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The dispute on whether the three-dimensional (3D) incompressible Eulerequations develop an infinitely large vorticity in a finite time (blowup) keepsincreasing due to ambiguous results from state-of-the-art direct numericalsimulations (DNS), while the available simplified models fail to explain theintrinsic complexity and variety of observed structures. Here, we propose a newmodel formally identical to the Euler equations, by imitating the calculus on a3D logarithmic lattice. This model clarifies the present controversy at thescales of existing DNS and provides the unambiguous evidence of the followingtransition to the blowup, explained as a chaotic attractor in a renormalizedsystem. The chaotic attractor spans over the anomalously large six-decadeinterval of spatial scales. For the original Euler system, our results suggestthat the existing DNS strategies at the resolution accessible now (andpresumably rather long into the future) are unsuitable, by far, for the blowupanalysis, and establish new fundamental requirements for the approach to thislong-standing problem.

Chaotic blowup in the 3D incompressible Euler equations on a logarithmic lattice