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 strainingout, (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.

A Case Study of the Merging of Two Misocyclones in the TOMACS Field Campaign Area of Tokyo on 26 August 2011

“…Before the merger, the radius of MC-A was 0.78 km and that of MC-B 0.48 km, and the distance between the two misocyclones was 1.8 km at 15:08 JST. Using these values and the method of Dritschel and Waugh (1992), we estimated that the diameter after the merger should be approximately 1.05 times that before the merger. By comparison, the observed diameter of MC-A at 15:08 JST (before the merger) was 1.55 km, and at 15:14 JST (after the merger) it was 1.45 km; thus, the diameter after the merger was about 0.94 times that before the merger, slightly less than the diameter estimated by the method of Dritschel and Waugh (1992).…”

“…We applied the method of Dritschel and Waugh (1992), who used two-dimensional vortex dynamics to predict the vortex radius following a merger from the ratio of the two pre-merger vortex radiuses and the distance between them before the merger, to estimate the radius of the vortex resulting from the merger. Before the merger, the radius of MC-A was 0.78 km and that of MC-B 0.48 km, and the distance between the two misocyclones was 1.8 km at 15:08 JST.…”

Evaluation of a reduced model for investigating hurricane formation from turbulence

“…The snapshots illustrate distinct stages of the transformation from turbulence to hurricane, but do not tell the complete story. The early stage involves 2D processes of self-organization, such as the coalescence of like-sign vorticity through mergers and more subtle mechanisms (Melander et al, 1988;Carnevale et al, 1991;Dritschel and Waugh, 1992;Lansky et al, 1997;Dubin, 1999,2001;Schecter, 2003). Mesoscale cyclones progressively dominate anticyclones.…”

Asymmetric vortex merger: mechanism and criterion

“…For the purposes of this study, t * de,2 is estimated using the velocity gradient tensor [3]. We consider the classifications developed for inviscid asymmetric vortex interactions [12,5] All interactions eventually result in a single vortex. In complete merger, the circulation of the final compound vortex is greater than that of either original vortex.…”

“…In the more general interaction of two unequal size and/or strength (asymmetric) vortices, there is a greater range of flow behavior and the interaction may result in the destruction of the smaller/weaker vortex. Previous inviscid flow studies have identified distinct flow regimes based on the efficiency of the interaction [5,12]. Elastic interaction occurs when there are only small deformations and essentially no change in circulation of the vortices.…”