Singularities in the Classical Rayleigh-Taylor Flow: Formation and Subsequent Motion

Abstract

This paper is concerned with the creation and subsequent motion of singularities of solution to classical Rayleigh-Taylor flow (two-dimensional inviscid, incompressible fluid over a vacuum). For a specific set of initial conditions, The author gives analytical evidence to suggest the instantaneous formation of one or more singularity(ies) specific point(s) in the unphysical plane, whose locations depend sensitively to small changes in initial conditions in the physical domain. One-half power singularities are created in accordance with an earlier conjecture; however, depending on initial conditions, other forms of singularities also are possible. For a specific initial condition, they follow a numerical procedure in the unphysical plane to compute the motion of a one-half singularity. This computation confirms their previous conjecture that the approach of a one-half singularity towards the physical domain corresponds to the development of a spike at the physical interface. Under some assumptions that appear to be consistent with numerical calculations, they present analytical evidence to suggest that a singularity of the one-half type cannot impinge the physical domain in finite time.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1992
Accession Number
ADA255609

Entities

People

  • S. Tanveer

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Aeronautics
  • Analytic Functions
  • Boundaries
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Differential Equations
  • Engineering
  • Equations
  • Flow
  • Fluid Dynamics
  • Integrals
  • Mathematics
  • Power Series
  • Two Dimensional
  • Water Waves

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Dynamics.