The Collapse of an Axi-Symmetric, Swirling Vortex Sheet

Russel Caflisch, L. Xiaofan, Michael Shelley

Research output: Contribution to journalArticle

Abstract

An axi-symmetric and swirling vortex sheet is investigated as the simplest flow in which there is non-trivial vortex stretching and as a possible setting for studying vortex cancellation and singularity formation. Rayleigh’s criterion indicates linear stability of a single sheet but instability for other configurations of sheets. Due to the simplicity of vortex sheet problems, the linear modes and growth rates (or frequencies) can be explicitly expressed. Subsequent nonlinear evolution is numerically simulated using a vortex method. The numerical results for an axi-symmetric swirling sheet with a vortex line along the axis of symmetry show detachment of a vortex ring from the sheet into the outer fluid, and collapse of the sheet onto the. vortex line at some points. Vortex cancellation, which in the presence of viscosity would likely lead to vortex line reconnection, seems to occur in both of these phenomena. The evolution of two co-axial, axi-symmetric, swirling vortex sheets is similar.

Original languageEnglish (US)
Pages (from-to)1093-1114
Number of pages22
JournalNonlinearity
Volume6
Issue number6
DOIs
StatePublished - 1993

Fingerprint

vortex sheets
Vortex Sheet
swirling
Vortex
Vortex flow
vortices
Cancellation
Line
cancellation
Vortex Method
Vortex Ring
Coaxial
Linear Stability
vortex rings
Rayleigh
detachment
Simplicity
Viscosity
Likely
Singularity

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

The Collapse of an Axi-Symmetric, Swirling Vortex Sheet. / Caflisch, Russel; Xiaofan, L.; Shelley, Michael.

In: Nonlinearity, Vol. 6, No. 6, 1993, p. 1093-1114.

Research output: Contribution to journalArticle

Caflisch, R, Xiaofan, L & Shelley, M 1993, 'The Collapse of an Axi-Symmetric, Swirling Vortex Sheet', Nonlinearity, vol. 6, no. 6, pp. 1093-1114. https://doi.org/10.1088/0951-7715/6/6/001
Caflisch, Russel ; Xiaofan, L. ; Shelley, Michael. / The Collapse of an Axi-Symmetric, Swirling Vortex Sheet. In: Nonlinearity. 1993 ; Vol. 6, No. 6. pp. 1093-1114.
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