Chaotic Blowup in the 3D Incompressible Euler Equations on a Logarithmic Lattice.
Phys Rev Lett
; 121(6): 064501, 2018 Aug 10.
Article
em En
| MEDLINE
| ID: mdl-30141686
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.
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Coleções:
01-internacional
Base de dados:
MEDLINE
Idioma:
En
Revista:
Phys Rev Lett
Ano de publicação:
2018
Tipo de documento:
Article
País de afiliação:
Brasil
País de publicação:
Estados Unidos