Meng, Yanghan;
Papageorgiou, Demetrios T;
Vanden-Broeck, Jean-Marc;
(2025)
Dynamics of nonlinear air-blown waves on falling viscous liquid films.
Journal of Fluid Mechanics
, 1018
, Article A49. 10.1017/jfm.2025.10560.
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Abstract
The dynamics of thin viscous liquid films flowing down an inclined wall under gravity in the presence of an upward flowing high-speed air stream is considered. The air stream induces nonlinear waves on the interface and asymptotic solutions are developed to derive a non-local evolution equation forced by the air pressure which is obtained analytically, and incorporating a constant tangential stress. Benney equations in the capillary (strong surface tension) and inertio-capillary regimes are derived and studied. The air stream produces Turing-type short wave instabilities in sub-critical Reynolds number regimes that would be stable in the absence of the outer flow. Extensive numerical experiments are carried out to elucidate the rich dynamics in the above-mentioned short-wave regime. The stability of different branches of solutions of non-uniform steady states is carried out, along with time-dependent nonlinear computations that are used to track the large-time behaviour of attractors. A fairly complete picture of different solution types are categorised in parameter space. The effect of the Reynolds number on the wave characteristics in the inertiocapillary regime is also investigated. It is observed that, for each value of the slenderness parameter δ, there exists a critical Reynolds number Rc above which the solutions become unbounded by encountering finite-time singularities. Increasing the air speed significantly decreases Rc, making the system more prone to large amplitude singular events even at low Reynolds numbers when the system would have been stable in the absence of the air stream.
| Type: | Article |
|---|---|
| Title: | Dynamics of nonlinear air-blown waves on falling viscous liquid films |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1017/jfm.2025.10560 |
| Publisher version: | https://doi.org/10.1017/jfm.2025.10560 |
| Language: | English |
| Additional information: | © The Author(s), 2025. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/ licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited. |
| Keywords: | interfacial flows (free surface), thin films, shallow water flows |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10214246 |
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