model simulations. Q. J. R. Meteorol. Soc. 130, 669–683 (2004)

    ADS  Article  Google Scholar 

  30. 30

    Lorenz, R. D. et al. The sand seas of Titan: Cassini RADAR observations of longitudinal dunes. Science 312, 724–727 (2006)

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

We thank R. Littlewood for discussions and assistance with the field work. This study was supported by an ANR grant.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Philippe Claudin.

Supplementary information

Supplementary Information

This file contains Supplementary Methods, Supplementary Data, Supplementary Figures 5-32 with Legends, Supplementary Tables 1-2 and Supplementary References. (PDF 2481 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Andreotti, B., Fourrière, A., Ould-Kaddour, F. et al. Giant aeolian dune size determined by the average depth of the atmospheric boundary layer. Nature 457, 1120–1123 (2009). https://doi.org/10.1038/nature07787

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.