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Two-dimensional patterns in Rayleigh-Taylor instability of a thin layer

Published online by Cambridge University Press:  26 April 2006

M. Fermigier ,
L. Limat ,
J. E. Wesfreid ,
P. Boudinet  and
C. Quilliet
M. Fermigier
Affiliation:
Laboratoire d'Hydrodynamique et Mécanique Physique, Ecole Supérieure de Physique et Chimie de Paris, 10, rue Vauquelin, 75231 Paris Cedex 05, France
L. Limat
Affiliation:
Laboratoire d'Hydrodynamique et Mécanique Physique, Ecole Supérieure de Physique et Chimie de Paris, 10, rue Vauquelin, 75231 Paris Cedex 05, France Laboratoire de Physico-Chimie Théorique, Ecole Supérieure de Physique et Chimie de Paris, 10, rue Vauquelin, 75231 Paris Cedex 05, France
J. E. Wesfreid
Affiliation:
Laboratoire d'Hydrodynamique et Mécanique Physique, Ecole Supérieure de Physique et Chimie de Paris, 10, rue Vauquelin, 75231 Paris Cedex 05, France
P. Boudinet
Affiliation:
Laboratoire d'Hydrodynamique et Mécanique Physique, Ecole Supérieure de Physique et Chimie de Paris, 10, rue Vauquelin, 75231 Paris Cedex 05, France
C. Quilliet
Affiliation:
Laboratoire d'Hydrodynamique et Mécanique Physique, Ecole Supérieure de Physique et Chimie de Paris, 10, rue Vauquelin, 75231 Paris Cedex 05, France
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Abstract

We study experimentally and theoretically the evolution of two-dimensional patterns in the Rayleigh—Taylor instability of a thin layer of viscous fluid spread on a solid surface. Various kinds of patterns of different symmetries are observed, with possible transition between patterns, the preferred symmetries being the axial and hexagonal ones. Starting from the lubrication hypothesis, we derive the nonlinear evolution equation of the interface, and the amplitude equation of its Fourier components. The evolution laws of the different patterns are calculated at order two or three, the preferred symmetries being related to the non-invariance of the system by amplitude reflection. We also discuss qualitatively the dripping at final stage of the instability.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 236 , March 1992 , pp. 349 - 383
Copyright
© 1992 Cambridge University Press

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