Three-dimensional rayleigh-taylor instability part 1. weakly nonlinear theory

J. W. Jacobs, I. Catton

Research output: Contribution to journalArticle

98 Scopus citations

Abstract

Three-dimensional weakly nonlinear Rayleigh-Taylor instability is analysed. The stability of a confined inviscid liquid and an overlying gas with density much lessthan that of the liquid is considered. An asymptotic solution for containers of arbitrary cross-sectional geometry, valid up to order e3 (where E is the root-meansquared 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.

Original languageEnglish (US)
Pages (from-to)329-352
Number of pages24
JournalJournal of Fluid Mechanics
Volume187
DOIs
StatePublished - Feb 1988
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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