Unlocking the Mysteries of Sandy “Megaripples”

Sandy beaches are often patterned with sunburned visitors, brightly colored towels, and poorly constructed sand castles. However, the wind can create much more intriguing patterns in sand, from tiny ripples to towering dunes.

Sand ripples at the northwest coast of the island Fanø in Denmark.
Image Credit: Klaus Kroy.

With research coming out soon in the journal Physical Review E, a team of scientists studying one of these sand structures has brought us closer to understanding how wind-blown grains of sand form these patterns. Their work could be helpful for modeling, predicting, and preventing hazardous conditions like drifting sands and violent erosion, and for understanding the surfaces of not only the Earth, but Mars, Venus, and other windy locales in the solar system.

The research team, from Universität Leipzig in Germany and Université de Rennes in France, studies giant ripples of sand that can be up to 40 meters long and over a meter high. Called megaripples, the patterned sand is both beautiful and curious. Why are they so large? That’s the key question behind this research. The details are still unclear, but observations tell us that size matters.

Large megaripples in the Negev, Israel. See the person in the center for scale.
Image Credit: Marc Lämmel.

When you buy a bag of sand from the store, you choose the size of the grains. The options go from very fine sand (diameters of 0.0625mm – 0.125mm) to very coarse sand (1mm – 2mm). Naturally occurring sandy areas don’t follow these neat divisions.

Pay attention next time a gust of wind blows down the street and you’ll see sand and other small particles be picked up and sent erratically “hopping” down the street. Heavier objects like rocks remain where they are unless the gust is unusually strong. Similarly, in a sandy area with a mixture of large and small sand grains, the lighter ones are more easily sent hopping.

The process of sand being carried by the wind is known as saltation.
Notice the hopping motion of individual grains.
Credit: Marc Lämmel

From what they’ve observed, scientists think that heavier sand particles that aren’t picked up by the wind act kind of like an armoring layer, stabilizing and protecting the ripple structure as it grows. Smaller grains of hopping sand hit the larger ones, leading to growth and patterning. Exactly how this process plays out to create megaripples and other patterns is still unclear. When the team tried to model the interactions between a small grain of sand hitting a bed of larger grains as part of their research, they realized there was no satisfying way to theoretically describe these collisions, according to the project leader Marc Lämmel.

A photograph of the cross section of one of the megaripples in Israel.
Image Credit: Marc Lämmel.

Scientists have been studying what happens when individual grains of a substance collide with a bed for more than 75 years, like what happens when you pour extra sugar back into the sugar jar. This is a surprisingly important question with applications in a wide range of industries that depend on granular materials, from construction to pharmaceuticals. However, most of the models address cases when particles of the same size collide.

In order to advance this work, the team needed a simple approach to model what happens when a small grain of sand hits a bed of large grains. Their goal was to determine a set of mathematical equations that describe the result for a range of situations, including different incoming angles and grain sizes.

The first step was splitting the problem into two parts: the collision and what happens next.

To model the collision, the team imagined a grain colliding with a bumpy surface of heavy grains packed tightly together. From basic physics principles and basic geometry, they found mathematical expressions for how the incoming grain rebounds off the surface. Their work includes a lot of simplifications and assumptions, but the resulting predictions agree well with more complicated models that takes all of the details into account.

What happens next? Observations show that when a grain hits a bed, other grains are ejected. They come from a large area, not the point of impact, so they aren’t directly knocked out by the incoming grain. Instead, some of the momentum and energy of the incoming grain travels through the closely packed grains and ultimately sends some hoping. Modeling this process mathematically is pretty complicated. However, when combined with recent work by other researchers, the resulting expressions can predict the average number and speed of grains that are ejected by different impacts.

When all of this is put together, tests show that the result is an excellent starting point for modeling how wind structures form. The team used these expressions to predict the results of impacts that had been previously studied with experiments. Side-by-side comparisons matched well. The simplicity of the approach means that this information can be safely and easily added to larger models of wind structure formation to increase their accuracy without significantly increasing the computing time.

From ripples in a pond to ripples in space time, nature is filled with patterns and symmetries that hint at how the universe works. Unlocking these mysteries often reveals new connections and exciting possibilities for the future, enabling us to see the world in a different way.

To see a World in a Grain of Sand
And a Heaven in a Wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour

-From Auguries of Innocence by William Blake

Kendra Redmond

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