Collapse of n vortices

TL;DR

This paper introduces a highly accurate numerical method to study finite vortex systems in the plane that collapse to a point in finite time, with detailed analysis of system behavior near collapse.

Contribution

It presents a new fast numerical approach for approximating vortex collapse and demonstrates its effectiveness with a seven-vortex example.

Findings

The method achieves high accuracy in vortex collapse simulations.

It provides detailed insights into system behavior near critical collapse time.

The approach is efficient for studying finite vortex systems.

Abstract

Numerical approximations of finite systems of vortices in the plane, collapsing to a point in finite time are studied. A fast method leading to highly accurate approximations is presented. The method is illustrated with an example of an approximate collapsing system of seven vortices. Special attention is given to the behaviour of the system near critical time (close to the collapse).