### 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 language | English (US) |
---|---|

Pages (from-to) | 329-352 |

Number of pages | 24 |

Journal | Journal of Fluid Mechanics |

Volume | 187 |

State | Published - Feb 1988 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Fluid Mechanics*,

*187*, 329-352.

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

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, vol. 187, pp. 329-352.

}

TY - JOUR

T1 - THREE-DIMENSIONAL RAYLEIGH-TAYLOR INSTABILITY. PART 1. WEAKLY NONLINEAR THEORY.

AU - Jacobs, Jeffrey W

AU - Catton, I.

PY - 1988/2

Y1 - 1988/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0023960581&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023960581&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0023960581

VL - 187

SP - 329

EP - 352

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -