The Motion of Dunes
Dunes are instabilities of mobile sand due to the action of wind.
I will present the equations of motion describing the evolution of a granular surface under the influence of a hydrodynamic drag and gravity. This set of three coupled non-linear integro-differential equations can be solved numerically. The resulting dunes do quantitatively reproduce real dunes measured in Barchan fields of Marocco and Brasil. Collisions of two Barchans exhibit solitary wave behaviour and breeding. Changing the parameters correspondingly one can also obtain Mars dunes. Adding a fourth equation it is possible to include vegetation growth and to describe the transition from Barchans to parabolic dunes.
Hans Herrmann, ETH Zurich, Switzerland