Instability of a dusty shear flow

TL;DR

This paper investigates a novel instability in dusty shear flows caused by the interaction between a shear flow and a localized particle band, revealing conditions under which the flow becomes unstable due to particle feedback.

Contribution

It demonstrates that a dusty shear flow with a localized particle band can become unstable through momentum feedback, a phenomenon not previously characterized.

Findings

Instability arises from particle-fluid momentum feedback.

Increasing particle inertia dampens the instability.

Stronger fluid-particle coupling enhances the instability.

Abstract

We study the instability of a dusty simple shear flow where the dust particles are distributed non-uniformly. A simple shear flow is modally stable to infinitesimal perturbations. Also, a band of particles remains unaffected in the absence of any background flow. However, we demonstrate that the combined scenario -- comprising a simple shear flow with a localised band of particles -- can exhibit destabilisation due to their two-way interaction. The instability originates solely from the momentum feedback from the particle phase to the fluid phase. Eulerian-Lagrangian simulations are employed to illustrate the existence of this instability. Furthermore, the results are compared with a linear stability analysis of the system using an Eulerian-Eulerian model. Our findings indicate that the instability has an inviscid origin and is characterised by a critical wavelength below which it is not persistent. We have observed that increasing particle inertia dampens the unstable modes, whereas the strength of the instability increases with the strength of the coupling between the fluid and particle phases.