Attracting fixed points for heavy particles in the vicinity of a vortex pair

TL;DR

This paper investigates the dynamics of heavy inertial particles near a vortex pair, revealing stable fixed points in a co-rotating frame that depend on particle Stokes number and viscosity effects.

Contribution

It identifies the existence and stability conditions of fixed points for heavy particles near vortex pairs, including the critical Stokes number and viscosity influence.

Findings

Stable fixed points exist for St<St_{cr}.

Viscosity slightly increases St_{cr}.

Fixed points become unstable and disappear at St=St_{cr}.

Abstract

We study the behaviour of heavy inertial particles in the flow field of two like-signed vortices. In a frame co-rotating with the two vortices, we find that stable fixed points exist for these heavy inertial particles; these stable frame-fixed points exist only for particle Stokes number $St<St_{cr}$. We estimate $St_{cr}$ and compare this with direct numerical simulations, and find that the addition of viscosity increases the $St_{cr}$ slightly. We also find that the fixed points become more stable with increasing $St$ until they abruptly disappear at $St=St_{cr}$. These frame-fixed points are between fixed points and limit cycles in character.