When Lei Fang asked whether an 80-year-old rule of physics could be broken, he didn't accept the textbook answer. For decades, scientists believed that in three-dimensional environments like oceans and the atmosphere, turbulent energy flows in only one direction—from larger structures down to smaller ones—a principle laid down by Andrey Kolmogorov in 1941. But Fang, an assistant professor at the University of Pittsburgh's Swanson School of Engineering, wondered if that immutable law might be more flexible than anyone realized.
Working with PhD student Xinyu Si and collaborators from the University of Turin in Italy, Fang discovered something remarkable: the direction of energy flow in turbulence can actually be altered. The finding, published in Science Advances, upends a foundational assumption in fluid dynamics and opens unexpected doors for managing ocean coasts, improving medical treatments, and refining climate forecasts.
The breakthrough came from Fang's decision to reframe turbulence as a mechanical problem rather than an abstract one. Instead of accepting the traditional energy cascade model, he translated the energy flux process into equations based on the Navier-Stokes framework—the governing equations of fluid motion. "Since this is a mechanical process, I could try to reverse it by changing the geometry between displacement and force," Fang explained. His solution relied on tensor geometry, mathematical objects that describe stress and deformation, properties central to how turbulence forms.
By developing a framework based on how tensors align with one another, Fang showed that energy transfer direction isn't fixed—it depends on how these tensors interact. Under specific conditions, energy can be redirected rather than following its traditionally expected path. His theoretical predictions proved solid when tested in the laboratory. Fang and Si created two-dimensional turbulent flows using a thin layer of water driven by electromagnetic forces, with an array of rods creating disturbances and tracer particles revealing the fluid's movement. The experiments matched computer simulations perfectly.
The practical implications are expansive. On coastlines, Fang noted that small physical boundaries—structures as modest as ten meters—could alter ocean transport barriers spanning kilometers. This could transform how coastal communities manage wastewater and contaminant dispersal, a critical concern as urbanization strains coastal ecosystems worldwide.
In medicine, the discovery offers new possibilities for microfluidic systems, where fluids flow through channels smaller than a millimeter. At such tiny scales, liquids mix poorly because turbulence barely exists. By aligning forces and displacement strategically, researchers could generate weak "low Reynolds number turbulence," accelerating the mixing of pharmaceutical agents and diagnostic fluids—potentially speeding drug delivery and medical testing.
Perhaps most consequentially, the research hints at improvements for climate modeling. Ocean currents and atmospheric circulation regulate global temperatures, and as climate change shifts wind patterns and ocean behavior, the forces acting on these systems may alter how energy moves through turbulent flows. While Fang cautioned the climate implications remain hypothetical, understanding how manipulating force geometry affects energy flux could deepen our ability to forecast how a warming world's disrupted flows reshape regional and global climates.
An 80-year-old rule hasn't been broken so much as revealed as incomplete. What seemed like an ironclad law of nature turns out to be a rule with exceptions—and those exceptions may hold the key to solving some of our most pressing environmental challenges.