The Global Phase Plane Analysis of Three Vortex Interactions

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.

Dana Knox Student Research Showcase

New Jersey Institute of Technology

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