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Mathematics > Analysis of PDEs

arXiv:1804.08238 (math)
[Submitted on 23 Apr 2018 (v1), last revised 18 Oct 2018 (this version, v2)]

Title:Local near-Beltrami structure and depletion of the nonlinearity in the 3D Navier-Stokes flows

Authors:Aseel Farhat, Zoran Grujic
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Abstract:Computational simulations of turbulent flows indicate that the regions of low dissipation/enstrophy production feature high degree of local alignment between the velocity and the vorticty, i.e., the flow is locally near-Beltrami. Hence one could envision a geometric scenario in which the persistence of the local near-Beltramy property might be consistent with a (possible) finite-time singularity formation. The goal of this note is to show that this scenario is in fact prohibited if the sine of the angle between the velocity and the vorticty is small enough with respect to the local enstrophy.
Comments: final version; to appear in JNLS
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1804.08238 [math.AP]
  (or arXiv:1804.08238v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.08238
Related DOI: https://doi.org/10.1007/s00332-018-9504-8

Submission history

From: Zoran Grujic [view email]
[v1] Mon, 23 Apr 2018 03:46:51 UTC (7 KB)
[v2] Thu, 18 Oct 2018 15:22:03 UTC (7 KB)
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