Chaotic Blowup in the 3D Incompressible Euler Equations on a Logarithmic Lattice

Physical Review Letters
Ciro S Campolina, Alexei A Mailybaev

Abstract

The dispute on whether the three-dimensional (3D) incompressible Euler equations develop an infinitely large vorticity in a finite time (blowup) keeps increasing due to ambiguous results from state-of-the-art direct numerical simulations (DNS), while the available simplified models fail to explain the intrinsic complexity and variety of observed structures. Here, we propose a new model formally identical to the Euler equations, by imitating the calculus on a 3D logarithmic lattice. This model clarifies the present controversy at the scales of existing DNS and provides the unambiguous evidence of the following transition to the blowup, explained as a chaotic attractor in a renormalized system. The chaotic attractor spans over the anomalously large six-decade interval of spatial scales. For the original Euler system, our results suggest that the existing DNS strategies at the resolution accessible now (and presumably rather long into the future) are unsuitable, by far, for the blowup analysis, and establish new fundamental requirements for the approach to this long-standing problem.

References

Mar 9, 1992·Physical Review Letters·A Pumir, E D Siggia
Dec 30, 1996·Physical Review Letters·S GrossmannA Reeh
Jan 4, 2001·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·J M Greene, R B Pelz
Feb 21, 2006·Physical Review Letters·Cyril CichowlasMarc Brachet
Sep 26, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexei A Mailybaev
Aug 27, 2014·Proceedings of the National Academy of Sciences of the United States of America·Guo Luo, Thomas Y Hou
Jan 1, 2011·Living Reviews in Relativity·Håkan Andréasson
Jul 16, 2017·Physical Review. E·Ö D Gürcan

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