Self-organizing effect of drift term against diffusion term in point vortex system evidenced by numerical simulations on PEZY-SC

Abstract

We have analytically obtained a kinetic equation for a two-dimensional (2D) point vortex system with a Fokker–Planck type collision term consisting of a diffusion term and a drift term (Yatsuyanagi and Hatori 2015 Fluid Dyn. Res. 47 065506). The equation describes a mechanism of a self-organization in the system. In this paper, analytically anticipated characteristics of the collision term is evidenced by numerical simulations on PEZY-SC supercomputer system. In the previous paper, it is shown that the collision term satisfies following physically good properties: (1) charge separated, self-organized distribution typical for negative absolute temperature is achieved by the drift term, (2) when a system reaches a thermal equilibrium state, stream function ψ and vorticity ω satisfies an inequality which is important for the next property, (3) the obtained kinetic equation conserves total mean field energy and satisfies the H theorem. In this paper we will evidence the above properties numerically. The time-asymptotic distribution of the vortices corresponds to the analytically anticipated local equilibrium state in which many small regions with different local temperatures exist. Especially, the transport process by the drift term is elucidated clearly, which gives a key mechanism of the self-organization, i.e. condensation of the same-sign vortices.