Intermittency in fractal Fourier hydrodynamics: Lessons from the Burgers Equation

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 ($D\lesssim 1$) 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.

9 pages, 7 figures

References in corpus (2)

• Burgers Turbulence
• Turbulence on a Fractal Fourier set

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