A sneeze, ocean currents, and smoke: what do these phenomena have in common? They are all instances of turbulence—unpredictable, chaotic fluid flows characterized by fluctuating velocity and pressure. Despite their prevalence in nature, these flows have long been a mystery, both theoretically and computationally. Recent advancements, however, are shedding light on this complex subject.
University of California, Santa Barbara mathematics professor Björn Birnir, alongside Luiza Angheluta from the University of Oslo, has made significant strides in characterizing turbulence. Their research, published in the journal Physical Review Research, offers a new approach to understanding the myriad complex phenomena occurring in turbulent flows.
Understanding the Complexity of Turbulence
Turbulence has been described as “the most important unsolved problem of classical physics,” a sentiment famously expressed by physicist Richard Feynman in 1964. Over the centuries, researchers have developed numerous laws and theories to tackle this complex issue. The challenge lies in the nonlinearity, unpredictability, and multi-scale nature of turbulence, making it difficult to create mathematical models that apply universally—from the tiniest fluctuations to the entire flow with its interacting vortices and eddies.
Particularly challenging is the study of Lagrangian turbulence, where an observer follows the flow, as in an airplane. This type of turbulence begins with a ballistic flow, transitions through large Lagrangian vortices, and eventually becomes Eulerian turbulence, characterized by smaller, more complex vortices.
“Most flows that we encounter in nature are turbulent—it does not matter whether it is the flow outside the airplane that makes us fasten our seatbelts, or the flow in a small stream,” said Björn Birnir.
New Theoretical Approaches
Birnir and Angheluta’s research focuses on the statistical properties of a fully turbulent Lagrangian velocity field. Using a modeling framework called stochastic closure theory, they capture the randomness inherent in the system. They also employ the Green-Kubo-Obukhov relations to characterize the effects of various forces on the flow, such as diffusion and viscosity, as well as the chaotic dynamics of the entire system.
Their findings reveal a Lagrangian scaling regime in the “passover region” between ballistic flows and Eulerian turbulence. This discovery connects the three scaling regimes as the turbulent flow evolves from its initial conditions through the ballistic region, superdiffuses into the chaotic, multi-scale fluctuations of the Lagrangian region, and transitions to the more homogeneous Eulerian region. Additionally, the researchers identify a fourth region, “free eddies,” characterized by free-floating, rapidly swirling vortices disconnected from the earlier turbulence.
Their results “show excellent agreement with Direct Navier-Stokes simulations,” according to an introduction of their work in Physical Review Research.
Implications for Real-World Applications
This enhanced understanding of Lagrangian turbulence has significant implications for real-world applications. It could improve our ability to track ocean currents, predict weather patterns, and understand how pollutants and airborne pathogens spread. For instance, Birnir plans to write a biomedical paper to provide insights on using this model to better calculate the infectiousness of diseases carried by airborne pathogens.
“This gives us a little more foundation for calculating things like the spread of COVID and other aerosols,” said Birnir.
The research by Birnir and Angheluta represents a significant step forward in the field of turbulence, offering a more comprehensive framework for understanding one of nature’s most complex phenomena. As these theories continue to develop, they promise to provide valuable tools for scientists and engineers working to solve some of the world’s most pressing environmental and health challenges.
