Cascades and Dissipative Anomalies in Fluid Turbulence, and Beyond
Gregory Eyink, Johns Hopkins University
Friday, April 6, 2018
In his famous undergraduate physics lectures, Richard Feynman remarked
about the problem of fluid turbulence: "Nobody in physics has really been able to analyze it
mathematically satisfactorily in spite of its importance to the sister sciences.” This statement
was already false when Feynman made it. Unbeknownst to him, Lars Onsager decades earlier
had made an exact mathematical analysis of the high Reynolds-number limit of incompressible
fluid turbulence, using a method that would now be described as a non-perturbative renormalization
group analysis and discovering the first “conservation-law anomaly” in theoretical physics.
Onsager’s results were only cryptically announced in 1949 and he never published any of his
detailed calculations. Onsager’s analysis was finally rescued from oblivion and reproduced
by the speaker in 1994. The ideas have subsequently been intensively developed in the mathematical
PDE community, where deep connections emerged with John Nash’s work on isometric embeddings.
Furthermore, the method has more recently been successfully applied to new physics problems,
compressible fluid turbulence and relativistic fluid turbulence, yielding many new testable predictions.
This talk will briefly review Onsager’s exact analysis of the original incompressible turbulence
problem and subsequent developments. Then a new application to kinetic plasma turbulence
will be described, with novel predictions for turbulence in nearly colllisionless plasmas such as the
solar wind and the terrestrial magnetosphere.