A novel particle-induced instability of a simple shear flow

We investigate the instability of a dusty simple shear flow with non-uniformly distributed dust particles. While a simple shear flow is typically stable to infinitesimal perturbations, and a band of particles remains unaffected in the absence of background flow, we demonstrate that their combination can lead to destabilisation through two-way interactions. This instability arises solely from the momentum feedback from the particle phase to the fluid phase. We employ Eulerian-Lagrangian simulations to illustrate the presence of this instability and compare the results with a linear stability analysis using an Eulerian-Eulerian model. Our findings reveal that the instability is inviscid in origin and characterised by a critical wavelength below which it does not persist.