Intermittency in fractal Fourier hydrodynamics: Lessons from the Burgers Equation
Michele Buzzicotti, Luca Biferale, Uriel Frisch, Samriddhi Sankar Ray
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 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≲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.