Attracting fixed points for heavy particles in the vicinity of a vortex pair

Abstract

We study the behaviour of heavy inertial particles in the flow field of two like-signed vortices. In a frame co-rotating with the two vortices, we find that stable fixed points exist for these heavy inertial particles; these stable frame-fixed points exist only for particle Stokes number $St<S{t}_{cr}$. We estimate $S{t}_{cr}$ and compare this with direct numerical simulations, and find that the addition of viscosity increases the $S{t}_{cr}$ slightly. We also find that the fixed points become more stable with increasing $St$ until they abruptly disappear at $St=S{t}_{cr}$. These frame-fixed points are between fixed points and limit cycles in character.

Comment: Figures 7 a,b added Comment: Section on stability analysis completely redone Comment: Several sections reordered for better readability Comment: Equation 6 rewritten in terms of rotating frame variables. Comment: Several typos corrected

References in corpus (6)

• Multifractal concentrations of inertial particles in smooth random flows
• Persistence Problem in Two-Dimensional Fluid Turbulence
• Where do small, weakly inertial particles go in a turbulent flow?
• Dust trapping in inviscid vortex pairs
• Tangling clustering of inertial particles in stably stratified turbulence
• Particle separation by Stokes number for small neutrally buoyant spheres in a fluid

Cited by in corpus (4)

• Orientation dynamics of two-dimensional concavo-convex bodies
• Trapping and extreme clustering of finitely-dense inertial particles near a rotating vortex pair
• Transport of condensing droplets in Taylor-Green vortex flow in the presence of thermal noise
• Levitation of heavy particles against gravity in asymptotically downward flows