The character of the equilibrium of an incompressible heavy viscous fluid of variable density
- 1 January 1955
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 51 (1) , 162-178
- https://doi.org/10.1017/s0305004100030048
Abstract
This paper is devoted to a consideration of the following problem: Given a static state in which an incompressible viscous fluid is arranged in horizontal strata and the density is a function of the vertical coordinate only, to determine the initial manner of development of an infinitesimal disturbance. The mathematical problem is reduced to one in characteristic values in a fourth-order differential equation and a variational principle characterizing the solution is enunciated. The particular case of two uniform fluids of different densities (but the same kinematic viscosity) separated by a horizontal boundary is considered in some detail. The mode of maximum instability in case the upper fluid is more dense and the manner of decay in case the lower fluid is more dense are determined; and the results of the calculations are illustrated graphically. Gravity waves (obtained in the limit when the density of the upper fluid is zero) are also treated.Keywords
This publication has 5 references indexed in Scilit:
- The character of the equilibrium of an incompressible heavy viscous fluid of variable density: an approximate theoryMathematical Proceedings of the Cambridge Philosophical Society, 1955
- The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. IIProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1950
- 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
- Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable DensityProceedings of the London Mathematical Society, 1882