Seminar on Qualitative Theory of Differential Equations - Roy Goodman (19.3.2026)

Thursday 19.3.2026 at 14:00, Lecture room M 223

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Roy Goodman (New Jersey Institute of Technology):
Leapfrogging and scattering of point vortices

Abstract: 
The interaction among vortices is a key process in fluid motion. The n-vortex problem, which models the movement of a finite number of vortices in a two-dimensional inviscid fluid, has been studied since the late 1800s and remains relevant due to its strong link to quantum fluid dynamics. A foundational document in this area is Walter Gröbli's 1877 doctoral dissertation. We apply modern tools from dynamical systems and Hamiltonian mechanics to several problems arising from this work. First, we study the linear stability and nonlinear dynamics of the so-called leapfrogging orbit of four vortices, utilizing Hamiltonian reductions and a numerical visualization method known as Lagrangian descriptors. Second, we analyze the scattering of vortex dipoles using tools from geometric mechanics.

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