The strength of a pair of point vortices in an incompressible inviscid fluid in 3d can blow up in finite time

TL;DR

This paper provides an exact solution for the evolution of a pair of point vortices in 3D incompressible inviscid fluid flow, demonstrating conditions under which vortex strength remains stable or blows up in finite time.

Contribution

It offers an exact analytical solution for vortex pair dynamics in 3D Euler equations, revealing finite-time blow-up conditions based on initial data.

Findings

Vortex strength can blow up in finite time

Stability depends on initial conditions

Exact solutions for symmetric initial configurations

Abstract

The evolution of a pair of point vortices in whole space, subject to the inviscid Euler equations for incompressible fluid flow, is solved exactly for rotationally symmetric initial conditions. This exact solution shows that the vortex strength for a pair of point vortices can either remain stable or blow up in finite time, depending on the initial data.