The Turbulent Relationship Between Sand Dunes

Fields of gently sloping sand dunes may look quiet and passive in photographs, but the serene patterns may be defined by turbulent negotiations. That’s the conclusion reached by scientists from the University of Cambridge in the UK who have spent the last few years studying how dunes interact with one another. The findings, published in the journal Physical Review Letters, offer new insight on a landscape that attracts tourists, threatens shipping lanes, buries highways, and colors the surface of Mars.

Left: Dune field. Credit: Photo by Meriç Dağlı on Unsplash. Right: Sand dunes in Death Valley National Park, United States. Credit: Photo by Joseph Driscoll on Unsplash.

Sand dunes are formed by strong winds or flowing water. Desert dunes and underwater dunes have differences, of course, but their formation can be described by essentially the same physics–the interaction between particles of sand, fluid in motion, and the environment.

Dunes usually occur in vast fields that evolve and migrate over time. They’ve been known to bury forests and hide the remnants of entire cities. Dunes hold secrets of their own too. Secrets of structure, motion, and interaction that have implications for archeology, climate studies, the exploration of other planets, and infrastructure planning.

Wood fence buried by a sand dune in southern New Mexico.

Karol Bacik, a graduate student in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge, has spent the last few years exploring how dunes interact with one another. He didn’t start out with that project in mind though. At first, Bacik was studying the motion of individual underwater dunes. Working in the fluid dynamics lab associated with his department, the GK Batchelor Laboratory, he would create a small dune inside of a water tank and observe how its migration speed varied with the water’s flow rate.

One day, he added an extra pile of sand.

According to theory, two dunes with the same size and flow conditions should migrate at the same speed. But that’s not what happened. The theory also assumes that interacting dunes exchange mass, but that didn’t happen either. To his surprise, Bacik saw the two same-sized dunes migrate at very different rates without exchanging any mass. Interest piqued, he began studying dune-dune interaction in detail, guided by supervisors from the BPI (an interdisciplinary research institute at the University of Cambridge) and Schlumberger Cambridge Research.

The team’s experiments took place inside of a cylindrical water tank about 2 meters in diameter. Twelve paddles dipped into the surface of the water, supported by a rotating unit. The water tank also rotated, in the opposite direction, and together the rotations produced a clockwise flow. When the flow was activated, piles of small glass beads on the bottom of the table took on the characteristic shape of sand dunes. Two cameras tracked their migration over time, one rotating with the table and another stationary.

The experimental apparatus. Water flow is driven by equally spaced paddles mounted on a turntable that rotates in the direction opposite of the water tank. Sample dunes are illustrated in red and blue. Credit: Bacik et al., Physical Review Letters.

Here’s the story of two same-sized dunes as it played out over 80 minutes.

When the clock started, the first dune (the downstream dune) sprinted ahead, traveling significantly faster than the trailing dune (the upstream dune). As the distance between them grew, the leading dune slowed down. Eventually, the leading dune slowed down to the same speed as the trailing dune, content to maintain the new separation distance. At this point the dunes were directly across the tank from each other.

Although the two were never in physical contact and didn’t exchange mass, some interaction had clearly taken place.

Dune migration depends on two things: size and fluid flow. The size relationship has been well studied; under the same fluid flow, smaller dunes migrate faster. But exactly how fluid flow influences the migration rate is not very well understood. Researchers know that different dunes migrate at different rates, yet they don’t coalesce as often as you might expect. Why?

The answer seems to be turbulence, according to the Cambridge team. Their data show that the downstream dune traveled at a constant rate. As water flowed around it, turbulent structures were likely generated in its wake. These turbulent structures gave the leading dune a kind of power burst that increased its velocity. The intensity of the boost faded with distance, so eventually the leading dune was beyond reach and the dunes migrated at the same rate.

Summary of the research results. Left: The trailing / downstream dune (blue) travels at the same rate the whole time. In contrast, the leading / upstream dune (red) starts off fast, increasing the distance between the two dunes, but slows down over time until it matches the rate of the trailing dune. This happens when the dunes are on opposite sides of the cylindrical tank. Right: A visual representation of the starting positions (bottom) and ending positions (top) of the two dunes. The water flows clockwise. Credit: Bacik et al.

Put another way, underwater dune interactions seem to be facilitated by a turbulent fluid flow. The flow acts like a repulsive force that keeps dunes apart, preventing collisions and stabilizing them into fields.

How does this translate to desert dunes? “That’s an open question,” says Bacik. Dunes in air and dunes in water have many common features, but also important differences. Underwater experiments may not be a perfect model of what happens in the desert, but fingerprints of a similar processes are visible in satellite images of deserts if you look back in time. “That’s confirmation that we’re not doing something outrageous,” says Bacik. “When the [turbulent wind] structure hits the dune, there might be some difference in how it reacts, but qualitatively we expect it to behave the same.”

body of water
Underwater dunes on a seabed. Photo by Juan Chavez on Unsplash.

A key next step will be validating the turbulent interaction model with high-quality field observations, but that will take time and creativity. These things happen on a very slow time scale in the field, says Bacik. What takes an hour to model underwater in the lab happens over decades on the scale of desert satellite images.

Kendra Redmond

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