Violent and slow relaxations to sinh‐Poisson equilibrium state in two‐dimensional point vortex system

Characteristics of numerically‐obtained typical distributions of a two‐dimensional point vortex system after a violent relaxation at positive and negative temperatures are examined. It is anticipated that like gravitational N ‐body systems, the point vortex system rapidly relaxes to a state near the thermal equilibrium state by the violent relaxation and after that the system evolves toward the genuine thermal equilibrium state driven by a collisional slow process (the slow relaxation). The time scale of the slow relaxation is proportional to the number of the point vortices. Namely, it takes a very long time to reach the final thermal equilibrium state. The detailed mechanism of the violent and slow relaxations are still unclear. In this paper, we examine the mechanism of the slow relaxation numerically. When the system temperature determined by the initial system energy is negative, the system evolves to a state consisting of many small areas with different temperatures by the violent relaxation. In this state, the vorticity is determined as a function of the stream function, which means that the motion of the vortices across an isosurface of the stream function is restricted. Due to this restriction, the collisional relaxation process following the violent relaxation is slow.