Hearing the word “turbulence” evokes images of bumpy airplane rides and stormy nights. While it does make passengers and potential air travelers nervous, the physics behind it is yet to be completely understood.

Nigel Goldenfeld, a physics professor at the University of Illinois at Urbana-Champaign (UIUC), director of the NASA Astrobiology Institute for Universal Biology and leader of the biocomplexity group at Carl R. Woese Institute for Genomic Biology, spoke about why turbulence is difficult to examine and what it would mean to solve this mystery during one of the public lectures the Kavli Institute of Theoretical Physics has throughout the year.

According to Goldenfeld, turbulence is the last great unsolved problem of classical physics. This seemingly random, unpredictable motion of fluids is pervasive and completely familiar to most.

Turbulence governs the speed at which rivers flow and the air drag as you drive your car; it is the bane of air travelers. Turbulence can kill by causing arteries and aneurysms to burst. Turbulence makes stars twinkle. Its random but structured patterns have inspired artists and scientists alike.

The plane above is creating turbulence; the sudden speed of the plane disturbs the air flow and vortices occur. If another plane were behind it that plane would experience the effects of turbulence. / Courtesy of aviationknowledge.wikidot.com

So, what, if anything, can theoretical physics tell us about turbulence? To Richard Feynman — an American theoretical physicist known for his path integral formulation of quantum mechanics and more notably for his contribution in the development of the atomic bomb — absolutely nothing.

Goldenfeld, however, believes that some progress has been made regarding turbulence and, to explain his reasoning, Goldenfeld broke down turbulence into a simple example.

“The simplest form of the problem is to take a pipe that is very long and push water through it at high speed. To push a given amount of water through that pipe, how much pressure is needed? No one can analyze it from first principles and the properties. If the water flows very slowly, or if we use a thick, goo-like honey, then we can [analyze] it nicely,” he said.  

What makes this simple example difficult to solve is when physical formulas that have been used for hundreds of years, such as Newton’s laws of motion, are applied.

According to Goldenfeld, when you apply Newton’s second law of motion (that the force on an object is equal to its mass multiplied by its acceleration) to every particle in the fluid, the problem becomes complex.

If all the particles in the fluid were to move in uniformity, then the problem simplifies to the pipe with steady water flow.

“This is called laminar [flow]. This is just flowing steadily, deterministically, predictably, no surprises,” Goldenfeld said. 

Once the fluid is disturbed, it becomes turbulent.

“The fluid particles start to go off in different directions, and how far they go depends on their velocity, and that depends on their acceleration. So you can’t predict in advance where they will go, because you have to know how they accelerated to get there,” Goldenfeld said.

The once-uniform motion of the fluid particles are now moving randomly and moving farther apart as their accelerations differentiate.

While the fluid particles may seem chaotic, Goldenfeld explains that that term does not properly describe the fluid.

Chaos is one particle, or one system, that behaves badly in time, such as a double pendulum. However, turbulence is many particles acting in both space and time. The structure of a double pendulum is simplistic, while the structure of a disturbed fluid is complex.

Most think that turbulence is something experienced while in an airplane or seen in a fluid, but as Goldenfeld points out, our blood flow is at the point between laminar and turbulent flow, so anything that could potentially disturb that flow may be fatal.

Turbulence is also seen in ecosystems. When there is a balance between prey and predators, it can be seen as laminar as there are no sudden changes, but introducing a disturbance may drive the ecosystem to extinction analogous to turbulence.

For a topic that is involved in every aspect of living systems, turbulence still has yet to be fully understood. The solution is so sought after that the Clay Mathematics Institute is offering a million-dollar prize for the person or group that solves the Navier-Stokes equations, equations that describe the motion of viscous fluids.

As of now, the problem of turbulence is not solved, but according to Goldenfeld, physicists understand it more now than back in Feynman’s day.

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