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Viscoelastic behaviour of cellular solutions to the Kuramoto-Sivashinsky model

Published online by Cambridge University Press:  21 April 2006

Uriel Frisch ,
Zhen Su She  and
Olivier Thual
Uriel Frisch
Affiliation:
CNRS, Observatoire de Nice, B.P. 139, 06003 NICE Cedex. France
Zhen Su She
Affiliation:
Observatoire de Meudon, 92195 MEUDON Principal Cedex, France and Observatoire de Nice, B.P. 139, 06003 NICE Cedex. France
Olivier Thual
Affiliation:
CNRM, 42 avenue Coriolis, 31057 TOULOUSE Cedex. France
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Abstract

A multiple-scale analysis of the Kuramoto-Sivashinsky one-dimensional model of a flame front with 2π-periodic boundary conditions is presented. For arbitrary large values of the number M of linearly unstable modes there exist stable steady solutions of period 2π/N where N = O(M). These ‘cellular solutions’ exhibit elastic behaviour under perturbations of wavelength much larger than 2π/N. The results are illustrated by numerical experiments. Elasticity has its origin in the translation and Galilean invariances. Similar invariance properties are likely to be at the root of the viscoelastic behaviour of turbulent flows conjectured by many authors.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 168 , July 1986 , pp. 221 - 240
Copyright
© 1986 Cambridge University Press

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