STABILITY OF LIQUID FLOW DOWN AN INCLINED PLANE
- 31 December 1962
- journal article
- research article
- Published by AIP Publishing in Physics of Fluids
- Vol. 6 (3), 321-334
- https://doi.org/10.1063/1.1706737
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 four cases (surface tension = 0 or ≠ 0 and angle of plate inclination = or <½π) are depicted. The effect of variability of surface tension is briefly assessed.This publication has 3 references indexed in Scilit:
- Wave formation in laminar flow down an inclined planeJournal of Fluid Mechanics, 1957
- Experiments on the onset of wave formation on a film of water flowing down a vertical planeJournal of Fluid Mechanics, 1957
- Stability of two-dimensional parallel flows for three-dimensional disturbancesQuarterly of Applied Mathematics, 1955