Department of Physics and INFN, University of Rome "Tor Vergata," Via della Ricerca Scientifica 1, 00133, Rome, Italy.
Lab. Lagrange, UCA, OCA, CNRS, CS, 34229, 06304, Nice Cedex 4, France.
Phys Rev E. 2016 Mar;93(3):033109. doi: 10.1103/PhysRevE.93.033109. Epub 2016 Mar 11.
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.
我们给出了一维随机强迫 Burgers 方程在分形 Fourier 集上的约简（降维）的理论和数值结果，维度为 D。我们通过改变 D 来研究能量传递机制和小尺度统计涨落的稳健性。我们发现，非常小的模式约简（D ≲ 1）百分比就足以破坏原始非约简方程的大部分特征。特别是，我们观察到 D < 1 时间歇性涨落的抑制，以及 D ≲ 1 时从完全间歇性（D=1）到非间歇性的准奇异转变。我们的结果表明，一维 Burgers 方程中强局域结构（激波）的存在是所有 Fourier 模式之间高度纠缠相关的结果。
