Collisional diffusion in a 2-dimensional point vortex gas

Simulations showing the effect of shear on the collisional diffusion of a 2D point vortex gas are compared to theory. For finite shear the diffusion is considerably smaller than previous zero-shear theories predict. Surprisingly, changing the sign of the applied shear changes the diffusion by an order of magnitude.  2001 Elsevier Science B.V. All rights reserved. The self-diffusion of a 2-dimensional (2D) gas of interacting point vortices is a classic problem in nonequilibrium statistical physics, with relevance to the behavior of type-II superconductors, dislocations in solids, rotating superfluid helium, and turbulence and transport in Euler fluids and plasmas. This Letter considers the effect of an applied shear on the diffusion. Early work on this problem focused on the case of a quiescent, homogeneous shear-free gas [1,2]. When the vortices are distributed randomly, representing high-temperature thermal fluctuations, Taylor and McNamara showed that the diffusion coefficient (for diffusion in 1 direction) has the following simple form: