Mathematicians Describe the Rounding of River Rocks

River rocks tend to be smoother than rocks found on the shore, and they get smaller the farther downstream they are found. However, experts disagree on whether abrasion causes the rocks to become significantly smaller as they are transported down the river, or if initially smaller rocks are more easily transported downstream.

Douglas Jerolmack, an associate professor at the University of Pennsylvania's Department of Earth and Environmental sciences, worked with mathematicians to answer questions surrounding varying rock sizes in riverbeds. He found mathematical evidence for a two step process. First, the rocks are rounded down by abrasion and then, when the rock is smooth, abrasion reduces the rocks diameter.

"It was a rather remarkable and simple result that helps to solve an outstanding problem in geology," Jerolmack said.

This discovery could allow researchers to determine the history of a river, such as how long it has flowed. Further studies could allow them to use rock size and smoothness to predict a narrative of the past in dry areas. The researchers pointed toward the smooth rocks found on Mars as an example of an area of potential study, according to a statement.

Before, most geologists assumed that "size-selective transportation" accounted for smaller rocks being found downriver. The process of abrasive forces making a noticeable difference in the diameter of rocks seemed too slow a process to be possible.

However, unlike the geological experiments run previously, Jerolmack enlisted mathematicians from Budapest University to approach the question from a geometric perspective.

In was on these mathematical models that the novel theory was predicated. Intuitively, protruding areas of the rock are worn down first with almost no change to the rocks diameter. In the second phase, the diameter begins to uniformly shrink.

"If you start out with a rock shaped like a cube, for example," Jerolmack said, "and start banging it into a wall, the model predicts that under almost any scenario that the rock will erode to a sphere with a diameter exactly as long as one of the cube's sides. Only once it becomes a perfect sphere will it then begin to reduce in diameter."

The study is published in PLOS One.