To anyone who has ever seen ocean waves or fast-moving water, turbulence may seem like pure chaos. The powerful current twists, swirls, and swirls, and the vortex splits into smaller and smaller vortices, until its energy dissipates.
For decades, scientists have believed that this process follows a predictable pattern. In three-dimensional environments such as the ocean and atmosphere, energy is thought to move from large structures to small structures. New research suggests the rules may not be as fixed as previously thought.
Researchers at the University of Pittsburgh, working with collaborators at the University of Turin in Italy, have discovered that the direction of energy flow in turbulent flows can indeed be changed. Their findings were; scientific progress The paper, “Manipulating the direction of turbulent energy fluxes through tensor geometry in two-dimensional flows,” has potential implications for medicine, coastal management, and climate science.
A challenge to the basic theory of turbulence
The research was led by Lei Fang, assistant professor in Pitt’s Swanson School of Engineering Department of Civil and Environmental Engineering, and doctoral students Xinyu Si, Filippo De Lillo, and Guido Boffetta.
“Since 1941, Andrei Kolmogorov’s work has predicted energy fluxes. In three-dimensional flows, such as in bodies of water, energy moves from large scales to small scales. For two-dimensional flows, which occur in thin layers of water, the flow reverses from small to large,” said Huang.
To investigate whether this behavior could be changed, Fang approached the problem from a different perspective.
“To understand this abstract concept at different scales, I reconstructed the energy flux process into a mechanical process based on the Navier-Stokes equations. And since this is a mechanical process, we can try to reverse it by changing the geometry between displacement and force,” Fang added.
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 arrays, 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 the traditionally expected path.
“We showed that we can generate turbulent flows that exhibit either forward or reverse energy flux,” Huang said. “Our framework also extends to 3D scale.”
Experiments confirm theory
The idea builds on Fang’s previous research showing that small swimmers can disrupt powerful ocean currents. In the new study, he shifted his attention to the background flow itself and how it interacts with external forces.
The researchers found that when these forces are adjusted in specific ways, they can change the way energy moves within a turbulent system.
To test their theory, Fang and Si conducted laboratory experiments using a thin layer of water driven by electromagnetic forces. A horizontal magnetic field created a two-dimensional flow, and an array of rods was used to disrupt it. Tracer particles suspended in a thin electrolyte layer allowed the team to visualize and measure fluid movement.
The experimental results were consistent with computer simulations and supported the predictions of the new framework.
Potential applications from marine to medical
The ability to influence turbulent energy flows could ultimately have practical benefits in a variety of fields.
“Through this theoretical framework, we found that small physical boundaries of up to 10 meters can be used to disrupt maritime transport barriers over many kilometers,” Huang said. “It is possible to redirect the energy flux, potentially improving the way wastewater and other pollutants are dispersed along coastlines.”
This discovery could also prove useful in medicine, particularly in microfluidic systems where fluid moves through channels smaller than a millimeter. At that scale, there is little turbulence, so liquids tend to mix poorly.
“In microfluidic flows of less than a millimeter, there is little or no turbulence, and the viscosity of the liquid makes mixing difficult. Force and displacement can be tuned to generate weak ‘low Reynolds number turbulence,’ which may enhance drug mixing,” Fang added.
Implications for climate modeling
This research may also contribute to improving future climate simulations.
Ocean currents and atmospheric circulation play an important role in regulating Earth’s temperature. As climate change changes wind patterns and ocean behavior, the forces acting on these systems can also affect the transfer of energy in turbulence.
“While hypothetical at this point, this study could improve climate modeling,” Huang said. “As climate change changes wind patterns and ocean currents, wind stresses and ocean currents can change the direction of energy flow. Understanding the forces driving this change can lead to more accurate models.”
Although additional research is needed, this study suggests that one of turbulence theory’s most established assumptions may be more flexible than scientists once believed. Rather than simply following a predetermined path, turbulent energy can be guided and redirected under appropriate conditions.
