Stability of Liquid Flow down an Inclined Plane
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In this paper, the stability of a liquid layer flowing down an inclined plane is investigated, and a new perturbation method is used to furnish information regarding stability of surface waves for three cases: the case of small wavenumbers, of small Reynolds numbers, and of large wavenifications.Abstract:
The stability of a liquid layer flowing down an inclined plane is investigated. A new perturbation method is used to furnish information regarding stability of surface waves for three cases: the case of small wavenumbers, of small Reynolds numbers, and of large wavenumbers. The results for small wavenumbers agree with Benjamin's result obtained by the use of power series expansion, and the results for the two other cases are new. The results for large wavenumbers, zero surface tension, and vertical plate contradict the tentative assertion of Benjamin. The three cases are then re‐examined for shear‐wave stability, and the results compared with those for confined plane Poiseuille flow. The comparison serves to indicate the vestiges of shear waves in the free‐surface flow, and to give a sense of unity in the understanding of the stability of both flows. The case of large wavenumbers also serves as a new example of the dual role of viscosity in stability phenomena.The topological features of the ci curves for...read more
Citations
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References
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Book
Conduction of Heat in Solids
H. S. Carslaw,John Conrad Jaeger +1 more
TL;DR: In this paper, a classic account describes the known exact solutions of problems of heat flow, with detailed discussion of all the most important boundary value problems, including boundary value maximization.
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Wave formation in laminar flow down an inclined plane
TL;DR: In this article, it was shown that a class of undamped waves exists for all finite values of the Reynolds number R, and that the rates of amplification of unstable waves become very small when R is made fairly small, and their wavelengths to become very large; this provides a satisfactory explanation for the apparent absence of waves in some experimental observations.
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Stability of two-dimensional parallel flows for three-dimensional disturbances
Journal ArticleDOI
Experiments on the onset of wave formation on a film of water flowing down a vertical plane
TL;DR: In this article, the supply of water to the outside of a long vertical tube was adjusted until the water film was seen to be only just disturbed by a train of travelling waves.