One Step Closer To A Mathematical Theory Of Turbulence

April 4, 2013


Nobel Laureate Richard Feynman once declared that turbulence is “the most important unsolved problem in classical physics.” The phenomenon of turbulence is quite common, apparent in the flow of air in our atmosphere, or the rise of smoke from a cigarette. Yet, a mathematical description of turbulence has continued to escape scientists, despite having been studied for hundreds of years.

In 1941 Soviet mathematician Andrey Kolmogorov developed a phenomenological approach to turbulence. He postulated that the turbulent motions of a fluid would emanate uniformly on small scales, given certain conditions. Namely, if the fluid had a sufficiently high Reynolds number (the ratio of inertial forces to viscous forces; in essence, internal frictional forces of fluids), then all turbulent flows would look the same on a small scale. Of course, taken as a whole, the turbulence appears anisotropic — a result of the fluid interacting with its boundary.

The thrust of Kolmogorov´s theory is still used today, and has been validated in the laboratory setting. But the theory lacks an underlying mathematical representation. The problem has so pervaded the minds of scientists that in the year 2000 the Clay Mathematics Institute offered a one million dollar prize for anyone who could successfully solve the problem. The prize went unclaimed.

New research from the Max Planck Institute for Gravitational Physics has offered some new insights into the problem. Colleagues David Radice and Luciano Rezzolla developed computer simulations to model relativistic turbulent flows, like those that would be expected near black holes.

What they discovered was that, while the basic principles of Kolmogorov´s theory were sound, there were some unexpected anomalies and new effects. While the work did not provide a solution as such, the team was able to identify some key ways that the previous theory could be modified to account for their findings.

According to Rezzolla, “Our calculations have not solved the problem, but we are demonstrating that the previous theory has to be modified and how this should be done. This brings us one step closer to a basic theory for the description of turbulence.”

Details of their work are published in The Astrophysical Journal Letters.


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