Investigation of Triggering Vortex Instabilities with Inertial Particles

In our previous study (Lee & Marcus, 2023, J. Fluid Mech.), we developed the mapped Legendre spectral method for analyzing wake vortices in an unbounded domain and obtained the linear eigenmodes of strong swirling q-vortices. A combination of these eigenmodes serves as an initial perturbation of the vortex, some of which may result in vortex destabilization as it nonlinearly grows. We present an extension of our numerical method in an Eulerian-Lagrangian framework that involves interactions between small inertial particles and the vortex structure. The effective computation of momentum exchange from the particles to the vortex and vice versa is discussed. By varying the initial position and velocity distribution of the particles, we investigate the evolution of the vortex perturbation resulting from the particle interaction. In particular, we examine whether the existence of particles is capable of creating viscous critical layers, which can trigger transient growth of the vortex, possibly leading to instabilities.