Lagrangian Theory for 3D Vortex Sheets with Axial or Helical Symmetry

Russel E. Caflisch; Xiao Fan Li

doi:10.1080/00411459208203798

Lagrangian Theory for 3D Vortex Sheets with Axial or Helical Symmetry

Russel E. Caflisch, Xiao Fan Li

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Consider a three-dimensional vortex sheet in inviscid, incompressible flow which is irrotational away from the sheet. We derive an equation for the evolution of a vortex sheet in Lagrangian coordinates, i.e. an equation that is restricted to the sheet itself and is analogous to the Birkhoff-Rott equation for a two-dimensional (planar) sheet. This general equation is specialized to sheets with axial or helical symmetry, with or without swirl.

Original language	English (US)
Pages (from-to)	559-578
Number of pages	20
Journal	Transport Theory and Statistical Physics
Volume	21
Issue number	4-6
DOIs	https://doi.org/10.1080/00411459208203798
State	Published - Aug 1 1992

ASJC Scopus subject areas

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

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10.1080/00411459208203798

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abstract = "Consider a three-dimensional vortex sheet in inviscid, incompressible flow which is irrotational away from the sheet. We derive an equation for the evolution of a vortex sheet in Lagrangian coordinates, i.e. an equation that is restricted to the sheet itself and is analogous to the Birkhoff-Rott equation for a two-dimensional (planar) sheet. This general equation is specialized to sheets with axial or helical symmetry, with or without swirl.",

author = "Caflisch, {Russel E.} and Li, {Xiao Fan}",

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N2 - Consider a three-dimensional vortex sheet in inviscid, incompressible flow which is irrotational away from the sheet. We derive an equation for the evolution of a vortex sheet in Lagrangian coordinates, i.e. an equation that is restricted to the sheet itself and is analogous to the Birkhoff-Rott equation for a two-dimensional (planar) sheet. This general equation is specialized to sheets with axial or helical symmetry, with or without swirl.

AB - Consider a three-dimensional vortex sheet in inviscid, incompressible flow which is irrotational away from the sheet. We derive an equation for the evolution of a vortex sheet in Lagrangian coordinates, i.e. an equation that is restricted to the sheet itself and is analogous to the Birkhoff-Rott equation for a two-dimensional (planar) sheet. This general equation is specialized to sheets with axial or helical symmetry, with or without swirl.

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Lagrangian Theory for 3D Vortex Sheets with Axial or Helical Symmetry

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