TY - JOUR
T1 - Generalized Contour Dynamics
T2 - A Review
AU - Llewellyn Smith, Stefan G.
AU - Chang, Ching
AU - Chu, Tianyi
AU - Blyth, Mark
AU - Hattori, Yuji
AU - Salman, Hayder
N1 - Funding Information:
Part of this research was supported by NSF Award CBET-1706934. Support from Collaborative Research Project 2017 and 2018, Institute of Fluid Science, Tohoku University, Project Codes J16R004 and J17R004 is also acknowledged.
Publisher Copyright:
© 2018, Pleiades Publishing, Ltd.
PY - 2018/9/1
Y1 - 2018/9/1
N2 - 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.
AB - 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.
KW - contour dynamics
KW - helical geometry
KW - vortex dynamics
KW - vortex patch
KW - vortex sheet
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U2 - 10.1134/S1560354718050027
DO - 10.1134/S1560354718050027
M3 - Article
AN - SCOPUS:85054667244
VL - 23
SP - 507
EP - 518
JO - Regular and Chaotic Dynamics
JF - Regular and Chaotic Dynamics
SN - 1560-3547
IS - 5
ER -