Turbulence on a Fractal Fourier Set

Physical Review Letters
Alessandra S LanotteLuca Biferale

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.

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Citations

Mar 24, 2016·The European Physical Journal. E, Soft Matter·Michele BuzzicottiMiguel D Bustamante
Apr 30, 2016·The European Physical Journal. E, Soft Matter·Alessandra S LanotteLuca Biferale
Mar 17, 2017·Physical Review. E·Mani Fathali, Saber Khoei
Apr 15, 2016·Physical Review. E·Michele BuzzicottiSamriddhi Sankar Ray
Mar 14, 2020·Physical Review Letters·Michele BuzzicottiFederico Toschi
Jul 18, 2018·Physical Review. E·Ö D Gürcan

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