Viscous vortices in two- and three-dimensional space (Q1308928)

Recent developments for the interaction, diffusion and merging of incompressible viscous vortices in two- and three-dimensional space are presented. We study the motion and evolution of vorticity fields \(\Omega(t,x)\) with total strength zero, \(\langle\Omega\rangle=0\), which is true for a three-dimensional vorticity field decaying exponentially in \(| x|\) and for a two-dimensional case if \(\langle\Omega\rangle=0\) initially. We called this type of vorticity field a viscous doublet. We show that the long-time behavior of the trajectory of a doublet center in three-dimensional space is different from that in two-dimensional space. Examples are the motion and merging of a slender vortex ring and a two- dimensional vortex pair. For the intersection of two slender filaments (the merging of two segments in a short time interval), a simple model to simulate the merging process and criteria for the reconnection of the filaments after the merging stage is proposed.