Singularity formation during Rayleigh-Taylor instability

Gregory Baker, Russel Caflisch, Michael Siegel

Research output: Contribution to journalArticle

Abstract

During the motion of a fluid interface undergoing Rayleigh-Taylor instability, vorticity is generated on the interface baronclinically. This vorticity is then subject to Kelvin-Helmholtz instability. For the related problem of evolution of a nearly flat vortex sheet without density stratification (and with viscosity and surface tension neglected), Kelvin-Helmholtz instability has been shown to lead to development of curvature singularities in the sheet. In this paper, a simple approximate theory is developed for Rayleigh-Taylor instability as a generalization of Moore's approximation for vortex sheets. For the approximate theory, a family of exact solutions is found for which singularities develop on the fluid interface. The resulting predictions for the time and type of the singularity are directly verified by numerical computation of the full equations. These computations are performed using a point vortex method, and singularities for the numerical solution are detected using a form fit for the Fourier components at high wavenumber. Excellent agreement between the theoretical predictions and the numerical results is demonstrated for small to medium values of the Atwood number A, i.e. for A between 0 and approximately 0.9. For A near 1, however, the singularities actually slow down when close to the real axis. In particular, for A = 1, the numerical evidence suggests that the singularities do not reach the real axis in finite time.

Original languageEnglish (US)
Pages (from-to)51-78
Number of pages28
JournalJournal of Fluid Mechanics
Volume252
Issue number4
DOIs
StatePublished - 1993

Fingerprint

Taylor instability
Vortex flow
Vorticity
vortex sheets
Kelvin-Helmholtz instability
vorticity
Fluids
Surface tension
fluids
Viscosity
predictions
stratification
interfacial tension
curvature
vortices
viscosity
approximation

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Singularity formation during Rayleigh-Taylor instability. / Baker, Gregory; Caflisch, Russel; Siegel, Michael.

In: Journal of Fluid Mechanics, Vol. 252, No. 4, 1993, p. 51-78.

Research output: Contribution to journalArticle

Baker, Gregory ; Caflisch, Russel ; Siegel, Michael. / Singularity formation during Rayleigh-Taylor instability. In: Journal of Fluid Mechanics. 1993 ; Vol. 252, No. 4. pp. 51-78.
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