Inviscid interaction of vortex rings: approach to singularity?

¹ Bldg. 1302, Code 8233 Naval Undersea Warfare Center Newport, RI 02841 USA
² Department of Mechanical Engineering & Institute of Hydraulic Research The University of Iowa Iowa City, IA 52242 USA

Abstract

The interaction of two vortex rings in an inviscid fluid is investigated numerically using a Lagrangian vorticity method. This method uses interpolation based on Delaunay triangulation of the computational points. The calculational results indicate that this method is well-suited to the computation of these and similar cases. In particular, one of the most useful features of the method in this context is the ability to refine the resolution of the flow as vorticity is concentrated onto increasingly small scales. Such concentration, along with increase in the maximum norm of the vorticity, is a prominent feature of the computed interaction. Two cases are presented. Analysis of the results from one case shows that through the first 80% of the interaction, the growth in the maximum norm is approximately exponential. Later the flow appears to undergo a transition to a new regime not inconsistent with a growth proportional to 1/(tc - t). However, the present calculations are not sufficiently long to confirm this behavior.