On the global evolution of vortex filaments, blobs, and small loops in 3D ideal flows

L. C. Berselli and M. Gubinelli

First issued 28 October 2005 · PDF

Abstract

We consider a wide class of approximate models of evolution of singular distributions of vorticity in three dimensional incompressible fluids and we show that they have global smooth solutions. The proof exploits the existence of suitable Hamiltonian functions. The approximate models we analyze (essentially discrete and continuous vortex filaments and vortex loops) are related to some problem of classical physics concerning turbulence and also to the numerical approximation of flows with very high Reynolds number. Finally, we interpret our results as a basis to theoretical validation of numerical methods used in state-of-the-art computations of turbulent flows.

Versions

1. Version 1 (arXiv v1) current
   28 October 2005
   arXiv comments: 22 pages, no figures
   PDF · LaTeX source · files and digests · arXiv:math-ph/0510091

Cite

L. C. Berselli and M. Gubinelli. On the global evolution of vortex filaments, blobs, and small loops in 3D ideal flows. Papers of Massimiliano Gubinelli, 2005, version 1. https://mgubi.org/papers/paper/vortex-filaments-blobs-loops/

Licence: arXiv.org non-exclusive license to distribute, assumed for submissions of 1991-2003; all other rights reserved to the authors

Pin in the collection (SHA-512 of the inventory it fixes): b7b0d4b21e4946d7a96be6ee1dba6e3d9eff739643f740c88edf90629b5dec3f5168b720f7159eddb5c26d9b7bff32e463abb516f5cf20175c9b1db57211747d

Papers of Massimiliano Gubinelli: an OpenSheaf archive (format 0.1, a draft); this page is generated by opensheaf-py from the archive.