Summary
Dunes are ubiquitous and exist in many forms in deserts and along coasts. They are a consequence of the wind moving sand grains by a mechanism called “saltation”. In order to describe the formation and evolution of dunes one must understand the surface flux of sand. Using the equation of motion of turbulent air in the approximation of Jackson and Hunt for gentle hills one obtains a set of equations for dune motion. These equations reproduce very well field measurements. They also allow to study in detail the collision of dunes and the stability of dune fields since their solution is many orders of magnitude faster that real time observations.
(on sabbatical leave from ICP, University of Stuttgart)
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bagnold, R. A. (1941). The physics of blown sand and desert dunes. London: Methuen.
Houghton, J. T. (1986). The physics of atmospheres, Volume 2nd edn. Cambridge: Cambridge Univ. Press.
Kármán, T. (1935). Some aspects of the turbulence problem. Proc. 4th Int. Congr. Appl. Mech. Cambridge, 54–91.
Prandtl, L. (1935). The mechanics of viscous fluids. In W. F. Durand (Ed.), Aerodynamic theory, Volume Vol. III, pp. 34–208. Berlin: Springer.
Sutton, O. G. (1953). Micrometeorology. New York: McGraw-Hill.
Launder, B. E. and Spalding, D. B. (1972). Lectures in Mathematical Models of Turbulence. London, England: Academic Press.
Fluent Inc. (1999). Fluent 5. Finite Volume Solver.
Jackson, P. S. and Hunt, J. C. R. (1975). Turbulent wind flow over a low hill. Q. J. R. Meteorol. Soc. 101, 929.
Sykes, R. I. (1980). An asymptotic theory of incompressible turbulent boundary layer flow over a small hump. J. Fluid Mech. 101, 647–670.
Zeman, O. and Jensen, N. O. (1988). Progress report on modeling permanent form sand dunes. Risø National Laboratory M-2738.
Carruthers, D. J. and Hunt J. C. R. (1990). Atmospheric Processes over Complex Terrain, Volume 23, Chapter Fluid Mechanics of Airflow over Hills: Turbulence, Fluxes, and Waves in the Boundary Layer. Am. Meteorological. Soc.
Weng, W. S., Hunt, J. C. R., Carruthers, D. J., Warren, A., Wiggs, G. F. S., Livingstone, I. and Castro, I. (1991). Air flow and sand transport over sand dunes. Acta Mechanica (Suppl.) 2, 1–22.
Hunt, J. C. R., Leibovich, S. and Richards, K. J. (1988). Turbulent wind flow over smooth hills. Q. J. R. Meteorol. Soc. 114, 1435–1470.
Schatz, V. and Herrmann H.J. (2005). Numerical investigation of flow separation in the lee side of transverse dunes. preprint for Geomorphology.
Pye, K. and Tsoar, H. (1990). Aeolian sand and sand dunes. London: Unwin Hyman.
Chepil, W. S. (1958). The use of evenly spaced hemispheres to evaluate aerodynamic forces on a soil surface. Trans. Am. Geophys. Union 39, 397–403.
Shields, A. (1936). Applications of similarity principles and turbulence research to bed-load movement. Technical Report Publ. No. 167, California Inst. Technol. Hydrodynamics Lab. Translation of: Mitteilungen der preussischen Versuchsanstalt für Wasserbau und Schiffsbau. W. P. Ott and J. C. van Wehelen (translators).
Bagnold, R. A. (1937). The size-grading of sand by wind. Proc. R. Soc. London 163(Ser. A), 250–264.
Nalpanis, P., Hunt, J. C. R. and Barrett, C. F. (1993). Saltating particles over flat beds. J. Fluid Mech. 251, 661–685.
Rioual, F., Valance, A. and Bideau, C. (2000). Experimental study of the collision process of a grain on a two-dimensional granular bed. Phys. Rev. E 62, 2450–2459.
Anderson, R. S. (1991). Wind modification and bed response during saltation of sand in air. Acta Mechanica (Suppl.) 1, 21–51.
Owen, P. R. (1964). Saltation of uniformed sand grains in air. J. Fluid. Mech. 20, 225–242.
Sørensen, M. (1991). An analytic model of wind-blown sand transport. Acta Mechanica (Suppl.) 1, 67–81.
McEwan, I. K. and Willetts, B. B. (1991). Numerical model of the saltation cloud. Acta Mechanica (Suppl.) 1, 53–66.
Willetts, B. B. and Rice, M. A. (1985). Inter-saltation collisions. In O. E. Barndorff-Nielsen (Ed.), Proceedings of International Workshop on Physics of Blown Sand, Volume 8, pp. 83–100. Memoirs.
Anderson, R. S. and Hallet, B. (1986). Sediment transport by wind: toward a general model. Geol. Soc. Am. Bull. 97, 523–535.
Almeida, M.P., Andrade Jr, J.S. and Herrmann, H.J. (2005). Aeolian transport layer. Phys.Rev.Lett. in print, cond-mat/0505626.
Butterfield, G. R. (1993). Sand transport response to fluctuating wind velocity. In N. J. Clifford, J. R. French, and J. Hardisty (Eds.), Turbulence: Perspectives on Flow and Sediment Transport, Chapter 13, pp. 305–335. John Wiley & Sons Ltd.
Rasmussen, K. R. and Mikkelsen, H. E. (1991). Wind tunnel observations of aeolian transport rates. Acta Mechanica Suppl 1, 135–144.
Lettau, K. and Lettau, H. (1978). Experimental and micrometeorological field studies of dune migration. In H. H. Lettau and K. Lettau (Eds.), Exploring the world’s driest climate. Center for Climatic Research, Univ. Wisconsin: Madison.
Ungar, J. E. and Haff, P. K. (1987). Steady state saltation in air. Sedimentology 34, 289–299.
Sørensen, M. (1985). Estimation of some eolian saltation transport parameters from transport rate profiles. In O. E. B.-N. et al. (Ed.), Proc. Int. Wkshp. Physics of Blown Sand., Volume 1, Denmark, pp. 141–190. University of Aarhus.
Werner, B. T. (1990). A steady-state model of wind blown sand transport. J. Geol. 98, 1–17.
Anderson, R. S. and Haff, P. K. (1988). Simulation of eolian saltation. Science 241, 820.
Sauermann, G., Kroy K. and Herrmann H. (2001), A continuum saltation model for sand dunes. Phys. Rev. E 64, 31305.
Kroy, K., Sauermann G. and Herrmann H. J. (2002), A minimal model for sand dunes. Phys. Rev. Lett. 88, 054301.
Kroy K., Sauermann G. and Herrmann H. J. (2002), Minimal model for aeolian sand dunes Phys. Rev. E 66, 31302
Bouchaud, J. P., Cates, M. E., Ravi Prakash J., and Edwards S. F. (1994). Hysteresis and metastability in a continuum sandpile model. J. Phys. France I 4, 1383.
Sauermann, G., Poliakov, A., Rognon, P. and Herrmann, H. J. (2000), The shape of the Barchan dunes of southern Marocco, Geomorphology 36, 47–62.
Schwämmle, V. and Herrmann, H. J. (2003). A model of Barchan dunes including lateral shear stress, EPJE 16, 591–594.
Sauermann G., Andrade J. S., Maia L. P. Costa U. M. S., Araújo A. D. and Herrmann H. J. (2003), Wind velocity and sand transport on a Barchan dune, Geomorphology 1325, 1–11.
Schwämmle V. and Herrmann H. J. (2003), Budding and solitary wave behaviour of dunes Nature 426, 619–620.
Meunier J. and Rognon P. (2000), Une méthode écologique pour détruire les dunes mobiles, Secheresse 11, 309–316.
Ribeiro Parteli E.J., Schatz V. and Herrmann H.J. (2005), Barchan dunes on Mars and on Earth, Powders and Grains 2005,eds. R. Garcia-Rojo, H.J. Herrmann and S. McNamara (Balkema, Leiden, 2005), p.959–962.
Duran O. and Herrmann H.J. (2005) Dune mobility competing with vegetation, submitted to Nature.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Herrmann, H.J. (2007). Dune Formation. In: Schadschneider, A., Pöschel, T., Kühne, R., Schreckenberg, M., Wolf, D.E. (eds) Traffic and Granular Flow’05. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-47641-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-47641-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-47640-5
Online ISBN: 978-3-540-47641-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)