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Nonlinear Sciences > Chaotic Dynamics

arXiv:nlin/0307033 (nlin)
[Submitted on 21 Jul 2003]

Title:Burgers Equation Revisited

Authors:V. Gurarie
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Abstract: 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 $p \approx 0.21 \pm 0.01$ 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.
Comments: 8 pages, 4 figures
Subjects: Chaotic Dynamics (nlin.CD); Disordered Systems and Neural Networks (cond-mat.dis-nn)
Cite as: arXiv:nlin/0307033 [nlin.CD]
  (or arXiv:nlin/0307033v1 [nlin.CD] for this version)
  https://doi.org/10.48550/arXiv.nlin/0307033

Submission history

From: Victor Gurarie [view email]
[v1] Mon, 21 Jul 2003 07:20:22 UTC (64 KB)
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