title: Intermittency in fractal Fourier hydrodynamics: Lessons from the Burgers equation.
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.
authors.affiliation: Department of Physics and INFN, University of Rome "Tor Vergata," Via della Ricerca Scientifica 1, 00133, Rome, Italy.
authors.forename: Michele
authors.initials: M
authors.lastname: Buzzicotti
authors.affiliation: Department of Physics and INFN, University of Rome "Tor Vergata," Via della Ricerca Scientifica 1, 00133, Rome, Italy.
authors.forename: Luca
authors.initials: L
authors.lastname: Biferale
authors.affiliation: Lab. Lagrange, UCA, OCA, CNRS, CS, 34229, 06304, Nice Cedex 4, France.
authors.forename: Uriel
authors.initials: U
authors.lastname: Frisch
authors.affiliation: International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India.
authors.forename: Samriddhi Sankar
authors.initials: SS
authors.lastname: Ray