Why can the stability of some flow systems be predicted, while others cannot, e.g. the famous Reynolds experiment of wet water running in a pipe? This classic puzzle in fluid mechanics may now be approached through an innovative lens: probability theory.
New research exploring the use of probability theory to predict fluid turbulence has been featured as a News & Views article in Advances in Atmospheric Sciences , highlighting its potential to address frontier issues in fluid dynamics and atmospheric prediction.
Led by Professor Ding Zijing of the International Research Center for Intelligent Fluid Mechanics at Harbin Institute of Technology (HIT), a research team is developing a unified theoretical framework to describe and predict the transition from smooth laminar flow to chaotic turbulence. The key idea? Treating turbulence onset not as a definite “yes or no,” but as a matter of probability.
Two Types of Flow, One Big Question
In some systems, like heated water in a pot (known as Rayleigh–Bénard convection), instability predictably occurs once a threshold, such as temperature, is passed. These are called “normal” systems.
But in many real-world flows—like air moving over an airplane wing, water through pipes, or wind shear in the atmosphere—transition does not follow a simple rule. It can appear unexpectedly, depending on tiny, random disturbances in the initial flow. These are “non-normal” systems and have been much harder to predict.
A Three-Part Framework: Making the Unpredictable Predictable
Professor Ding's team proposes a novel three-step approach:
Why This Matters Beyond the Lab: Implications for Atmospheric Science
This probabilistic approach isn't just theoretical—it offers powerful new tools for understanding the atmosphere:
Better Prediction of Extreme Weather: The sudden onset of storms or severe convection can be seen as a “transition” in atmospheric flow. Professor Ding’s framework could help estimate the likelihood of such events, moving beyond simple yes/no forecasts toward probabilistic early warnings.
Understanding Climate Tipping Points: Large-scale climate shifts, such as changes in ocean currents, behave like global “transitions.” This research provides tools to assess their probability, improving long-term climate risk assessment.
Sharper Weather and Climate Models: Turbulence in small-scale atmospheric processes is a major source of error in forecasts. A probability-based theory could lead to more accurate and reliable models.
A New Toolbox for Fluid Science
“This is an attempt to build a bridge between fundamental fluid mechanics and the complex, unpredictable flows we see in nature and engineering,” said Professor Ding. “By viewing transition through probability, we can better quantify uncertainty and make more informed predictions in fields from aviation to meteorology.”
The research, conducted in collaboration with Professor Yang Dazhi (HIT), Associate Professor Xie Jin-Han (Peking University), and Academician Li Hui (Director of the International Research Center for Intelligent Fluid Mechanics at HIT), represents a step toward a more unified and practical theory of turbulence.
Advances in Atmospheric Sciences
Sketching a Probability Theory of Transition to Turbulence
7-Feb-2026