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Updated: Mar 22, 2026

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Published on: December 4, 2017
Intermittency in fractal Fourier hydrodynamics: Lessons from the Burgers equation
Michele Buzzicotti1, Luca Biferale1, Uriel Frisch2
1Department of Physics and INFN, University of Rome "Tor Vergata," Via della Ricerca Scientifica 1, 00133, Rome, Italy.
Abstract:
We present theoretical and numerical results for the one-dimensional stochastically forced Burgers equation decimated on a fractal Fourier set of dimension D. We investigate the robustness of the energy transfer mechanism and of the small-scale statistical fluctuations by changing D. We find that a very small percentage of mode-reduction (D ≲ 1) is enough to destroy most of the characteristics of the original nondecimated equation. In particular, we observe a suppression of intermittent fluctuations for D < 1 and a quasisingular transition from the fully intermittent (D=1) to the nonintermittent case for D ≲ 1. Our results indicate that the existence of strong localized structures (shocks) in the one-dimensional Burgers equation is the result of highly entangled correlations amongst all Fourier modes.
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