Instability of a dusty vortex. (10th October 2022)

• Record Type: Journal Article
• Authors: Shuai, Shuai; Jeswin Dhas, Darish; Roy, Anubhab; Kasbaoui, M. Houssem
• Is Part Of: Journal of fluid mechanics. Volume 948(2022)
• Publication Date: 2022-10-10
• Subjects: particle/fluid flow -- vortex instability; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2022.687
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: 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 with 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 spiralling arms of concentrated particles emanating out of the core, while regions of particle-free flow are sucked inward. The vorticity field displays a similar pattern which leads 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.