# Coaxial collisions of a vortex ring and a sphere in an inviscid incompressible fluid

## TL;DR

This paper investigates the complex interactions between a vortex ring and a sphere moving along its axis in an ideal fluid, using Hamiltonian mechanics and numerical solutions to understand their coupled dynamics.

## Contribution

It introduces a Hamiltonian framework for modeling vortex ring-sphere interactions and provides numerical solutions for various initial conditions.

## Key findings

- Total energy and momentum are conserved in the system.
- Numerical solutions reveal diverse collision behaviors.
- Hydrodynamic interactions significantly influence the dynamics.

## Abstract

The dynamics of a circular thin vortex ring and a sphere moving along the symmetry axis of the ring in an inviscid incompressible fluid is studied on the basis of Euler's equations of motion. The equations of motion for position and radius of the vortex ring and those for position and velocity of the sphere are coupled by hydrodynamic interactions. The equations are cast in Hamiltonian form, from which it is seen that total energy and momentum are conserved. The four Hamiltonian equations of motion are solved numerically for a variety of initial conditions.