Cartes, Carlos, Bustamante, Miguel D. and Brachet, Marc E. (2007) Generalized Eulerian-Lagrangian description of Navier-Stokes dynamics. Physics of Fluids, Vol.19 (No.7). Article: 077101. doi:10.1063/1.2748447

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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. (c) 2007 American Institute of Physics.

Item Type:	Journal Article
Subjects:	T Technology > TJ Mechanical engineering and machinery Q Science > QC Physics
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Physics of Fluids
Publisher:	American Institute of Physics
ISSN:	1070-6631
Official Date:	July 2007
Dates:	Date Event July 2007 Published
Volume:	Vol.19
Number:	No.7
Number of Pages:	7
Page Range:	Article: 077101
DOI:	10.1063/1.2748447
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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