Contents | PDF file (193 KB)

ESAIM: Proceedings, Vol. 7, 1999, 183-194
Third International Workshop on Vortex Flows
and Related Numerical Methods
http://www.emath.fr/proc/Vol.7/

Inviscid Interaction of Vortex Rings: Approach to Singularity?

John R. Grant
Bldg. 1302, Code 8233
Naval Undersea Warfare Center
Newport, RI 02841 USA

Jeffrey S. Marshall
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.
 
Contents | PDF file (193 KB)