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.

Lanotte, A., Benzi, R., Malapaka, S., Toschi, F., & Biferale, L. (2015). Turbulence on a Fractal Fourier Set. PHYSICAL REVIEW LETTERS, 115(26), 264502 [10.1103/PhysRevLett.115.264502].

Turbulence on a Fractal Fourier Set

BENZI, ROBERTO;BIFERALE, LUCA
2015-12-29

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.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
English
Turbulence, Intermittency, Fractals
Lanotte, A., Benzi, R., Malapaka, S., Toschi, F., & Biferale, L. (2015). Turbulence on a Fractal Fourier Set. PHYSICAL REVIEW LETTERS, 115(26), 264502 [10.1103/PhysRevLett.115.264502].
Lanotte, A; Benzi, R; Malapaka, S; Toschi, F; Biferale, L
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/173390
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