Faraday instability: Linear analysis for viscous fluids
- 1 February 1995
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 51 (2) , 1162-1168
- https://doi.org/10.1103/physreve.51.1162
Abstract
We present a linear stability analysis of parametrically excited surface waves for the case of viscous fluids. We show that the inclusion of viscosity leads to an extension of Mathieu’s differential equation, which is valid for the case of inviscid fluids, in the form of an integrodifferential equation. We numerically solve this equation for the case of a single as well as a double frequency excitation.Keywords
This publication has 5 references indexed in Scilit:
- Parametrically excited quasicrystalline surface wavesPhysical Review E, 1993
- Ordered capillary-wave states: Quasicrystals, hexagons, and radial wavesPhysical Review Letters, 1992
- Order-Disorder Transition in Capillary RipplesPhysical Review Letters, 1989
- The stability of the plane free surface of a liquid in vertical periodic motionProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1954
- XVII. On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfacesPhilosophical Transactions of the Royal Society of London, 1831