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Nonlinear waves in three-dimensional co-current gas–liquid film flow

Published online by Cambridge University Press:  09 June 2026

Wei Xie  and
Zhan Wang Open the ORCID record for Zhan Wang [Opens in a new window]
Wei Xie
Affiliation:
Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, PR China
Zhan Wang*
Affiliation:
Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, PR China State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
*
Corresponding author: Zhan Wang, zwang@imech.ac.cn
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Abstract

We investigate the dynamics of a three-dimensional thin laminar liquid film flowing down an inclined plane, influenced by both gravity and wind forces. The gas phase is modelled using a quasi-laminar approximation, in which viscosity is neglected. We expand Miles’ theory of wind-induced pressure, which previously focused on a one-dimensional interface, to a two-dimensional framework. From this, we derive evolution equations for the liquid film, including Benney-type and Nepomnyashchy-type models that capture the effects of wind on flow instability and wave dispersion. Our findings reveal two families of travelling-wave solutions and their bifurcation structures through numerical continuation. We analyse secondary instabilities using the centre-manifold method and Floquet theory, discovering finite-wavenumber bands in which oblique perturbations are more unstable than longitudinal ones. Based on these secondary-instability characteristics, we propose a classification framework for various flow regimes. Time-dependent numerical simulations support our predictions of secondary instabilities and reveal a range of nonlinear phenomena that occur after their onset. These phenomena include checkerboard-symmetric patterns, strip-like structures, phase-type instabilities and localised wave packets, some of which have been observed experimentally in previous studies.

JFM classification

Interfacial Flows (free surface): Thin films Multiphase and Particle-laden Flows: Gas/liquid flow Waves/Free-surface Flows: Surface gravity waves

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JFM Papers
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Journal of Fluid Mechanics , Volume 1036 , 10 June 2026 , A56
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© The Author(s), 2026. Published by Cambridge University Press

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