Discover the mathematical law of sand dunes on Earth and Mars

A “surprisingly consistent” number appears in the ripples of a class of sand dunes. It happens on Earth as it happens on Mars.

There are laws Maths General, constant, it is especially found in the geometric shapes that surround us. The golden ratio is the best known ratio, but there is another ratio. And mathematicians have just discovered a completely new one, they report in a study they published Nature CommunicationsJanuary 10, 2022.

Their discovery relates to a phenomenon of rare beauty: the ripples of large sand dunes. It is generated by high winds that hit the grains of sand, making them take this undulating shape. They are medium-sized sand dunes, ranging from the tiny fine lines you see on the beach to the fairly stable giant sand dunes in the deserts. This thus represents a few metres. In English, they are called “mega waves”, and can be translated as “mega waves”. They are fragile and change quickly.

Found on Earth, but also on Mars (Though sand and wind Don’t act exactly the same way from our planet). And whether they’re on one planet or another, these wind-driven ripples have one thing in common.

Sand dunes (megaripples) pictured on Mars. // source: NASA/JPL-Caltech/University of Arizona

The already known peculiarity of these sand dunes is a recurring pattern present in their formation: when these medium-sized ripples form, the inner grain is very fine when the outer grain is very large. The dunes are not exactly the same, the winds blow the grains randomly, but whatever happens, their formation will always, systematically, be like this. This pattern continues as the ripples change as the winds change.

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The discovery is certainly astonishing, but mathematicians from the University of Leipzig I discovered, for the first time, an even more surprising law. If you divide the diameter of the thickest grain on the outside, with the diameter of the best grain on the inside, the number you get is consistently the same,” consistent amazement ».

Code established with terrestrial and extraterrestrial data

This law applies to Earth…but also to Mars. The authors of this study studied samples from China, India, Israel, Namibia, Jordan, New Mexico (US), and Antarctica. But there is also data from observations made on Mars by the probe. The discovery was then tested under laboratory conditions, in a wind tunnel.

« A comprehensive set of terrestrial and extraterrestrial data, covering a wide range of geographical sources and environmental conditions, confirms the accuracy and robustness of this unexpected theoretical discovery. Explain the authors of the discovery.

The grain size distribution evolves concurrently with the evolution of these medium-sized sand dunes, always following this law: “ The distinct grain-wide transport signature is encoded in grain size distributions ».

This discovery is not without benefit. number can now They are used to determine which class of newly discovered sandbars (…) they belong and by which physical transfer process they were most reliably formed. “.it could also be a very useful tool for the study of Mars, in particular,” A better explanation of the formation of some mysterious new sand waves recently observed on Mars ».

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