Plop.
Plop.
Water drips from stalactites hanging from cave ceilings.
Each successive drop adds a thin layer of minerals to a growing stalagmite below. These remarkable structures are found on the floors of caves all over the world. Although they grow only a fraction of an inch each year, they serve as record keepers of past environmental conditions, such as droughts.
But while there has been a lot of research focused on how stalactites form, relatively little has been done on stalagmites.
Simulations of their growth tend to assume that water droplets fall straight down, resulting in candlestick shapes. But that is not what is observed in nature. Stalagmites are found with cone, dome and even “pile-of-plates” formations, which resemble stacked dishes.
New research published last week in Proceedings of the Royal Society A sheds light on why stalagmites have diverse shapes. The study presented a physics-based model that shows that stalagmite forms are dictated by how far water droplets fall from their stalactite of origin. Drips that fall farther tend to result in wider stalagmites. These findings can be used to reconstruct a cave’s geometry over time, the research team suggests.
In 2015 and 2016, scientists visited seven caves in the south of France to understand this diversity. They brought high-speed cameras to study the caves’ stalagmites, many of which were milky white and glistening with moisture.
“They’re beautiful,” said Tristan Gilet, a fluid dynamicist at the University of Liège in Belgium who participated in the fieldwork. The researchers photographed water droplets falling onto 65 stalagmites and recorded videos at 5,400 frames per second.
Justine Parmentier, who led the data analysis and is pursuing an engineering doctorate at the University of Liège, and her colleagues found that the sizes of the falling droplets were remarkably similar, all about one-tenth of an inch in radius.
High-speed videos revealed that the droplets created a splash when they impacted a stalagmite. But the extent of the spray — up to roughly 0.7 inches in radius — was much smaller than the stalagmites themselves. That left the team wondering: What explained stalagmites’ widths?
The answer, the researchers realized, was that the water droplets were not falling in a straight line. “The drops don’t fall in the same place each time,” Ms. Parmentier said.
Instead, successive droplets were dispersed by as much as a few inches each time they struck stalagmites.
Were air currents within the caves causing the discrepancy? Probably not, the team concluded. The air speed in one of the caves the team visited was far too low to explain the droplets’ lateral movements.
What did explain it, Ms. Parmentier and her colleagues concluded, were aerodynamic forces induced by the droplets themselves. Most objects moving through a medium — air or water, for example — create a turbulent wake.
“Me walking in the room here, I actually shed vortices behind me,” Dr. Gilet said.
The effect is exacerbated as an object moves faster: More and more asymmetrical vortices form, each exerting a random force on the object.
“The force is tiny for one individual vortex,” said Dr. Gilet. But if you have hundreds or even thousands of them acting during a free fall, he says, “ultimately that matters.”
Using Newton’s second law of motion, and considering the force applied by each individual vortex, the researchers calculated that water droplets falling from more than about 100 feet would be jostled enough to be displaced by up to a few inches.
Droplets falling less than a few feet, on the other hand, would meander by less than a tenth of an inch because they do not build up as much speed and they fall for a shorter time.
This link between stalagmite shape and droplet fall distance can be used to better understand caves. For instance, it can be used to reconstruct how a cave’s height has changed over time because of events such as partial collapses.
“We might be able to obtain some information about cave history,” Dr. Gilet said, “based on stalagmite width.”
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