title: Turbulence on a Fractal Fourier Set.
abstract: A novel investigation of the nature of intermittency in incompressible, homogeneous, and isotropic turbulence is performed by a numerical study of the Navier-Stokes equations constrained on a fractal Fourier set. The robustness of the energy transfer and of the vortex stretching mechanisms is tested by changing the fractal dimension D from the original three dimensional case to a strongly decimated system with D=2.5, where only about 3% of the Fourier modes interact. This is a unique methodology to probe the statistical properties of the turbulent energy cascade, without breaking any of the original symmetries of the equations. While the direct energy cascade persists, deviations from the Kolmogorov scaling are observed in the kinetic energy spectra. A model in terms of a correction with a linear dependency on the codimension of the fractal set E(k)∼k(-5/3+3-D) explains the results. At small scales, the intermittency of the vorticity field is observed to be quasisingular as a function of the fractal mode reduction, leading to an almost Gaussian statistics already at D∼2.98. These effects must be connected to a genuine modification in the triad-to-triad nonlinear energy transfer mechanism.
authors.affiliation: ISAC-CNR and INFN Sez. Lecce, 73100 Lecce, Italy.
authors.forename: Alessandra S
authors.initials: AS
authors.lastname: Lanotte
authors.affiliation: Department of Physics and INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy.
authors.forename: Roberto
authors.initials: R
authors.lastname: Benzi
authors.affiliation: Department of Physics and INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy.|IIIT- Bangalore, Electronics City, Hosur Road, Bangalore 560100, India.
authors.forename: Shiva K
authors.initials: SK
authors.lastname: Malapaka
authors.affiliation: Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands and IAC CNR, Via dei Taurini 19, 00185 Roma, Italy.
authors.forename: Federico
authors.initials: F
authors.lastname: Toschi
authors.affiliation: Department of Physics and INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy.
authors.forename: Luca
authors.initials: L
authors.lastname: Biferale