Rotating vortices in two-dimensional inhomogeneous strongly coupled dusty plasmas: Shear and spiral density waves

Dusty plasma experiments can be performed quite easily in a strong coupling regime. In our previous work [V. S. Dharodi, S. K. Tiwari, and A. Das, Physics of Plasmas 21, 073705 (2014)], we numerically explored such plasmas with constant density and observed the transverse shear (TS) waves from the rotating vortex. Laboratory dusty plasmas are good examples of homogeneous plasmas; however, heterogeneity (e.g., density, temperature, and charge) may be due to the existence of voids, different domains with different orientations, presence of external forces like magnetic and/or electric, size or charge imbalance, etc. Here, we examine how the density heterogeneity in dusty plasmas responds to the circularly rotating vortex monopoles, specifically, smooth and sharp cutoff. For this purpose, we have carried out a series of two-dimensional fluid simulations in the framework of the incompressible generalized hydrodynamics fluid model. The rotating vortices are placed at the interface of two incompressible fluids with different densities. The smooth rotating vortex causes two effects: First, the regions are stretched to form the spiral density waves; second, there is a shear in flows which consequently induces the TS waves. The TS waves move slower in the denser side than in the lighter side. The difference in speeds of the waves induces the net flow of the medium towards the lower density side. We notice that the spiral density arms are distinguishable in the early time while later they get smeared out. In sharp flows, the interplay between the TS waves and the vortices of Kelvin-Helmholtz instability distorts the formation of the regular spiral density arms around the rotor.