Towards theoretical modeling of the sand dunes motion

  • O.I. Gerasymov
  • I.S. Andrianova
Keywords: sand dunes, wind flow, shear stress, granular viscosity


The transport of sand by wind is a potent erosion force, creates sand dunes and ripples, and loads the atmosphere with suspended dust aerosols. This article presents a short review of the physics of wind-driven sand. Specifically, we review the physics of saltation, the formation and development of sand dunes and ripples. We also discuss some classes of the governing equations which describe the physics of wind-driven sand and dune formation. We describe selected types of dunes and conditions under which they occur, and also some features of dunes as well as processes that they are involved in. We show that the normalized dunes height collapses using a simple product of the Froude and Reynolds numbers. This would obscure the effects of frictional dissipation, which clearly plays an important role in all mentioned upper process. Ignoring friction, one can construct a simple energy balance between the kinetic energy of the impacting and the potential energy of the dunes, where we assume the dunes thickness is proportional to ds. This produces the following scaling. In other words, was one to increase the grain diameter ds by a factor of 10 ~ i.e., reduce Re by 100! for the same impact conditions, then the frictionless flow would predict a 10-fold reduction in , whereas the experiments suggest a 100-fold reduction. This shows clearly that viscous forces play a role in the granular dunes formation (and their relevant dynamics), as well as gravity and inertia.

These circumstances move us to conclude   the vide range of (non-dissipative) hydrodynamic approaches to describe dunes formation and their dynamics just as a robust model approaches.


Bagnold R.A. The size-grading of sand by wind. Proc. R. Soc. (Ser. A), 1937, no. 163, pp. 250-264.

Houghton J.T. The physics of atmospheres, 2nd edn. Cambridge: Cambridge Univ. Press., 1986.

Prandtl L. The mechanics of viscous fluids. Aerodynamic theory. Berlin: Springer, 1935, vol. III, pp. 34-208.

Friedman G.M., Sunders J.E. Principles of sedimentology. New York: Wiley, 1978, 439 р.

Pye K., Tsoar H. Aeolian sand and sand dunes. London: Unwin Hyman, 1990.

Sorensen M. Estimation of some aeolian sultation transport parameters from transport rate profiles. Proc. Int. Wkshp. Physics of Blown. Sand. Denmark, 1985, vol. I, pp. 141-190. In Barndorf-Nielsen et al (Eds).

Sorensen M. An analytic model of wind-blown sand transport. Acta Mechanica (Suppl.), 1991, no. 1, pp. 67-81.

Bagnold R.A. The movement of desert sand. Proc. R. Soc. (Ser. A), 1936, no. 157, pp. 594-620.

Zeman O., Jensen N.O. Progress report on modeling permanent form sand dunes. Risø National Laboratory M-2738, 1988.

Bagnold R.A. The nature of saltation and bed-load transport in water. Proc. R. Soc. (Ser. A), 1973, no. 332, pp. 473-504.

Shields A. Applications of similarity principles and turbulence research to bed-load movement. Technical Report Publ., no. 167, California Inst. Technol. Hydrodynamics Lab., 1936.

Herrmann H.J., Sauermann G. The shape of dunes. Physica A, 2000, no. 283, pp. 24-30.

Weng W.S., Hunt J.C.R., Carruthers D.J., Warren A., Wiggs G.F.S., Livingstone I., Castro I. Air flow and sand transport over sand–dunes. Acta Mechanica (Suppl.), 1991, no. 2, pp. 1-22.

Sauermann G., Rognon P., Polyakov A., Herrmann H.J. The shape of the barchan dunes of southern Morocco. Geomorphology, 2000, no. 36, pp. 47-62.

Kadanoff Leo P. Built upon sand: Theoretical ideas inspired by granular flows. Rev. Mod. Phys., 1999, no. 71, pp. 435.

How to Cite
Gerasymov, O., & Andrianova, I. (2015). Towards theoretical modeling of the sand dunes motion. Ukrainian Hydrometeorological Journal, (16), 17-23.
Hydrometeorological Aspects of Environmental Monitoring