An interpretation of the Navier-Stokes-alpha model as a frame-indifferent Leray regularization

J. L. Guermond; J. T. Oden; S. Prudhomme

doi:10.1016/S0167-2789(02)00748-0

An interpretation of the Navier-Stokes-alpha model as a frame-indifferent Leray regularization

J. L. Guermond^*, J. T. Oden, S. Prudhomme

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

53 Scopus citations

Abstract

We show in this note that the Leray regularization of the Navier-Stokes equations is almost frame-indifferent but for one second-order term. Neglecting this term, we readily recover the Navier-Stokes-alpha equations introduced by Holm et al. [Adv. Math. 137 (1998) 1; Phys. Fluids 11 (8) (1999) 2343]. Hence, as an alternative to the exposition in [Adv. Math. 137 (1998) 1; Phys. Fluids 11 (8) (1999) 2343], we propose to interpret the Navier-Stokes-alpha model as a frame-indifferent perturbation of the Leray regularization. Published by Elsevier Science B.V.

Original language	English (US)
Pages (from-to)	23-30
Number of pages	8
Journal	Physica D: Nonlinear Phenomena
Volume	177
Issue number	1-4
DOIs	https://doi.org/10.1016/S0167-2789(02)00748-0
State	Published - Mar 15 2003
Externally published	Yes

Bibliographical note

Funding Information:
The first author gratefully acknowledges the support of Centre National de la Recherche Scientifique (CNRS) and of Texas Institute for Computational and Applied Mathematics (TICAM) under a TICAM Visiting Faculty Fellowship. The other authors acknowledge support of this work through the Office of Naval Research under grant N00014-95-0401.

Keywords

Filtering
Large eddy simulation
Navier-Stokes equations
Navier-Stokes-alpha model
Turbulence

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/S0167-2789(02)00748-0

Cite this

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title = "An interpretation of the Navier-Stokes-alpha model as a frame-indifferent Leray regularization",

abstract = "We show in this note that the Leray regularization of the Navier-Stokes equations is almost frame-indifferent but for one second-order term. Neglecting this term, we readily recover the Navier-Stokes-alpha equations introduced by Holm et al. [Adv. Math. 137 (1998) 1; Phys. Fluids 11 (8) (1999) 2343]. Hence, as an alternative to the exposition in [Adv. Math. 137 (1998) 1; Phys. Fluids 11 (8) (1999) 2343], we propose to interpret the Navier-Stokes-alpha model as a frame-indifferent perturbation of the Leray regularization. Published by Elsevier Science B.V.",

keywords = "Filtering, Large eddy simulation, Navier-Stokes equations, Navier-Stokes-alpha model, Turbulence",

author = "Guermond, {J. L.} and Oden, {J. T.} and S. Prudhomme",

note = "Funding Information: The first author gratefully acknowledges the support of Centre National de la Recherche Scientifique (CNRS) and of Texas Institute for Computational and Applied Mathematics (TICAM) under a TICAM Visiting Faculty Fellowship. The other authors acknowledge support of this work through the Office of Naval Research under grant N00014-95-0401.",

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doi = "10.1016/S0167-2789(02)00748-0",

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T1 - An interpretation of the Navier-Stokes-alpha model as a frame-indifferent Leray regularization

AU - Guermond, J. L.

AU - Oden, J. T.

AU - Prudhomme, S.

N1 - Funding Information: The first author gratefully acknowledges the support of Centre National de la Recherche Scientifique (CNRS) and of Texas Institute for Computational and Applied Mathematics (TICAM) under a TICAM Visiting Faculty Fellowship. The other authors acknowledge support of this work through the Office of Naval Research under grant N00014-95-0401.

PY - 2003/3/15

Y1 - 2003/3/15

N2 - We show in this note that the Leray regularization of the Navier-Stokes equations is almost frame-indifferent but for one second-order term. Neglecting this term, we readily recover the Navier-Stokes-alpha equations introduced by Holm et al. [Adv. Math. 137 (1998) 1; Phys. Fluids 11 (8) (1999) 2343]. Hence, as an alternative to the exposition in [Adv. Math. 137 (1998) 1; Phys. Fluids 11 (8) (1999) 2343], we propose to interpret the Navier-Stokes-alpha model as a frame-indifferent perturbation of the Leray regularization. Published by Elsevier Science B.V.

AB - We show in this note that the Leray regularization of the Navier-Stokes equations is almost frame-indifferent but for one second-order term. Neglecting this term, we readily recover the Navier-Stokes-alpha equations introduced by Holm et al. [Adv. Math. 137 (1998) 1; Phys. Fluids 11 (8) (1999) 2343]. Hence, as an alternative to the exposition in [Adv. Math. 137 (1998) 1; Phys. Fluids 11 (8) (1999) 2343], we propose to interpret the Navier-Stokes-alpha model as a frame-indifferent perturbation of the Leray regularization. Published by Elsevier Science B.V.

KW - Filtering

KW - Large eddy simulation

KW - Navier-Stokes equations

KW - Navier-Stokes-alpha model

KW - Turbulence

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DO - 10.1016/S0167-2789(02)00748-0

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SN - 0167-2789

VL - 177

SP - 23

EP - 30

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 1-4

ER -

An interpretation of the Navier-Stokes-alpha model as a frame-indifferent Leray regularization

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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