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 liquid
film switches from destabilizing to stabilizing, as the flow confinement is increased. We
confront this linear effect with the response of nonlinear surface waves resulting from
long-wave interfacial instability. For the strongest confinement studied, the gas flow damps
both the linear growth rate and the amplitude of nonlinear travelling waves, and this holds
for waves of the most-amplified frequency and for low-frequency solitary waves. In the
latter case, waves are shaped into elongated humps with a flat top that resist secondary
instabilities. For intermediate confinement, the linear and nonlinear responses are opposed
and can be non-monotonic. The linear growth rate of the most-amplified waves first
decreases and then increases as the gas velocity is increased, whereas their nonlinear
amplitude is first amplified and then damped. Conversely, solitary waves are amplified
linearly but damped nonlinearly. For the weakest confinement, solitary waves are prone
to two secondary instability modes that are not observed in unconfined falling films. The
first involves waves of diminishing amplitude slipstreaming towards their growing leading
neighbours. The second causes wave splitting events that lead to a train of smaller, shorter
waves.
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