Pitt researchers rewire the energy pathways of turbulence

Anyone who has spent time near an ocean or other body of turbulent water can appreciate the seemingly immutable, chaotic power of currents. Yet amid the churning chaos, there appears some order: large eddies break off from a current, and those eddies break into smaller eddies until the energy dissipates.

This forward transfer of energy in three-dimensional bodies such as oceans or the air has been a foundational theory for decades, but that is changing. The University of Pittsburgh Professor Lei Fang and his PhD student Xinyu Si, with Filippo De Lillo and Guido Boffetta from the University of Turin, have challenged the assumption. Using a geometric framework, they have shown, via experiments and simulations, that energy flux direction is in fact mutable.

Their research, which can have far-reaching effects in fields such as medicine, coastal waterway management, and climate modeling, is detailed in the article “Manipulating the direction of turbulent energy flux via tensor geometry in a two-dimensional flow” (DOI: 10.1126/sciadv.adv0956), published in Science Advances.

Challenging a long-held assumption

“Since 1941, with Andrey Kolmogorov’s research, energy flux has been predicted. In 3D flows like in bodies of water, energy moves from larger to smaller scales. For 2D flows, which occur in thin layers of water, that flux is reversed, from smaller to larger,” said Fang, assistant professor in the Department of Civil and Environmental Engineering at Pitt’s Swanson School of Engineering.

“To understand this abstract concept at different scales,” Fang added, “I recast the energy flux process into a mechanical process based on Navier-Stokes equations. And since this is a mechanical process, I could try to reverse it by changing the geometry between displacement and force.”

Fang developed a geometric framework using tensors (objects mathematicians use to explore, for example, the direction of stress and deformation, which create turbulence). He found that depending on how the tensors aligned, they could flux energy in different ways depending on how the forces come into contact.

“We showed that we could produce turbulent flows that either exhibit forward or inverse energy flux,” Fang said. “Our framework extends to the 3D scale as well.”

In previous research, Fang showed how tiny swimmers can disrupt strong ocean flows. Now, by focusing on the background flow and its interaction with other forces, like a group of tiny swimmers, he found that if correctly aligned, they can flux energy in different ways depending on how the forces come into contact.

Fang and Si validated their framework using a thin-layer, electromagnetically driven flow apparatus. In a tank with shallow water depth, they generated a horizontal magnetic field that drives a 2D flow. To perturb the flow, they used a rod array. In a thin layer of electrolytes, tracer particles produced images of the flow’s movement.

Harnessing energy flux

“Through this theoretical framework, we found that we can use small physical boundaries up to ten meters to perturb ocean transport barriers that spans kilometers,” said Fang. “It is possible to change the direction of the energy flux, which can improve how wastewater or other contaminants along a coastline are dispersed.”

Beyond coastal transport barrier management, the research can be used in medicine. “In microfluidic flows of less than one millimeter, where the viscosity of a liquid makes mixing difficult because there is little to no turbulence,” added Fang, “we could align the forces and displacement to generate weak ‘low Reynolds number turbulence,’ which could speed up mixing of agents.” 

The research also has the potential to advance how scientists model ocean currents and temperatures in a changing climate.

“While it’s hypothetical at this point, the research could improve climate modeling,” said Fang. “As climate change alters wind patterns and ocean flows, wind stress and currents could change the direction of energy flux. Understanding the forces that create this change can lead to more accurate models.”