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Three-dimensional instabilities of quasi-solitary waves in a falling liquid film

Published online by Cambridge University Press:  29 September 2014

N. Kofman ,
S. Mergui  and
C. Ruyer-Quil
N. Kofman
Affiliation:
UPMC Université Paris 06, Université Paris-Sud, CNRS, laboratoire FAST, bâtiment 502, Campus universitaire, Orsay F-91405, France
S. Mergui*
Affiliation:
UPMC Université Paris 06, Université Paris-Sud, CNRS, laboratoire FAST, bâtiment 502, Campus universitaire, Orsay F-91405, France
C. Ruyer-Quil
Affiliation:
Université de Savoie, CNRS, laboratoire LOCIE, Savoie Technolac, Le Bourget du Lac 73376 CEDEX, France Institut Universitaire de France (IUF), France
*
†Email address for correspondence: [email protected]
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Abstract

The stability of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\gamma _2$ travelling waves at the surface of a film flow down an inclined plane is considered experimentally and numerically. These waves are fast, one-humped and quasi-solitary. They undergo a three-dimensional secondary instability if the flow rate (or Reynolds number) is sufficiently high. Rugged or scallop wave patterns are generated by the interplay between a short-wave and a long-wave instability mode. The short-wave mode arises in the capillary region of the wave, with a mechanism of capillary origin which is similar to the Rayleigh–Plateau instability, whereas the long-wave mode deforms the entire wave and is triggered by a Rayleigh–Taylor instability. Rugged waves are observed at relatively small inclination angles. At larger angles, the long-wave mode predominates and scallop waves are observed. For a water film the transition between rugged and scallop waves occurs for an inclination angle around 12°.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Waves/Free-surface Flows: Solitary waves Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 757 , 25 October 2014 , pp. 854 - 887
Copyright
© 2014 Cambridge University Press 

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