Clustering of heavy inertial particles in an elliptical vortex

In open vortical flows, suspended heavy inertial particles are generally centrifuged out from the regions of high vorticity, making the vortex centre unstable fixed points or sources. The Kirchhoff vortex, an isolated elliptical patch of uniform vorticity that rotates with a self-induced constant angular velocity, is an example of an open vortical flow that contains sinks for heavy inertial particles. In the co-rotating reference frame with the elliptical patch, heavy inertial particles find two sinks and three sources in the flow domain. The locations of sources and sinks depend on the particle inertia/Stokes number (St); their stability characteristics change when the St exceeds a critical value. However, the dynamics of inertial particles can not become chaotic in the Kirchhoff vortex, which is proven by showing time-independent correction to Hamiltonian in the limit of St << 1. We next analyze the transport of heavy inertial particles in a Kida vortex, an elliptical vortex patch in a background shear flow, where evidence of chaotic transport is probed as a function of St and background shear rate. AVSN thanks the Prime Minister's Research Fellows (PMRF) scheme, Ministry of Education, Government of India. The authors also acknowledge the support of the Complex Systems and Dynamics Group at Indian Institute of Technology Madras.