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Three-dimensional Rayleigh-Taylor instability Part 1. Weakly nonlinear theory

Published online by Cambridge University Press:  21 April 2006

J. W. Jacobs  and
I. Catton
J. W. Jacobs
Affiliation:
Department of Mechanical, Aerospace and Nuclear Engineering, University of California, Los Angeles, CA 90024, USA Present address: California Institute of Technology, Pasadena, CA 91125, USA.
I. Catton
Affiliation:
Department of Mechanical, Aerospace and Nuclear Engineering, University of California, Los Angeles, CA 90024, USA
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Abstract

Three-dimensional weakly nonlinear Rayleigh-Taylor instability is analysed. The stability of a confined inviscid liquid and an overlying gas with density much less than that of the liquid is considered. An asymptotic solution for containers of arbitrary cross-sectional geometry, valid up to order ε3 (where ε is the root-mean-squared initial surface slope) is obtained. The solution is evaluated for the rectangular and circular geometries and for various initial modes (square, hexagonal, axisymmetric, etc.). It is found that the hexagonal and axisymmetric instabilities grow faster than any other shapes in their respective geometries. In addition it is found that, sufficiently below the cutoff wavenumber, instabilities that are equally proportioned in the lateral directions grow faster than those with longer, thinner shape. However, near the cutoff wavenumber this trend reverses with instabilities having zero aspect ratio growing faster than those with aspect ratio near 1.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 187 , February 1988 , pp. 329 - 352
Copyright
© 1988 Cambridge University Press

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