Instability of a dusty vortex

TL;DR

This paper reveals a new instability mechanism in dusty vortices caused by particle feedback forces, leading to vortex breakdown, validated through linear stability analysis and Eulerian-Lagrangian simulations.

Contribution

It introduces a novel instability in dusty vortices driven by particle feedback, with detailed analysis and simulation validation, expanding understanding of dusty flow dynamics.

Findings

Dust particles induce instability in Rankine vortices.

Critical mass loading determines mode stability.

High-wavenumber modes cause particle spirals and vortex breakdown.

Abstract

We investigate the effect of inertial particles dispersed in a circular patch of finite radius on the stability of a two-dimensional Rankine vortex in semi-dilute dusty flows. Unlike the particle-free case where no unstable modes exist, we show that the feedback force from the particles triggers a novel instability. The mechanisms driving the instability are characterized using linear stability analysis for weakly inertial particles and further validated against Eulerian-Lagrangian simulations. We show that the particle-laden vortex is always unstable if the mass loading $M>0$. Surprisingly, even non-inertial particles destabilize the vortex by a mechanism analogous to the centrifugal Rayleigh-Taylor instability in radially stratified vortex with density jump. We identify a critical mass loading above which an eigenmode $m$ becomes unstable. This critical mass loading drops to zero as m increases. When particles are inertial, modes that fall below the critical mass loading become unstable, whereas, modes above it remain unstable but with lower growth rates compared to the non-inertial case. Comparison with Eulerian-Lagrangian simulations shows that growth rates computed from simulations match well the theoretical predictions. Past the linear stage, we observe the emergence of high-wavenumber modes that turn into spiraling arms of concentrated particles emanating out of the core, while regions of particle-free flow are sucked inward. The vorticity field displays similar pattern which lead to the breakdown of the initial Rankine structure. This novel instability for a dusty vortex highlights how the feedback force from the disperse phase can induce the breakdown of an otherwise resilient vortical structure.