Generalized Eulerian-Lagrangian description of Navier-Stokes dynamics

Carlos Gabriel Cartés, Miguel D. Bustamante, Marc E. Brachet

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

Generalized equations of motion for the Weber-Clebsch potentials that reproduce Navier-Stokes dynamics are derived. These depend on a new parameter, with the dimension of time, and reduce to the Ohkitani and Constantin equations in the singular special case where the new parameter vanishes. Let us recall that Ohkitani and Constantin found that the diffusive Lagrangian map became noninvertible under time evolution and required resetting for its calculation. They proposed that high frequency of resetting was a diagnostic for vortex reconnection. Direct numerical simulations are performed. The Navier-Stokes dynamics is well reproduced at small enough Reynolds number without resetting. Computation at higher Reynolds numbers is achieved by performing resettings. The interval between successive resettings is found to abruptly increase when the new parameter is varied from 0 to a value much smaller than the resetting interval.

Original languageEnglish
Article number077101
JournalPhysics of Fluids
Volume19
Issue number7
DOIs
StatePublished - Jul 2007
Externally publishedYes

Bibliographical note

Funding Information:
We acknowledge very useful scientific discussions with Peter Constantin and Edriss S. Titi. One of the authors (M.E.B.) acknowledges support from an ECOS/CONICYT action.

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