“Researchers from EPFL have found the mechanism that lies behind a mysterious physics phenomenon in fluid mechanics: the fact that turbulence in fluids spontaneously self-organizes into parallel patterns of oblique turbulent bands – an example of order emerging spontaneously from chaos. In so doing, they solved a problem that had stumped generations of physicists.
For decades, physicists, engineers and mathematicians failed to explain a remarkable phenomenon in fluid mechanics: the natural tendency of turbulence in fluids to move from disordered chaos to perfectly parallel patterns of oblique turbulent bands. This transition from a state of chaotic turbulence to a highly structured pattern was observed by many scientists, but never understood.
At EPFL’s Emerging Complexity in Physical Systems Laboratory (School of Engineering), Tobias Schneider and his team have identified the mechanism that explains this phenomenon. Their findings have been published in Nature Communications.
From chaos to order
The equations used to describe the large variety of phenomena occurring in fluid flows are well known. These equations capture the fundamental laws of physics that govern fluid dynamics, a subject taught to all physics and engineering students from undergraduate level onwards.
But when turbulence comes into play, the solutions to the equations become non-linear, complex and chaotic. This makes it impossible, for example, to predict weather over an extended time horizon. Yet turbulence has a surprising tendency to move from chaos to a highly structured pattern of turbulent and laminar bands. This is a remarkable phenomenon, yet the underlying mechanism remained hidden in the equations until now.
Here’s what happens: when a fluid is placed between two parallel plates, each moving in an opposite direction, turbulence is created. At first, the turbulence is chaotic, then it self-organizes to form regular oblique bands, separated by zones of calm (or laminar flows). No obvious mechanism selects the oblique orientation of the bands or determines the wavelength of the periodic pattern.
Concealed in simple equations
Schneider and his team solved the mystery. “As the physicist Richard Feynman predicted, the solution was not to be found in new equations, but rather within the equation that was already available to us,” explains Schneider. “Until now, researchers didn’t have powerful enough mathematical tools to verify this.”
The researchers combined one such tool, known as dynamical systems theory, with existing theories on pattern formation in fluids and advanced numerical simulations. They calculated specific equilibrium solutions for each step of the process, enabling them to explain the transition from the chaotic to the structured state.
“We can now describe the initial instability mechanism that creates the oblique pattern,” explains Florian Reetz, the study’s lead author. “We have thus solved one of the most fundamental problems in our field. The methods we developed will help clarify the chaotic dynamics of turbulent-laminar patterns in many flow problems. They may one day allow us to better control flows.””