The hidden mathematics of avalanches
“What looks like ordinary sand, rocks or snow flowing in one direction can actually hide swirling currents that move in multiple directions beneath the surface.”
Thus describes Professor of Geomechanics Itai Einav a ground-breaking scientific observation conducted with LJMU mathematician Dr James Baker.
He writes, in The Conversation: “When grains move in a landslide, most follow the steepest downhill path. But some grains move sideways or swirl in hidden patterns, forming “secondary flows” that subtly influence how far and fast the material travels.”
It sounds theoretical but understanding how grains move beneath the surface could help explain the physics of avalanches and landslides and even improve how we handle everyday materials like wheat in silos or powders in pharmaceuticals.
Dr Baker has been studying the eddies and vortices of granular materials for several years and is fascinated by the complex geometry in action.
“Granular materials are surprising versatility,” he says. “They can behave like solids that support buildings or like complex fluids with intricate internal currents.”
This latest study, led by Einav at the University of Sydney and published in the journal Nature Communications, looked deeper into the hidden physics than any before
Observing the flows in sand, soil or cereals has been almost impossible. To look inside the flow, you’d either have to keep stopping the grains for standard X-ray scans or add a liquid that makes them see-through. Unfortunately, both approaches change how the grains naturally behave.
Granular materials can behave like solids or like liquids
Dr James Baker, School of Computer Science and Mathematics, LJMU
In the lab, Einav, Baker and the team bulldozed glass beads, pushing them into a wall, causing them to pile up. Using a new method called X-ray rheography they took three-dimensional images of moving grains, which revealed the secondary flow suggested by ripples on the surface.
To really pin down the secondary flows, they developed another X-ray method to map the surface of the flowing heap from X-ray images, linking tiny ripples on top to the swirling motion underneath. We also measured how grains move through the full depth of the pile, including sideways motions.
The main flow goes all in the same direction. So, the sideways movements we detected were the first direct experimental proof of secondary flows.
So what does this tell us about the behaviour of landslides or grains in a silo?
“I think the first thing is we now know that secondary flows are at play whenever particles are pushed, such as when ploughing snow,” continues Baker.
“This means that future models – whether for protection from landslides or snowslides or whatever, really ought to integrate this new data. Current models often ignore secondary flows.
“Potentially, it could help predict details about these phenomena that we didn’t previous know.”
