image: Ziyue Yu and Lei Fang generating turbulent flows in a test tank.
Credit: Thomas Altany, the University of Pittsburgh
Turbulent flows, with all their chaos and complexity, remain an unsolved problem. With better, more nuanced models, scientists can improve forecasts of how air and water move, from how pollution disperses to how efficiently turbines and other systems perform.
Lei Fang, assistant professor in the Department of Civil and Environmental Engineering, has received a three-year, $372,882 National Science Foundation (NSF) grant, his third in three years, to use data analysis and machine learning to reveal subtle behaviors in turbulence that today’s models miss.
The project “CDS&E: Uncovering Self-Competition and Weak Asymmetry in Turbulence through Data-Enabled Diagnostics and Learning,” will help strengthen large-eddy simulation (LES), a widely used approach for modeling turbulence in engineering and the geosciences.
“Although Kolmogorov proposed his foundational theory of turbulence [K41] in 1941, and numerous refinements have been introduced over the past century, our understanding of turbulence remains rudimentary,” said Fang, the principal investigator. “With advances in machine learning and data mining, we can develop algorithms and graphical neural networks that uncover the physics and build better models.”
Inside the chaos: hidden patterns
Fang’s project focuses on two defining features of turbulent flows: self-competition and weak asymmetry. In self-competition, advection, the very mechanism responsible for transferring energy between eddies of different sizes, acts to dampen that same transfer process.
A useful analogy is a crowded highway. When traffic flows smoothly, motion is efficiently transmitted downstream. But as vehicles begin accelerating, braking, and weaving too aggressively, their very efforts to move forward generate congestion that slows everyone down. The mechanism that enables transport ultimately undermines it.
In turbulence, advection behaves in a similar way: when it becomes sufficiently strong, it disrupts the coherent pathways needed for sustained energy transfer across scales. The flow, in effect, competes with itself.
Weak asymmetry refers to a slight imbalance in how energy transfers across scales. The mental image is that large swirls often break into smaller ones, but smaller swirls can also merge into larger structures. While the process occurs simultaneously, one direction will be slightly stronger than the other. Though a weak asymmetry, the difference is important.
“Current modeling fails to sufficiently capture what may seem counterintuitive within turbulent flows,” said Fang. “They don’t clearly identify where, when, or why self-competition and weak asymmetry arise, which limits our understanding.”
To bridge that gap, Fang will analyze high-resolution simulations from the Johns Hopkins Turbulence Database alongside controlled experiments from his own lab. He will use machine learning to develop new diagnostics that uncover these patterns. He will create predictive models to advance how simulation accounts for the physical constraints within flows.
Beyond improving simulation in weather forecasting, climate modeling, and engineering design, the project will increase understanding of fluid mechanics and create a framework that helps researchers in other fields involving complex, multiscale dynamics.