Instabilities of three-dimensional viscous falling films
- 1 September 1992
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 242, 529-547
- https://doi.org/10.1017/s0022112092002489
Abstract
A long-wave evolution equation is used to study a falling film on a vertical plate. For certain wavenumbers there exists a two-dimensional strongly nonlinear permanent wave. A new secondary instability is identified in which the three-dimensional disturbance is spatially synchronous with the two-dimensional wave. The instability grows for sufficiently small cross-stream wavenumbers and does not require a threshold amplitude; the two-dimensional wave is always unstable. In addition, the nonlinear evolution of three-dimensional layers is studied by posing various initial-value problems and numerically integrating the long-wave evolution equation.Keywords
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