Abstract
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.
Highlights
IntroductionCharacteristics of numerically-obtained typical distributions of a two-dimensional (2D) point vortex system after a violent relaxation at positive and negative temperatures are examined [7]
Characteristics of numerically-obtained typical distributions of a two-dimensional (2D) point vortex system after a violent relaxation at positive and negative temperatures are examined [7].The point vortex model is a simple tool for investigations of 2D turbulence
We numerically examine the mechanism of the slow relaxation following the violent relaxation
Summary
Characteristics of numerically-obtained typical distributions of a two-dimensional (2D) point vortex system after a violent relaxation at positive and negative temperatures are examined [7]. Its calculation cost is proportional to N2 where N is the total number of point vortices It may take several months for point vortex simulations using a normal PCs with 104 vortices. To overcome this difficulty, we use a GPU (Graphics Processing Unit) to accelerate the calculation of the Biot-Savart integral. In this state, the vorticity is determined as a function of the stream function, in other words, ∇ · (uω) = 0 where u is the velocity field and ω is the vorticity.
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