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Instabilities of three-dimensional viscous falling films

Published online by Cambridge University Press:  26 April 2006

S. W. Joo  and
S. H. Davis
S. W. Joo
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA Department of Mechanical Engineering, Wayne State University, Detroit, MI 48202, USA.
S. H. Davis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
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Abstract

A long-wave evolution equation is used to study a falling film on a vertical plate. For certain wavenumbers there exists a two-dimensional strongly nonlinear permanent wave. A new secondary instability is identified in which the three-dimensional disturbance is spatially synchronous with the two-dimensional wave. The instability grows for sufficiently small cross-stream wavenumbers and does not require a threshold amplitude; the two-dimensional wave is always unstable. In addition, the nonlinear evolution of three-dimensional layers is studied by posing various initial-value problems and numerically integrating the long-wave evolution equation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 242 , September 1992 , pp. 529 - 547
Copyright
© 1992 Cambridge University Press

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