Nonlinear waves in a sheared liquid film on a horizontal plane at small Reynolds numbers

The nonlinear waves in a sheared liquid film on a horizontal plate at small Reynolds numbers are examined by theoretical and numerical approaches. The analysis employs the long-wave approximation along with finite difference schemes. The results show that the surface tension can suppress disturbance...

Full description

Saved in:
Bibliographic Details
Published in:Journal of fluid mechanics 2024-11, Vol.999, Article A14
Main Authors: Hu, Kai-Xin, Du, Kang, Chen, Qi-Sheng
Format: Article
Language:English
Subjects:
Approximation
Cooling
Disturbances
Finite difference method
Fluid flow
Gas flow
Gravitational effects
Gravity
Gravity effects
Interface stability
Investigations
JFM Papers
Mathematical analysis
Nonlinear waves
Oscillations
Parameter sensitivity
Quasi-Periodic Oscillations
Reynolds number
Shear stress
Solitary waves
Surface tension
Thin films
Traveling waves
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The nonlinear waves in a sheared liquid film on a horizontal plate at small Reynolds numbers are examined by theoretical and numerical approaches. The analysis employs the long-wave approximation along with finite difference schemes. The results show that the surface tension can suppress disturbances and prevent the occurrence of singularities. While the film flow is driven by the shear stress on the interface, its instability highly depends on the magnitude and direction of gravity. Specifically, when the direction of gravity is opposite to the wall-normal direction, perturbations are stabilized by gravity. In contrast, when these two directions are the same, the gravitational force is destabilizing, and stationary travelling waves can exist if a balance is reached between the effects of gravity and surface tension. For the steady solitary waves, there are quasi-periodic oscillations occurring between two stationary points, indicating the presence of heteroclinic trajectories. For periodic waves, the evolutions are sensitive to several parameters and initial disturbances, while one steady-state wave exhibits a sine function-like behaviour.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2024.895