Generalized  eulerian-lagrangian description of navier-stokes dynamics

Carlos Cartes; Miguel D. Bustamante; Marc E. Brachet

doi:10.1063/1.2748447

Generalized eulerian-lagrangian description of navier-stokes dynamics

Carlos Cartes, Miguel D. Bustamante^*, Marc E. Brachet

^*Autor correspondiente de este trabajo

Facultad de Ingeniería y Ciencias Aplicadas

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

17 Citas (Scopus)

Resumen

New generalized equations of motion for the Weber-Clebsch potentials that describe both the Navier-Stokes and MHD dynamics are derived. These depend on a new parameter, which has dimensions of time for Navier-Stokes and inverse velocity for MHD. Direct numerical simulations are performed. For Navier-Stokes, the generalized formalism captures the intense reconnection of vortices of the Boratav, Pelz and Zabusky flow, in agreement with the previous study by Ohkitani and Constantin. For MHD, the new formalism is used to detect magnetic reconnection in several flows: the 3D Arnold, Beltrami and Childress (ABC) flow and the (2D and 3D) Orszag-Tang vortex. It is concluded that periods of intense activity in the magnetic enstrophy are correlated with periods of increasingly frequent resettings. Finally, the positive correlation between the sharpness of the increase in resetting frequency and the spatial localization of the reconnection region is discussed.

Idioma original	Inglés
Número de artículo	077101
Número de páginas	8
Publicación	Physics of Fluids
Volumen	19
N.º	7
DOI	https://doi.org/10.1063/1.2748447
Estado	Publicada - jul. 2007

Nota bibliográfica

Acceder al documento

10.1063/1.2748447

Otros archivos y enlaces

Enlace a la publicación en Scopus

Citar esto

@article{dd11ac94f9fe46b7aa8447e162cb35dc,

title = "Generalized eulerian-lagrangian description of navier-stokes dynamics",

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.",

author = "Carlos Cartes and Bustamante, {Miguel D.} and Brachet, {Marc E.}",

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. ",

year = "2007",

month = jul,

doi = "10.1063/1.2748447",

language = "English",

volume = "19",

journal = "Physics of Fluids",

issn = "1070-6631",

publisher = "American Institute of Physics",

number = "7",

}

TY - JOUR

T1 - Generalized eulerian-lagrangian description of navier-stokes dynamics

AU - Cartes, Carlos

AU - Bustamante, Miguel D.

AU - Brachet, Marc E.

N1 - 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.

PY - 2007/7

Y1 - 2007/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34547772047&partnerID=8YFLogxK

U2 - 10.1063/1.2748447

DO - 10.1063/1.2748447

M3 - Article

AN - SCOPUS:34547772047

SN - 1070-6631

VL - 19

JO - Physics of Fluids

JF - Physics of Fluids

IS - 7

M1 - 077101

ER -