NONLINEAR THEORY OF TAYLOR INSTABILITY OF SUPERPOSED FLUIDS OF DIFFERENT DENSITIES IN THREE DIMENSIONS

1 January 1977

journal article
Published by Oxford University Press (OUP) in The Quarterly Journal of Mechanics and Applied Mathematics

Vol. 30 (2) , 131-142
https://doi.org/10.1093/qjmam/30.2.131

Abstract

The problem of three-dimensional instability of superposed fluids of different densities is considered here. The two-dimensional Taylor instability of superposed fluids is extended to the three-dimensional case when the horizontal planform consists of rectangular cells. A third-order nonlinear perturbation theory is given by using the method of strained coordinast for this singular perturbation problem. Marginal stability curves are given for different values of the density ratio. The results for the case of an air-liquid interface are also derived in the Appendix.

Keywords

EQUATION OF MOTION
THREE DIMENSIONAL
THREE DIMENSIONS
POTENTIAL FLOW
PERTURBATION THEORY
NONLINEAR EQUATION

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