Kelvin–Helmholtz instability in strongly coupled dusty plasma with rotational shear flows and tracer transport

Abstract

Kelvin–Helmholtz (KH) instability plays a significant role in transport and mixing in various media such as hydrodynamic fluids, plasmas, geophysical flows and astrophysical situations. In this paper, we numerically explore this instability for a two-dimensional strongly coupled dusty plasma medium with rotational shear flows. We study this medium using a generalized hydrodynamic fluid model which treats it as a viscoelastic fluid. We consider the specific cases of rotating vorticity with abrupt radial profiles of rotation. In particular, single-circulation and multi-circulation vorticity shell profiles have been chosen. We observe the KH vortices at each circular interface between two relative rotating flows along with a pair of ingoing and outgoing wavefronts of transverse shear waves. Our studies show that due to the interplay between KH vortices and shear waves in the strongly coupled medium, the mixing and transport behaviour are much better than those of standard inviscid hydrodynamic fluids. In the interest of substantiating the mixing and transport behaviour, the generalized hydrodynamic fluid model is extended to include Lagrangian tracer particles. The numerical dispersion of these tracer particles in a flow provides an estimate of the diffusion in such a medium. We present the preliminary observations of tracer distribution (cluster formation) and diffusion (mean square displacement) across the medium.