Why small dunes move faster than big dunes

Larger objects have less surface area per volume than smaller objects with the same shape. This concept is relevant to the motion of sand dunes, because only the sediment that is exposed at the surface is available for transportation. To examine how a dune's size is related to its migration rate (u), this study uses satellite images to measure dune sizes and migration rates by comparing barchan dune displacements across time-stamped satellite photos. Subaerial dunefields on 10 locations on the Earth as well as one dunefield under water and one dunefield on Mars are measured. Despite large differences in environment, driving fluid and sediment type, velocity to surface area trendlines are always parabolic, with a consistent exponent of -0.5. This relationship can be derived from the link between surface area and its corresponding surface-to-volume ratio (A/V), which is shown to be linearly proportional to dune velocities, so that u=b*A/V. Here, b is a parameter that is roughly consistent within a dunefield, but highly variable across different environments, and is proportional to the amount of fluid energy that is converted into dune motion. A/V and b are also shown to control barchan dune shapes, whereby a higher b limits the lengths of the dune's stoss side. Ratios between the length of the lee face (1) and the stoss side (s) are thus correlated with b, enabling reasonably accurate, universal predictions of barchan dune velocities.