Global Phase Plane Analysis of the three-vortex problem

Nov 1, 2024·
Atul Anurag
Atul Anurag
· 0 min read
Image credit: SIAM
Abstract
We investigate two problems in point-vortex dynamics within a two-dimensional, inviscid, incompressible fluid. We derive a new reduction of a system involving three vortices, initially employing Jacobi coordinates followed by Nambu brackets. First, we conduct a global phase analysis of a three-vortex problem with arbitrary circulations. Second, we generalize the reduction method to study the dynamics of four vortices with vanishing total circulation. The novel reduction method eliminates coordinate singularities that made understanding the dynamics difficult.
Event
Location

Gosnell Hall

Gosnell Hall, 84, Rochester, Rochester, NY 14623

Talks
Atul Anurag
Authors
Atul Anurag
Research Assistant, Department of Mathematical Sciences