Quantification of the inelastic interaction of unequal vortices in two-dimensional vortex dynamics

Abstract

The interaction of two isolated vortices having uniform vorticity is examined in detailed contour dynamics calculations, and quantified using a diagnostic that measures the coherence of the final state. The two vortices have identical vorticity, leaving two basic parameters that determine the evolution: the radius ratio and separation distance. It is found that the term ‘‘vortex merger’’ inadequately describes the general interaction that takes place. Five regimes are found: (1) elastic interaction, (2) partial straining-out, (3) complete straining-out, (4) partial merger, and (5) complete merger. Regime 5 is what used to be called ‘‘merger,’’ but occurs in less than one-quarter of the parameter space. Contrary to popular belief, inelastic vortex interactions (IVI’s) do not always lead to vortex growth. In fact, in over half of the parameter space, smaller vortices are produced. These results bring into question commonly accepted ideas about nearly inviscid two-dimensional turbulence.