Generalized Contour Dynamics: A Review

Llewellyn-Smith, Stefan, Chang, Ching, Chu, Tianyi, Blyth, Mark, Hattori, Yuji and Salman, Hayder (2018) Generalized Contour Dynamics: A Review. Regular and Chaotic Dynamics, 23 (5). pp. 507-518. ISSN 1468-4845

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    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.

    Item Type: Article
    Uncontrolled Keywords: vortex dynamics,contour dynamics,vortex patch,vortex sheet,helical geometry
    Faculty \ School: Faculty of Science > School of Mathematics
    Depositing User: LivePure Connector
    Date Deposited: 12 Sep 2018 12:32
    Last Modified: 12 Feb 2019 00:52
    DOI: 10.1134/S1560354718050027

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