There’s a Hidden Mathematical ‘Law’ in The Sand Megaripples Found All Over Earth

Wherever there is sand and air, prevailing winds may push the grains into undulating shapes, pleasing the eye with their soothing repetition.

Certain sand waves, with wavelengths ranging from 30 cm (12 in) to several meters (about 30 ft), are known as megaripples: they lie between regular beach ripples and sand dunes full in size, and we’ve seen them not only on Earth, but even on planets Others are Mars, which is well known for blanket dust storms.

Aside from their size, the main feature of these Middle-earth ripples is the size of the involved grains – a surface of coarse grains over an interior of a finer material. However, this combination of grain is never the same, and the winds blowing through the sand don’t cause the ripples in the first place.

Researchers have now discovered a surprising mathematical advantage of massive grains: dividing the diameter of the coarser grains in a mixture by the diameter of the smallest grains always equals a similar number – something that has not been observed before through several decades of research.

Aeolian transverse ridges, a type of massive ring seen on Mars. (NASA/JPL-Caltech/University of Arizona)

The study authors concluded that in the future, this number could be used to classify different types of ripples and any particular grain transfers that formed these ripples.

“We find that the characteristic signature of grain-scale transport is encoded in grain size distributions (GSDs) that co-evolve with megaripples,” the researchers wrote in their published paper.

“Our compilation of original and literary data strongly establishes the accuracy and robustness of theoretical prediction across a wide range of geographic locations and prevailing environmental conditions.”

When the wind blows through the sand, massive rings occur as a result of the fine grain kicking off the coarse grain. They move at different rates, coarse grains collect on the crests of ripples, while fine grains usually settle in troughs.

Specimens were studied from megaripple fields in Israel, China, Namibia, India, Israel, Jordan, Antarctica and New Mexico in the United States. Further analysis has been added from observations made on Mars and in the laboratory’s wind tunnel.

“A comprehensive set of terrestrial and extraterrestrial data, covering a wide range of geographic sources and environmental conditions, supports the accuracy and robustness of this unexpected theoretical discovery,” the researchers wrote.

What also distinguishes huge rings is that they are more fragile than small sand ripples and large dunes, and more susceptible to the whims of changing wind patterns – if the winds become too strong, the mechanisms that create these huge waves overcome them.

The researchers suggest that their calculations could also be used to predict when this might happen, and even to look at past weather and climate conditions based on the sediment left by previous mega-waves.

The findings apply even beyond Earth: They could give us a better understanding of how giant rings form on planets like Mars, and what kind of weather conditions are needed to produce them rather than other types of sand waves.

“If we can use prevailing weather conditions to explain the origin and migration of terrestrial and extraterrestrial sand waves, this would be an important step,” says theoretical physicist Katharina Tholen, from the University of Leipzig.

“It may then be possible to evaluate sand structures that we currently observe, for example on Mars or in fossils and remote locations on Earth, as complex archives of past climatic conditions.”

The search was published in Nature Communications.


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