A contour dynamics algorithm for axisymmetric flow

The method of contour dynamics, developed for two-dimensional vortex patches by Zabusky et al. [N.J. Zabusky, M.H. Hughes, K.V. Roberts, Contour dynamics for the Euler equations in two-dimensions, J. Comp. Phys. 30 (1979) 96–106] is extended to vortex rings in which the vorticity distribution varies linearly with normal distance from the symmetry axis. The method tracks the motion of the boundaries of the vorticity regions and hence reduces the dimensionality of the problem by one. We discuss the formulation and implementation of the scheme, verify its accuracy and convergence, and present illustrative examples.