2023/09/13 by David Meyer, Meyer, David
Chemical Engineering · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Rheology and Fluid Dynamics Studies
paper · pdf · doi:10.48550/arxiv.2309.07004
openalex publication_date 2023/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We consider a model that approximates vortex rings in the axisymmetric 3D Euler equation by the movement of almost rigid bodies described by Newtonian mechanics. We assume that the bodies have a circular cross-section and that the fluid is irrotational and interacts with the bodies through the pressure exerted at the boundary. We show that this kind of system can be described through an ODE in the positions of the bodies and that in the limit, where the bodies shrink to massless filaments, the system converges to an ODE system similar to the point vortex system. In particular, we can show that in a suitable set-up, the bodies perform a leapfrogging motion.