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

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Bibliographic Details
Title: Nonlinear waves in three-dimensional co-current gas-liquid film flow.
Authors: Xie, Wei1,2, Wang, Zhan1,2,3 zwang@imech.ac.cn
Source: Journal of Fluid Mechanics. 6/10/2026, Vol. 1036, p1-43. 43p.
Subjects: Nonlinear waves, Three-dimensional flow, Liquid films, Wind pressure, Gas-liquid interfaces, Flow instability, Traveling waves (Physics)
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. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
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. [ABSTRACT FROM AUTHOR]
ISSN:00221120
DOI:10.1017/jfm.2026.11667