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A new upward-convective short-wave instability mode in gas-sheared falling liquid films

Published online by Cambridge University Press:  02 December 2025

Misa Ishimura Open the ORCID record for Misa Ishimura [Opens in a new window] ,
Sophie Mergui Open the ORCID record for Sophie Mergui [Opens in a new window] ,
Christian Ruyer-Quil Open the ORCID record for Christian Ruyer-Quil [Opens in a new window]  and
Georg Friedrich Dietze Open the ORCID record for Georg Friedrich Dietze [Opens in a new window]
Misa Ishimura*
Affiliation:
Department of Mechanical Engineering, Yokohama National University , Kanagawa 240-8501, Japan
Sophie Mergui
Affiliation:
Sorbonne Université, CNRS, FAST, Université Paris-Saclay, Orsay 91405, France
Christian Ruyer-Quil
Affiliation:
CNRS, LOCIE, Université Savoie Mont Blanc, Le Bourget du Lac 73376, France
Georg Friedrich Dietze*
Affiliation:
Université Paris-Saclay, CNRS, FAST, Orsay 91405, France
*
Corresponding authors: Misa Ishimura, ishimura-misa-kx@ynu.ac.jp; Georg Friedrich Dietze, georg.dietze@cnrs.fr
Corresponding authors: Misa Ishimura, ishimura-misa-kx@ynu.ac.jp; Georg Friedrich Dietze, georg.dietze@cnrs.fr
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Abstract

We investigate a short-wave instability mode recently identified via temporal stability analysis in weakly inclined falling liquid films sheared by a confined turbulent counter-current gas flow (Ishimura et al. J. Fluid Mech. vol. 971, 2023, p. A37). We perform spatio-temporal linear stability calculations based on the Navier–Stokes equations in the liquid film and the Reynolds-averaged Navier–Stokes equations in the gas, and compare these with our own experiments. We find that the short-wave instability mode is always upward-convective. The range of unstable group velocities is very wide and largely coincides with negative values of the wave velocity. Turbulence affects this mode both through the level of gas shear stress imparted and via the shape of the primary-flow gas velocity profile. Beyond a critical value of the counter-current gas flow rate, the short-wave mode merges with the long-wave Kapitza instability mode. The thus obtained merged mode is unstable for group velocities spanning from large negative to large positive values, i.e. it is absolute. The onset of the short-wave mode is precipitated by decreasing the channel height and inclination angle, and by increasing the liquid Reynolds number or the gas-to-liquid dynamic viscosity ratio. For vertically falling liquid films, merging occurs before the short-wave mode can become unstable on its own. Nonetheless, the ability to generate upward-travelling ripples is endowed to the merged mode. Preliminary calculations neglecting the linear perturbation of the turbulent viscosity suggest that three-dimensional perturbations could be more unstable than two-dimensional ones.

JFM classification

Interfacial Flows (free surface): Thin films Instability: Absolute/convective instability Multiphase and Particle-laden Flows: Gas/liquid flow

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 1024 , 10 December 2025 , A30
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© The Author(s), 2025. Published by Cambridge University Press

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