The vortex ring merger problem at infinite reynolds number

Abstract

Abstract : The physics of three-dimensional incompressible fluid flow, as is well known, is an extremely difficult and not well understood subject. The mathematical theory of the Navier-Stokes and the Euler equations is incomplete and a detailed qualitative understanding of the dynamics is, for the most part, lacking. One focus of recent research which aims at an understanding of key features of turbulence and of the possible breakdown in regularity of solutions of the fluid equations has been on the motion of vortex filaments. Motivations for the study of vortex filaments are the prevalence of thin vortex tubes in experimentally observed flows, the fact that the Euler equations can be thought of as an evolution equation for a continuum of interacting vortex filaments, and a view of turbulence as being characterized by wildly stretching and dissipating vortex filaments. A vortex flow problem which has been the subject interesting laboratory and numerical experiments is the vortex ring merger problem. In this problem the evolution over a short interval of time of two initially parallel (or slightly inclined) co-rotating vortex rings of the same strength is studied. The rings are observed to come together and reconnect, in the sense that much of the vorticity field becomes composed of vortex lines which join the two initially distinct vortex rings. This merger occurs on a timescale which is much shorter than that expected from a simple dimensional analysis based on the magnitude of viscosity and on the vortex ring radius.(kr)