Dynamics of Two-Sign Point Vortices in Positive and Negative Temperature States

Abstract

Dynamics of two-sign point vortices in two-dimensional circular boundary is examined by numerical simulations with MDGRAPE-2. The vortex system is characterized by the inverse temperature beta as determined from the density of states of the microcanonical ensemble of numerically generated 10(7) states. The massive simulation shows that different configurations appear in the time-asymptotic state depending on the sign of beta. Condensation of the same-sign vortices is observed when beta<0, while the both-sign vortices tend to be uniformly neutralized when beta>0. During the condensation, a part of the vortices gains energy to form clumps (patches), and the other part of the vortices loses energy to keep the total energy constant and mixes with vortices of the other sign. This observation demonstrates a characteristic feature of negative beta states that the system energy concentrates into the clumps of the same-sign vortices.