2003/07/21 by Victor Gurarie, V. Gurarie, Gurarie, V.
Earth and Planetary Sciences · Environmental Science · Physics and Astronomy · #Atmospheric and Environmental Gas Dynamics #Chaotic Dynamics (nlin.CD) #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Geophysics and Gravity Measurements #cond-mat.dis-nn #nlin.CD
paper · pdf · doi:10.48550/arxiv.nlin/0307033
8 pages, 4 figures
arxiv created 2003/07/21 · openalex publication_date 2003/07/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies the 1D pressureless turbulence (the Burgers equation). It shows that reliable numerics in this problem is very easy to produce if one properly discretizes the Burgers equation. The numerics it presents confirms the 7/2 power law proposed for probability of observing large negative velocity gradients in this problem. It also suggests that the entire probability function for the velocity gradients could be universal, perhaps in some approximate sense. In particular, the probability that the velocity gradient is negative appears to be p ≈ 0.21 ± 0.01 irrespective of the details of the random force. Finally, I speculate that the theory initially proposed by Polyakov, with a particular value of the "anomaly" parameter, may indeed be exact, at least as far as velocity gradients are concerned.