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On the solution of Stokes' equations between confocal ellipses

Identifieur interne : 000F66 ( PascalFrancis/Corpus ); précédent : 000F65; suivant : 000F67

On the solution of Stokes' equations between confocal ellipses

Auteurs : Estéban Saatdjian ; Noël Midoux ; Jean Claude André

Source :

RBID : Pascal:94-0689029

Descripteurs français

English descriptors

Abstract

The analytical solution of Stokes' equations between two concentric, confocal ellipses is derived here. This bounded flow, similar in certain respects to the journal bearing flow, was imagined in order to investigate two-dimensional mixing and Lagrangian chaos in a bounded flow with two symmetry axis. The derived streamfunction is in the form of a Fourier cosine series and, when the eccentricity ratio of the inner ellipse is not very low, the solution converges very rapidly. When the ellipses turn in opposite directions, there are cases where two saddle points are connected by two different streamlines, a necessary and sufficient condition for structural instability according to Peixoto's theorem. This flow geometry could be particularly effective for mixing of viscous fluids since the number of low period hyperbolic and elliptical points during time periodic boundary motion is greater than for the eccentric rotating cylinder system. The Poincaré sections obtained with a discontinuous velocity protocol suggest that the size of regions of poor mixing can be reduced by increasing the inner ellipse motion per period. For this geometry, the Poincaré sections indicate that counter-rotation yields a more chaotic long term behavior than co-rotation. © 1994 American Institute of Physics.

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Pour connaître la documentation sur le format Inist Standard.

pA  
A01 01  1    @0 1070-6631
A02 01      @0 PHFLE6
A03   1    @0 Phys. Fluids
A05       @2 6
A06       @2 12
A08 01  1  ENG  @1 On the solution of Stokes' equations between confocal ellipses
A11 01  1    @1 SAATDJIAN (Estéban)
A11 02  1    @1 MIDOUX (Noël)
A11 03  1    @1 ANDRÉ (Jean Claude)
A14 01      @1 ENSIC-LSGC, 1 rue Grandville, BP 451, 54001 Nancy Cédex, France @Z 1 aut. @Z 2 aut.
A14 02      @1 GRAPP-CNRS, 1 rue Grandville, BP 451, 54001 Nancy Cédex, France @Z 3 aut.
A20       @1 3833-3846
A21       @1 1994-12
A23 01      @0 ENG
A43 01      @1 INIST @2 8651A
A44       @0 8100 @1 © AIP
A47 01  1    @0 94-0689029
A60       @1 P
A61       @0 A
A64 01  1    @0 Physics of Fluids
A66 01      @0 USA
C01 01    ENG  @0 The analytical solution of Stokes' equations between two concentric, confocal ellipses is derived here. This bounded flow, similar in certain respects to the journal bearing flow, was imagined in order to investigate two-dimensional mixing and Lagrangian chaos in a bounded flow with two symmetry axis. The derived streamfunction is in the form of a Fourier cosine series and, when the eccentricity ratio of the inner ellipse is not very low, the solution converges very rapidly. When the ellipses turn in opposite directions, there are cases where two saddle points are connected by two different streamlines, a necessary and sufficient condition for structural instability according to Peixoto's theorem. This flow geometry could be particularly effective for mixing of viscous fluids since the number of low period hyperbolic and elliptical points during time periodic boundary motion is greater than for the eccentric rotating cylinder system. The Poincaré sections obtained with a discontinuous velocity protocol suggest that the size of regions of poor mixing can be reduced by increasing the inner ellipse motion per period. For this geometry, the Poincaré sections indicate that counter-rotation yields a more chaotic long term behavior than co-rotation. © 1994 American Institute of Physics.
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C02 02  3    @0 001B40G52
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C03 04  3  FRE  @0 Ecoulement visqueux @2 T1
C03 04  3  ENG  @0 Viscous flow @2 T1
C03 05  3  FRE  @0 Ecoulement incompressible
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C03 06  3  FRE  @0 Equation Navier Stokes
C03 06  3  ENG  @0 Navier-Stokes equations
C03 07  3  FRE  @0 Configuration elliptique
C03 07  3  ENG  @0 Elliptical configuration
C03 08  3  FRE  @0 Problème valeur limite
C03 08  3  ENG  @0 Boundary-value problems
C03 09  3  FRE  @0 Solution analytique
C03 09  3  ENG  @0 Analytical solution
C03 10  3  FRE  @0 Ligne courant
C03 10  3  ENG  @0 Streamlines
C03 11  3  FRE  @0 Ecoulement laminaire @2 T2
C03 11  3  ENG  @0 Laminar flow @2 T2
C03 12  3  FRE  @0 Stabilité construction
C03 12  3  ENG  @0 Structural stability
C03 13  3  FRE  @0 Section Poincaré
C03 13  3  ENG  @0 Poincaré mapping
C03 14  3  FRE  @0 Système chaotique @2 Q1 @2 Q2
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N21       @1 338
N47 01  1    @0 9422M1221

Format Inist (serveur)

NO : PASCAL 94-0689029 AIP
ET : On the solution of Stokes' equations between confocal ellipses
AU : SAATDJIAN (Estéban); MIDOUX (Noël); ANDRÉ (Jean Claude)
AF : ENSIC-LSGC, 1 rue Grandville, BP 451, 54001 Nancy Cédex, France (1 aut., 2 aut.); GRAPP-CNRS, 1 rue Grandville, BP 451, 54001 Nancy Cédex, France (3 aut.)
DT : Publication en série; Niveau analytique
SO : Physics of Fluids; ISSN 1070-6631; Coden PHFLE6; Etats-Unis; Da. 1994-12; Vol. 6; No. 12; Pp. 3833-3846
LA : Anglais
EA : The analytical solution of Stokes' equations between two concentric, confocal ellipses is derived here. This bounded flow, similar in certain respects to the journal bearing flow, was imagined in order to investigate two-dimensional mixing and Lagrangian chaos in a bounded flow with two symmetry axis. The derived streamfunction is in the form of a Fourier cosine series and, when the eccentricity ratio of the inner ellipse is not very low, the solution converges very rapidly. When the ellipses turn in opposite directions, there are cases where two saddle points are connected by two different streamlines, a necessary and sufficient condition for structural instability according to Peixoto's theorem. This flow geometry could be particularly effective for mixing of viscous fluids since the number of low period hyperbolic and elliptical points during time periodic boundary motion is greater than for the eccentric rotating cylinder system. The Poincaré sections obtained with a discontinuous velocity protocol suggest that the size of regions of poor mixing can be reduced by increasing the inner ellipse motion per period. For this geometry, the Poincaré sections indicate that counter-rotation yields a more chaotic long term behavior than co-rotation. © 1994 American Institute of Physics.
CC : 001B40G15G; 001B40G52
FD : Etude théorique; 4715G; 4752; Ecoulement visqueux; Ecoulement incompressible; Equation Navier Stokes; Configuration elliptique; Problème valeur limite; Solution analytique; Ligne courant; Ecoulement laminaire; Stabilité construction; Section Poincaré; Système chaotique; Espace annulaire
ED : Theoretical study; Viscous flow; Incompressible flow; Navier-Stokes equations; Elliptical configuration; Boundary-value problems; Analytical solution; Streamlines; Laminar flow; Structural stability; Poincaré mapping; Chaotic systems; Annular space
LO : INIST-8651A
ID : 94-0689029

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