Home https://server7.kproxy.com/servlet/redirect.srv/sruj/smyrwpoii/p2/ Science https://server7.kproxy.com/servlet/redirect.srv/sruj/smyrwpoii/p2/ Mathematicians may have unlocked the secret behind how “stone forests” are formed

Mathematicians may have unlocked the secret behind how “stone forests” are formed

The stone forest (Shilin) ​​in China's Yunnan province may be the result of solids dissolving in liquids in the presence of gravity, giving natural convective currents.
Enlarge / The stone forest (Shilin) ​​in China’s Yunnan province may be the result of solids dissolving in liquids in the presence of gravity, giving natural convective currents.

There are many wonderful geological formations in nature, from Giant’s Causeway in Ireland to Castleton Tower in Utah, and the various processes by which such structures form are of long-term interest to scientists. A team of applied mathematicians from New York University has turned their attention to the so-called “stone forests” that are common in certain regions of China and Madagascar. These pointed rock formations, like the famous stone forest in China’s Yunnan province, are the result of solids dissolving in liquids in the presence of gravity, producing natural convective currents, according to the NYU team. They described their findings in a recent article published in the Proceedings of the National Academy of Sciences.

Co-author Leif Ristroph told Ars that his group at NYU’s Applied Math Lab became interested in studying rock forests (technically a type of karst topography) along a somewhat indirect route. They used simulations and experiments to explore the interesting shapes that develop in landscapes due to a number of “shaping” processes, especially erosion and dissolution.

“We first discovered spikes formed by dissolution when we left candy in a water tank and later came back to find a needle-like spire,” he said. “The graduate student, first author Mac Huang, even accidentally cut himself when he admired the shape. This drew us into the problem, and we were very excited when we realized the connection to stone heights and stone forests, which have been quite mysterious. “We hope our experiments tell a simple ‘origin story’ behind these landforms.”

To test their simulations in the laboratory, the team combined granulated table sugar, corn syrup and water in molds to make blocks and single columns of solidified candy (hard crack) candy – an approximation to the soluble rocks that typically form karst topographies. The shape of the blocks contained arrays of upright metal rods to “seed” the blocks with pores for an even closer approximation. They placed these candy blocks and columns in a plexiglass container filled with degassed water at room temperature – deep enough for the dissolved sugars to settle to the bottom away from the objects being tested. They captured the resolution by taking digital photographs at one-minute intervals.

You can watch an hour-long video of the experiment below, in which a dissolving block of candy turns into a series of sharp spikes that look like a nail bed. The block starts with inner pores and is completely submerged under water, where it dissolves and becomes a “candy forest” before collapsing.

This happens even in still water. “We found that the dissolution process itself generates the currents that are responsible for cutting out the tip shape,” Ristroph said. “Basically, the mineral dissolves – or in our experiments candy flowers candy that serve as ‘mock rock’ and the surrounding liquid becomes heavy and then flows downwards due to gravity. So our mechanism requires no special flow conditions or other external or environmental conditions: The recipe just involves dissolving in fluid and gravity. “

Ristrof et al. suggests that a similar mechanism is underway in the formation of stone forests, just on a much longer time scale. Soluble rocks such as limestone, dolomite and gypsum are immersed under water, where the minerals slowly dissolve in the surrounding water. The heavier water then sinks during the downward pull of gravity, and the currents gradually form karst topographies. When the water recedes, the pillars and stone forests emerge.

On the surface, these stone forests resemble something like “penitentes”: snow-covered icebergs formed in very dry air found high in the Andean glaciers. Some physicists have suggested that penitentes are formed when sunlight evaporates the snow directly into steam without passing a water phase (sublimation). Small ridges and troughs are formed, and sunlight is trapped in them, creating extra heat that cuts out even deeper troughs, and the curved surfaces again act as a lens, speeding up the sublimation process even more. An alternative proposal adds an additional mechanism to take into account the strangely periodic fixed distance between penitentes: a combination of vapor diffusion and heat transport that produces a steep temperature gradient and thus a higher sublimation rate.

Physicists have been able to recreate artificial versions of penitentes in the laboratory. But penitentes and stone forests are actually quite different in terms of the mechanisms involved in their formation. “I think the similarities are pretty superficial,” Ristroph said. “Certainly, the ‘sculpture’ process is very different in terms of the main driving effects. Mainly, our tips are very cut out of currents, which I do not think plays a big role in the formation of penitentes.”

Admittedly, the NYU researchers achieved their results under idealized conditions – deliberately, according to the authors, the better to clearly identify and characterize the grinding process, the underlying mechanism, and the mathematical structure. As a result, “This study reveals a minimal set of ingredients that are essential for the needle motifs,” the authors wrote. In the future, they hope to further test this formation process under various environmental conditions in the laboratory, such as how precipitation and surface runoff or burial under loose sediment may affect peak formation.

DOI: PNAS, 2020. 10.1073 / pnas.2001524117 (About DOIs).

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