Barchan Animation: The Dynamics of Barchan Dunes. Courtesy of Hans Herrmann
The following animations illustrate the dynamics of barchan dunes, sand aggregates that form under a unidirectional wind regime and in an area with limited amounts of sand. Such dunes migrate in the same direction as the wind at speeds that may reach tens of meters per year and maintain their overall shapes.
Barchan dune movement is inversely proportional to barchan height, i.e., the higher dunes move more slowly than the lower varieties. The animations derive from numeric solutions of mathematical models that describe the dynamics of a system of two barchan dunes, differing only in height, where the lower dune is behind the higher one (facing the direction of the blowing wind). In terms of the ratio of the dune heights (r = rs/rl), we can distinguish three major cases:
- Coalescence, in which the smaller dune combines and consolidates within the larger dune (e.g., r = 0.04);
- Solitary wave behavior, in which the small dune “passes through” the large dune and maintains its shape (e.g., r = 0.27); and
- Proliferation, in which additional barchan dunes are formed (e.g., r = 0.48).
The animated simulations start with a symmetrical distribution of sand piles, which develop, in time, into barchan dunes with their typical crescent shapes and horns pointing downwind.
Animation 1 (r = 0.27):
Solitary Wave Behavior
In this case, the low dune “passes through’ the high dune. Because the small dune moves more rapidly than the large dune in front of it, it eventually approaches it, creating a temporary, partial coalescence of the two dunes. This intermediate state continues to develop because the wind speed on the slope of the two dunes is modified. The lower slope of the large dune facing the wind experiences a decrease in wind power (due to blockage by the smaller dune), while the upper slope still experiences a strong wind, causing the top grains to roll down the sheltered slope of the dune and decreasing amount of sand moving up the exposed slope. This net loss slowly reduces the height of the larger dune. However, the smaller dune experiences the opposite effect, as its protected slope experiences an increase in sand buildup, leading to an increase in height. As a result, the large dune is reduced in size and its movement increases, while the opposite occurs to the formerly small dune, whose height has increased and whose movement decreased. As a certain point, when there is a large enough difference in speeds, the now smaller dune succeeds in breaking away from the new large dune. At the end of the transformation, it seems as if the small dune passed through the large dune — something that, as we now understand, does not actually take place.
Animation 2 (r = 0.48):
Proliferation — Transformation of Two Barchans into Three
Clear here for watching the animation.
In this case, the small dune combines with the large dune as seen in Animation 1. However here, the dune in the foreground — due to the very small difference in dune heights — lacks a large exposed upper slope facing the wind. It is, therefore, unable to transform into a small, single barchan dune. It therefore loses stability and breaks into two smaller barchan dunes formed from its two horns.
Click here for a detailed description of the model developed by Hans Herman and coworkers. | 