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On solitary waves running down an inclined plane

Published online by Cambridge University Press:  20 April 2006

A. Pumir ,
P. Manneville  and
Y. Pomeau
A. Pumir
Affiliation:
Division de la physique, CEN-Saclay, 91191 Gif-sur-Yvette, France
P. Manneville
Affiliation:
Division de la physique, CEN-Saclay, 91191 Gif-sur-Yvette, France Permanent address: DPh-G/PRSM, Orme des Merisiers 91191 Gif-sur-Yvette, France.
Y. Pomeau
Affiliation:
Division de la physique, CEN-Saclay, 91191 Gif-sur-Yvette, France
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Abstract

We study the existence and the role of solitary waves in the instability of a fluid layer flowing down an inclined plane. The approach presented is fully nonlinear. Solitary waves steady in a moving frame are described by homoclinic trajectories of an associated ordinary differential equation. They are searched numerically for a given value of viscosity and surface tension. Several kinds of solitary waves can exist, characterized by their number n of humps. We investigate the stability of these waves by integrating the initial-value problem directly. Solitary waves with more than 1 hump did not appear in the simulation, and moreover a catastrophic behaviour took place for too large a Reynolds number (R [gsim ] R*1) or too large an amplitude, suggesting a finite-time singularity. The long-term evolution is shown to be a very slow relaxation to a steady state in a moving frame. The relation to the experimental observation of localized wavetrains is also discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 135 , October 1983 , pp. 27 - 50
Copyright
© 1983 Cambridge University Press

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