Regular and Chaotic Dynamics

, Volume 23, Issue 5, pp 507–518 | Cite as

Generalized Contour Dynamics: A Review

  • Stefan G. Llewellyn SmithEmail author
  • Ching Chang
  • Tianyi Chu
  • Mark Blyth
  • Yuji Hattori
  • Hayder Salman


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.


vortex dynamics contour dynamics vortex patch vortex sheet helical geometry 

MSC2010 numbers

76B47 76W05 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • Stefan G. Llewellyn Smith
    • 1
    • 2
    Email author
  • Ching Chang
    • 1
  • Tianyi Chu
    • 1
  • Mark Blyth
    • 3
  • Yuji Hattori
    • 4
  • Hayder Salman
    • 3
  1. 1.Department of Mechanical and Aerospace EngineeringJacobs School of EngineeringLa JollaUSA
  2. 2.Scripps Institution of OceanographyLa JollaUSA
  3. 3.School of MathematicsUniversity of East Anglia NorwichAngliaUK
  4. 4.Institute of Fluid ScienceTohoku University 2-1-1 KatahiraAoba, SendaiJapan

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