For anyone who has watched ocean waves or fast moving water, turbulence can seem like pure chaos. Powerful currents twist and churn, creating swirling eddies that split into smaller and smaller vortices until their energy eventually fades away.
For decades, scientists have believed this process follows a predictable pattern. In three dimensional environments such as oceans and the atmosphere, energy is thought to move from larger structures down to smaller ones. New research suggests that rule may not be as fixed as previously thought.
Researchers at the University of Pittsburgh, working with collaborators from the University of Turin in Italy, have discovered that the direction of energy flow in turbulence can actually be altered. Their findings, published in Science Advances in the paper "Manipulating the direction of turbulent energy flux via tensor geometry in a two-dimensional flow," could have implications for medicine, coastal management, and climate science.
Challenging a Fundamental Theory of Turbulence
The work was led by Lei Fang, assistant professor in the Department of Civil and Environmental Engineering at Pitt's Swanson School of Engineering, along with PhD student Xinyu Si, Filippo De Lillo, and Guido Boffetta.
"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.
To investigate whether this behavior could be changed, Fang approached the problem from a different perspective.
"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."
His approach relied on tensors, mathematical objects commonly used to describe quantities such as stress and deformation. These properties play a major role in the formation of turbulence.
By developing a geometric framework based on tensor alignment, Fang discovered that the direction of energy transfer depends on how these tensors interact. Under certain conditions, the flow of energy can be redirected rather than following its traditionally expected path.
"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."
Experiments Confirm the Theory
The idea builds on Fang's earlier work showing that tiny swimmers can disrupt powerful ocean currents. In the new study, he shifted attention to the background flow itself and how it interacts with external forces.
The researchers found that when those forces are aligned in specific ways, they can alter how energy moves through a turbulent system.
To test the theory, Fang and Si conducted laboratory experiments using a thin layer of water driven by electromagnetic forces. A horizontal magnetic field generated a two dimensional flow, while an array of rods was used to disturb it. Tracer particles suspended in a thin electrolyte layer allowed the team to visualize and measure the movement of the fluid.
The experimental results matched computer simulations and supported the predictions of the new framework.
Potential Applications From Oceans to Medicine
The ability to influence turbulent energy flow could eventually provide practical benefits in a variety of fields.
"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."
The findings may also prove useful in medicine, particularly in microfluidic systems where fluids move through channels smaller than a millimeter. At that scale, liquids tend to mix poorly because turbulence is largely absent.
"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."
Implications for Climate Modeling
The research may also contribute to future improvements in climate simulations.
Ocean currents and atmospheric circulation play critical roles in regulating global temperatures. As climate change alters wind patterns and ocean behavior, the forces acting on these systems may also affect how energy moves through turbulent flows.
"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."
Although additional research is needed, the study suggests that one of turbulence theory's most established assumptions may be more flexible than scientists once believed. Instead of simply following predetermined pathways, turbulent energy may be guided and redirected under the right conditions.
