Collisional diffusion in a two-dimensional point vortex gas or a two-dimensional plasma

Abstract

This paper analyzes collisional diffusion of a multispecies two-dimensional (2D) point vortex gas, or a 2D plasma, in the presence of retrograde shear. Diffusion both along and across the shear flow is calculated using Boltzmann, Kubo, Klimontovitch and resonance-broadening theories. It is shown that diffusion is reduced in the presence of shear, just as for the shear reduction of transport observed in fusion plasmas. Here, however, fluctuations are thermal rather than turbulent, allowing a rigorous calculation of the transport. When there are several species of point vortices, Onsager relations require that the diffusive flux conserves the total vorticity ρ(r), which is proportional to charge density in the plasma analogue. Surprisingly, the diffusive flux concentrates vortices with large positive (or negative) circulations at maxima (or minima) of the mean vorticity profile.