Existence and Stability of Finite-Amplitude States in Plane Couette Flow

Cherhabili, A.; Ehrenstein, U.

doi:10.1007/978-94-009-0297-8_89

A. Cherhabili³ &
U. Ehrenstein³

Part of the book series: Fluid Mechanics and its Applications ((FMIA,volume 36))

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Abstract

To elucidate the transition mechanism in plane Couette flow we compute finite-amplitude equilibrium solutions by extending numerically 2D nonlinear waves in plane Poiseuille flow to the plane Couette flow limit. The 2D nonlinear states in plane Couette flow take the form of spatially localized (solitarylike) stationary waves, they represent a new basic state for a secondary stability analysis. Secondary stability characteristics are computed as well as secondary bifurcation branches leading to 3D nonlinear states spatially localized in the streamwise direction and periodic in the spanwise direction.

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References

Busse F.H, Clever R.M., 1992, J. Fluid Mech., 234, 511–527.
Article MathSciNet ADS MATH Google Scholar
Cherhabili A., Ehrenstein U., 1995, Eur. J. Mech. B/Fluids, 14, 667–696
MathSciNet Google Scholar
Dauchot O., Daviaud F., 1995, Phys. Fluids, 7, 901–903.
Article Google Scholar
Ehrenstein U., Koch W., 1991, J. Fluid Mech., 228, 111–148.
ADS MATH Google Scholar
Milinazzo F.A., Saffman P.G., 1985, J. Fluid Mech., 160, 281–295.
Article MathSciNet ADS MATH Google Scholar
Nagata M., 1990, J. Fluid Mech., 217, 519–527.
Article MathSciNet ADS Google Scholar
Romanov V.A., 1973, Funct. Anal. Applies, 7, 137–146
Article MATH Google Scholar
Saffman P.G., 1983, Ann. N. Y. Acad. Sci., 404, 12–24.
Article ADS Google Scholar
Tillmark N., Alfredsson P.H., 1992, J. Fluid Mech., 235, 89–102.
Article ADS Google Scholar

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Authors and Affiliations

Laboratoire de Mécanique de Lille, URA CNRS, Université Lille I, 1441 Bd. P. Langevin, F - 59655, Villeneuve d’Ascq Cedex, France
A. Cherhabili & U. Ehrenstein

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A. Cherhabili
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U. Ehrenstein
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Editors and Affiliations

Fluid Mechanics Laboratory, Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland
S. Gavrilakis , L. Machiels & P. A. Monkewitz , &

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Cherhabili, A., Ehrenstein, U. (1996). Existence and Stability of Finite-Amplitude States in Plane Couette Flow. In: Gavrilakis, S., Machiels, L., Monkewitz, P.A. (eds) Advances in Turbulence VI. Fluid Mechanics and its Applications, vol 36. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0297-8_89

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DOI: https://doi.org/10.1007/978-94-009-0297-8_89
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6618-1
Online ISBN: 978-94-009-0297-8
eBook Packages: Springer Book Archive

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