Intermittency in fractal Fourier hydrodynamics: Lessons from the Burgers Equation
| Autor: | Buzzicotti, Michele, Biferale, Luca, Frisch, Uriel, Ray, Samriddhi Sankar |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Phys. Rev. E 93, 033109 (2016) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevE.93.033109 |
| Popis: | 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 ($D \lesssim 1$) is enough to destroy most of the characteristics of the original non-decimated equation. In particular, we observe a suppression of intermittent fluctuations for $D <1$ and a quasi-singular transition from the fully intermittent ($D=1$) to the non-intermittent case for $D \lesssim 1$. 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. Comment: 9 pages, 7 figures |
| Databáze: | arXiv |
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