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.

Buzzicotti, M., Biferale, L., Frisch, U., Ray, S. (2016). Intermittency in fractal Fourier hydrodynamics: lessons from the Burgers equation. PHYSICAL REVIEW. E, 93(3), 033109 [10.1103/PhysRevE.93.033109].

Intermittency in fractal Fourier hydrodynamics: lessons from the Burgers equation

BUZZICOTTI, MICHELE;BIFERALE, LUCA;
2016-01-01

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.
2016
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore FIS/02 - FISICA TEORICA, MODELLI E METODI MATEMATICI
English
Buzzicotti, M., Biferale, L., Frisch, U., Ray, S. (2016). Intermittency in fractal Fourier hydrodynamics: lessons from the Burgers equation. PHYSICAL REVIEW. E, 93(3), 033109 [10.1103/PhysRevE.93.033109].
Buzzicotti, M; Biferale, L; Frisch, U; Ray, S
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/173964
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