Initial value problem for Rayleigh–Taylor instability of viscous fluids
- 1 October 1978
- journal article
- Published by AIP Publishing in Physics of Fluids
- Vol. 21 (10) , 1674-1687
- https://doi.org/10.1063/1.862107
Abstract
The initial value problem associated with the development of small amplitude disturbances in Rayleigh–Taylor unstable, viscous, incompressible fluids is studied. Solutions to the linearized equations of motion which satisfy general initial conditions are obtained in terms of Fourier–Laplace transforms of the hydrodynamic variables, without restriction on the density or viscosity of either fluid. When the two fluids have equal kinematic viscosities, these transforms can be inverted explicitly to express the fluid variables as integrals of Green’s functions multiplied by initial data. In addition to normal modes, a set of continuum modes, not treated explicitly in the literature, makes an important contribution to the development of the fluid motion.Keywords
This publication has 17 references indexed in Scilit:
- Taylor Instability in a Viscous LiquidPhysics of Fluids, 1966
- On the stability of two superposed fluidsMathematical Proceedings of the Cambridge Philosophical Society, 1965
- The effects of surface tension and viscosity on the stability of two superposed fluidsMathematical Proceedings of the Cambridge Philosophical Society, 1961
- On an initial value problem concerning Taylor instability of incompressible fluidsQuarterly of Applied Mathematics, 1959
- Stability of Oscillations of Superposed FluidsJournal of Applied Physics, 1956
- The Character of the Instability of an Incompressible Fluid of Constant Kinematic Viscosity and Exponentially Varying Density.The Astrophysical Journal, 1955
- The character of the equilibrium of an incompressible heavy viscous fluid of variable densityMathematical Proceedings of the Cambridge Philosophical Society, 1955
- Effects of surface tension and viscosity on Taylor instabilityQuarterly of Applied Mathematics, 1954
- The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. IProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1950
- The Influence of Viscosity on the Oscillations of Superposed FluidsProceedings of the London Mathematical Society, 1908