Generalized Contour Dynamics: A Review

Stefan G. Llewellyn Smith, Ching Chang, Tianyi Chu, Mark Blyth, Yuji Hattori, Hayder Salman

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Contour dynamics is a computational technique to solve for the motion of vortices in incompressible inviscid flow. It is a Lagrangian technique in which the motion of contours is followed, and the velocity field moving the contours can be computed as integrals along the contours. Its best-known examples are in two dimensions, for which the vorticity between contours is taken to be constant and the vortices are vortex patches, and in axisymmetric flow for which the vorticity varies linearly with distance from the axis of symmetry. This review discusses generalizations that incorporate additional physics, in particular, buoyancy effects and magnetic fields, that take specific forms inside the vortices and preserve the contour dynamics structure. The extra physics can lead to time-dependent vortex sheets on the boundaries, whose evolution must be computed as part of the problem. The non-Boussinesq case, in which density differences can be important, leads to a coupled system for the evolution of both mean interfacial velocity and vortex sheet strength. Helical geometry is also discussed, in which two quantities are materially conserved and whose evolution governs the flow.

Original languageEnglish
Pages (from-to)507-518
Number of pages12
JournalRegular and Chaotic Dynamics
Volume23
Issue number5
DOIs
Publication statusPublished - 2018 Sep 1

Keywords

  • contour dynamics
  • helical geometry
  • vortex dynamics
  • vortex patch
  • vortex sheet

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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    Llewellyn Smith, S. G., Chang, C., Chu, T., Blyth, M., Hattori, Y., & Salman, H. (2018). Generalized Contour Dynamics: A Review. Regular and Chaotic Dynamics, 23(5), 507-518. https://doi.org/10.1134/S1560354718050027