Pointed Bubbles Rising in a Two-Dimensional Tube.

Abstract

This document considers a periodic array of plane bubbles rising in a gravity field. This configuration can serve as a model for an advanced stage of Rayleigh-Taylor instability. Vanden-Broeck solved the problem numerically and showed that two classes of solutions are possible. One class is characterized by a bubble profile with a continuous slope at the apex of the bubble whereas the other is characterized by the presence of a cusp at the apex. In a recent paper Garabedian and Modi conjectured that solutions with a 120 deg. angle at the apex might also exist. In this paper a scheme is presented to compute such solutions. It is found that a solution exists at a unique Froude number of 0.36. This result does not support Garabedian's conjecture that bubbles with a 120 deg. angle at the apex exist for all values of F between 0.23 and 0.36. Keywords: Free surface flow.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1985
Accession Number
ADA163624

Entities

People

  • Jean-marc Vanden-broeck

Organizations

  • University of Wisconsin–Madison

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  • Air Platforms

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  • Froude Number
  • Instability
  • Instructions
  • Mathematics
  • Military Research
  • Nonlinear Algebraic Equations
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  • Rayleigh Taylor Instability
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  • Surface Tension
  • Two Dimensional
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  • Fluid Dynamics.