Insights into symmetric and asymmetric vortex mergers using the core growth model

TL;DR

This paper investigates symmetric and asymmetric vortex mergers using a core growth model, revealing complex topological bifurcations and identifying areas for model improvement.

Contribution

It introduces a detailed analysis of vortex merger stages with a coupled vorticity and passive particle model, highlighting new topological bifurcations.

Findings

Rich sequence of topological bifurcations identified

Model reveals detailed vortex merger stages

Highlights deficiencies and suggests improvements

Abstract

We revisit the two vortex merger problem (symmetric and asymmetric) for the Navier-Stokes equations using the core growth model for vorticity evolution coupled with the passive particle field and an appropriately chosen time-dependent rotating reference frame. Using the combined tools of analyzing the topology of the streamline patterns along with careful tracking of passive fields, we highlight the key features of the stages of evolution of vortex merger, pinpointing deficiencies in the low-dimensional model with respect to similar experimental/numerical studies. The model, however, reveals a far richer and delicate sequence of topological bifurcations than has previously been discussed in the literature for this problem, and at the same time points the way towards a method of improving the model.