The Global Phase Plane Analysis of Three Vortex Interactions

Apr 23, 2025·
Atul Anurag (अतुल अनुराग)
Atul Anurag (अतुल अनुराग)
· 0 min read
Abstract
We investigate global phase planes in point-vortex dynamics in a two-dimensional, inviscid, incompressible fluid. We derive a symplectic reduction of a system involving three vortices, initially employing Jacobi coordinates followed by Lie-Poisson reduction. We conduct a global phase analysis of a three-vortex problem with arbitrary circulations with novel bifurcation analysis. This reduction method eliminates coordinate singularities that made understanding the dynamics challenging.
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New Jersey Institute of Technology

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