Some notes on periodic Beltrami fields in Cartesian geometry

D. Mclaughlin; O. Pironneau

doi:10.1063/1.529373

Some notes on periodic Beltrami fields in Cartesian geometry

D. Mclaughlin, O. Pironneau

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

17 Scopus citations

Abstract

Some mathematical facts about Beltrami fields, which are timeindependent solutions of the threedimensional incompressible Euler equations with nontrivial helicity, are assembled. The linearization about an arbitrary, fixed Beltrami field is studied in a Hamiltonian framework. A factorization of this linearization is introduced and used to characterize null spaces for Beltrami fields with ergodic streamlines. An interesting property of unstable modes is noticed and its consequences concerning the nature of potential instabilities are discussed.

Original language	English
Pages (from-to)	797-804
Number of pages	8
Journal	Journal of Mathematical Physics
Volume	32
Issue number	3
DOIs	https://doi.org/10.1063/1.529373
State	Published - Mar 1991
Externally published	Yes

Keywords

CARTESIAN COORDINATES
CHAOTIC SYSTEMS
HAMILTONIANS
HELICITY
IDEAL FLOW
INCOMPRESSIBLE FLOW
INTEGRABLE SYSTEMS
NAVIERSTOKES EQUATIONS
STRANGE ATTRACTORS
THREEDIMENSIONAL CALCULATIONS
TURBULENT FLOW

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title = "Some notes on periodic Beltrami fields in Cartesian geometry",

abstract = "Some mathematical facts about Beltrami fields, which are timeindependent solutions of the threedimensional incompressible Euler equations with nontrivial helicity, are assembled. The linearization about an arbitrary, fixed Beltrami field is studied in a Hamiltonian framework. A factorization of this linearization is introduced and used to characterize null spaces for Beltrami fields with ergodic streamlines. An interesting property of unstable modes is noticed and its consequences concerning the nature of potential instabilities are discussed.",

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author = "D. Mclaughlin and O. Pironneau",

year = "1991",

month = mar,

doi = "10.1063/1.529373",

language = "English",

volume = "32",

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journal = "Journal of Mathematical Physics",

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AU - Mclaughlin, D.

AU - Pironneau, O.

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AB - Some mathematical facts about Beltrami fields, which are timeindependent solutions of the threedimensional incompressible Euler equations with nontrivial helicity, are assembled. The linearization about an arbitrary, fixed Beltrami field is studied in a Hamiltonian framework. A factorization of this linearization is introduced and used to characterize null spaces for Beltrami fields with ergodic streamlines. An interesting property of unstable modes is noticed and its consequences concerning the nature of potential instabilities are discussed.

KW - CARTESIAN COORDINATES

KW - CHAOTIC SYSTEMS

KW - HAMILTONIANS

KW - HELICITY

KW - IDEAL FLOW

KW - INCOMPRESSIBLE FLOW

KW - INTEGRABLE SYSTEMS

KW - NAVIERSTOKES EQUATIONS

KW - STRANGE ATTRACTORS

KW - THREEDIMENSIONAL CALCULATIONS

KW - TURBULENT FLOW

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SN - 0022-2488

VL - 32

SP - 797

EP - 804

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 3

ER -

Some notes on periodic Beltrami fields in Cartesian geometry

Abstract

Keywords

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