THREE-DIMENSIONAL RAYLEIGH-TAYLOR INSTABILITY. PART 1. WEAKLY NONLINEAR THEORY.

Jeffrey W Jacobs, I. Catton

Research output: Contribution to journalArticle

91 Citations (Scopus)

Abstract

Three-dimensional weakly nonlinear Rayleigh-Taylor instability is analyzed. 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 epsilon **3 (where epsilon 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 instabilitie grow faster than any other shapes in their respective geometries. In addition it is found that, sufficiently below the cutoff wavenumber, instabiilties 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
StatePublished - Feb 1988
Externally publishedYes

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Taylor instability
Geometry
aspect ratio
Aspect ratio
cut-off
geometry
Liquids
liquids
containers
Containers
slopes
trends
Gases
gases

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

THREE-DIMENSIONAL RAYLEIGH-TAYLOR INSTABILITY. PART 1. WEAKLY NONLINEAR THEORY. / Jacobs, Jeffrey W; Catton, I.

In: Journal of Fluid Mechanics, Vol. 187, 02.1988, p. 329-352.

Research output: Contribution to journalArticle

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