Stefan Llewellyn Smith
9500 Gilman Drive, La Jolla CA 920930411, USA
Department of Mechanical and Aerospace Engineering, University of California
Publications:
Llewellyn Smith S. G., Chang C., Chu T., Blyth M., Hattori Y., Salman H.
Generalized Contour Dynamics: A Review
2018, vol. 23, no. 5, pp. 507518
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 bestknown 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 timedependent vortex sheets on the boundaries, whose
evolution must be computed as part of the problem. The nonBoussinesq 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.

Llewellyn Smith S. G., Nagem R. J.
Vortex Pairs and Dipoles
2013, vol. 18, no. 12, pp. 194201
Abstract
Point vortices have been extensively studied in vortex dynamics. The generalization to higher singularities, starting with vortex dipoles, is not so well understood.We obtain a family of equations of motion for inviscid vortex dipoles and discuss limitations of the concept.We then investigate viscous vortex dipoles, using two different formulations to obtain their propagation velocity. We also derive an integrodifferential for the motion of a viscous vortex dipole parallel to a straight boundary.
