Generalized contour dynamics: A review

TitleGeneralized contour dynamics: A review
Publication TypeJournal Article
Year of Publication2018
AuthorsSmith SGL, Chang C., Chu T.Y, Blyth M., Hattori Y., Salman H.
Volume23
Pagination507-518
Date Published2018/09
Type of ArticleReview
ISBN Number1560-3547
Accession NumberWOS:000447268600002
Keywords2 dimensions; contour dynamics; euler equations; evolution; flow; geometry; helical; instability; magnetic eddies; Mathematics; mechanics; numerical algorithms; physics; simulations; vortex dynamics; vortex patch; vortex sheet; vortices
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.

DOI10.1134/s1560354718050027
Student Publication: 
No
sharknado