Leif Ristroph, a physicist and applied mathematician at New York University, was conducting experiments on how clay erodes in response to flowing water when he noticed tiny shapes emerging that resembled seated lions—in essence, miniature versions of the Great Sphinx of Giza in Egypt. Further experiments provided evidence in support of a longstanding hypothesis that natural processes first created a land formation known as a yardang, after which humans added additional details to create the final statue. Initial results were first presented last year as part of the American Physical Society’s Gallery of Fluid Motion, with a full paper being published this week in the journal Physical Review Fluids.
“Our results suggest that Sphinx-like structures can form under fairly commonplace conditions,” Ristroph et al. wrote in their paper. “These findings hardly resolve the mysteries behind yardangs and the Great Sphinx, but perhaps they provoke us to wonder what awe-inspiring landforms ancient people could have encountered in the deserts of Egypt and why they might have envisioned a fantastic creature.”
In 2018, Ristroph’s applied mathematics lab fine-tuned the recipe for blowing the perfect bubble based on experiments with soapy thin films, pinpointing exactly what wind speed is needed to push out the film and cause it to form a bubble, and how that speed depends on parameters like the size of the wand. (You want a circular wand with a 1.5-inch perimeter, and you should gently blow at a consistent 6.9 cm/s.)
Last year, Ristroph’s group conducted a series of experiments involving paper airplanes to explore the underlying aerodynamics, developing a handy mathematical model to predict flight stability. It was already well-known that displacing the center of mass results in various flight trajectories, some more stable than others.
The team verified this by test-flying various rectangular sheets of paper, changing the front weight by adding thin metallic tape to one edge. If the weight was centered, or nearly so, at the center of the wing, the plate would flutter and tumble erratically. Displace the center of mass too far toward one edge, and the plate would rapidly nosedive and crash. The proverbial “sweet spot” was placing the weight between those extremes. In that case, the aerodynamic force on the plane’s wing will push the wing back down if it moves upward and push the wing back up if it moves downward. In other words, the center of pressure will vary with the flight angle, thereby ensuring stability.
Most relevant to this latest study is Ristroph’s 2020 paper on so-called “stone forests” common in certain regions of China and Madagascar (technically a type of karst topography), like the famed Stone Forest in China’s Yunnan Province. They conducted simulations and experiments to explore the interesting shapes that evolve in landscapes due to a number of “shaping” processes, most notably erosion and dissolving.
Ristroph et al. concluded that these pointed rock formations result from solids dissolving into liquids in the presence of gravity, which produces natural convective flows. Soluble rocks like limestone, dolomite, and gypsum are submerged under water, where the minerals slowly dissolve into the surrounding water. The heavier water then sinks under the downward pull of gravity, and the flows gradually form karst topographies. When the water recedes, the pillars and stone forests emerge.
Now Ristroph has turned his attention to the mystery of the Great Spinx of Giza. In the early 1980s, an Egyptian geologist named Farouk El-Baz proposed that the sphinx’s head might have been carved first out of an existing yardang, as these natural formations can sometimes resemble animals. Then, workers would have quarried the ditch around the statue later to complete the sphinx’s body. He argued that the Nile Valley is replete with conical hills whose shape causes the wind to blow upslope to the apex, dissipating the wind’s erosive power into the air and ensuring the conical shapes survived over the ages. El-Baz suggested that Egyptian builders were aware of this phenomenon and built their pyramids in a similar conical shape, as well as carving the sphinx from a yardang.
El-Baz’s theory proved controversial, although there is some research on the formation of yardangs resembling seated lions that would appear to support it. Ristroph wanted to test El-Baz’s hypothesis more thoroughly in the lab. They mimicked the terrain in northeastern Egypt by creating mounds of bentonite clay smeared in layers on a platform that served as a bedrock. The mounds were shaped into half ellipsoids, with a long axis aligned with water flowing from a tunnel. And the team embedded a short plastic cylinder resistant to erosion within the clay mounds. Then they let the water flow triplicate the effects of wind on such structures.
Video footage showed that sphinx-like yardangs did indeed develop. The hard cylinder gradually became the “head” of a miniature “mud lion” while the water eroded away the clay in other areas to create a “neck,” an arched “back,” and “paws” extended out front on the ground. It’s a kind of feedback mechanism in which the fluid erodes the solid, but the solid then forces the flow to its shape, per Ristroph, changing the erosion rate and how that erosion is distributed across the object’s surface.
Ristroph et al. acknowledge that their experiments are merely an approximation of the natural processes at work in the case of the Great Sphinx and land formations like yardangs. Clay in running water isn’t quite the same thing as the wind-driven processes involving abrasion by wind-borne grains of sand. The lab setting compresses time and space, compared to nature, with structures developing over a matter of mere hours. And the objects studied in the lab are typically only about 10 centimeters, while the water flows are orders of magnitude lower than would be needed to form natural yardangs.
Those caveats aside, “Our findings offer a possible ‘origin story’ for how sphinx-like formations can come about from erosion,” said Ristroph. “Our laboratory experiments showed that surprisingly sphinx-like shapes can come from materials being eroded by fast flows. There are, in fact, yardangs in existence today that look like seated or lying animals, lending support to our conclusions. The work may also be useful to geologists as it reveals factors that affect rock formations—namely, that they are not homogeneous or uniform in composition. The unexpected shapes come from how the flows are diverted around the harder or less-erodible parts.”