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A full-scale numerical study of interfacial instabilities in thin-film flows

Published online by Cambridge University Press:  26 April 2006

B. Ramaswamy ,
S. Chippada  and
S. W. Joo
B. Ramaswamy
Affiliation:
Department of Mechanical and Environmental Engineering, University of California, Santa Barbara CA 93106-5130, USA
S. Chippada
Affiliation:
TICAM, University of Texas, Austin, TX 78712, USA
S. W. Joo
Affiliation:
School of Mechanical Engineering, Yeungnam University, Kyongsan, Korea
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Abstract

Surface wave instabilities in a two-dimensional thin draining film are studied by a direct numerical simulation of the full nonlinear system. A finite element method is used with an arbitrary Lagrangian–Eulerian formulation to handle the moving boundary problem. Both temporal and spatial stability analysis of the finite-amplitude nonlinear wave regimes are done. As the wavenumber is decreased below the linear cut-off wavenumber, supercritical sinusoidal waves occur as reported earlier from weakly nonlinear analysis and experiments. Further reduction in wavenumber makes the Fourier spectrum broad-banded resulting in solitary humps. This transition from nearly sinusoidal permanent waveforms to solitary humps is found to go through a quasi-periodic regime. The phase boundaries for this quasi-periodic regime have been determined through extensive numerical parametric search. Complex wave interaction processes such as wave merging and wave splitting are discussed. In the exhaustive numerical simulations performed in this paper, no wave-breaking tendency was observed, and it is speculated that the complex wave-interaction processes such as wave merging and wave splitting curb the tendency of the film to break.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 325 , 25 October 1996 , pp. 163 - 194
Copyright
© 1996 Cambridge University Press

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