Superconfined falling liquid films: linear versus nonlinear dynamics
Résumé
The effect of a counter-current gas flow on the linear stability of an inclined falling liquidfilm switches from destabilizing to stabilizing, as the flow confinement is increased. Weconfront this linear effect with the response of nonlinear surface waves resulting fromlong-wave interfacial instability. For the strongest confinement studied, the gas flow dampsboth the linear growth rate and the amplitude of nonlinear travelling waves, and this holdsfor waves of the most-amplified frequency and for low-frequency solitary waves. In thelatter case, waves are shaped into elongated humps with a flat top that resist secondaryinstabilities. For intermediate confinement, the linear and nonlinear responses are opposedand can be non-monotonic. The linear growth rate of the most-amplified waves firstdecreases and then increases as the gas velocity is increased, whereas their nonlinearamplitude is first amplified and then damped. Conversely, solitary waves are amplifiedlinearly but damped nonlinearly. For the weakest confinement, solitary waves are proneto two secondary instability modes that are not observed in unconfined falling films. Thefirst involves waves of diminishing amplitude slipstreaming towards their growing leadingneighbours. The second causes wave splitting events that lead to a train of smaller, shorterwaves.
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