Numerical Simulation of Vortex Crystals and Merging in N-Point Vortex Systems with Circular Boundary(Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics and Fluid Mechanics)
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概要
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In two-dimensional (2D) inviscid incompressible flow, low background vorticity distribution accelerates intense vortices (clumps) to merge each other and to array in the symmetric pattern which is called "vortex crystals"; they are observed in the experiments on pure electron plasma and the simulations of Euler fluid. Vortex merger is thought to be a result of negative "temperature" introduced by Onsager [Nuovo Cimento 6 (1949) 279]. Slight difference in the initial distribution from this leads to "vortex crystals". We study these phenomena by examining N-point vortex systems governed by the Hamilton equations of motion. First, we study a three-point vortex system without background distribution. It is known that a N-point vortex system with boundary exhibits chaotic behavior for N>3. In order to investigate the properties of the phase space structure of this three-point vortex system with circular boundary, we examine the Poincare plot of this system. Then we show that topology of the Poincare plot of this system drastically changes when the parameters, which are concerned with the sign of "temperature", are varied. Next, we introduce a formula for energy spectrum of a N-point vortex system with circular boundary. Further, carrying out numerical computation, we reproduce a vortex crystal and a vortex merger in a few hundred point vortices system. We confirm that the energy of vortices is transferred from the clumps to the background in the course of vortex crystallization. In the vortex merging process, we numerically calculate the energy spectrum introduced above and confirm that it behaves as k^<-α> (α≈2.2-2.8), at the region 10^0 < k < 10^1 after the merging.
- 社団法人日本物理学会の論文
- 2005-02-15
著者
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SANO Mitsusada
Graduate School of Human and Environmental Studies, Kyoto University
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YOSHIDA Takeshi
Graduate School of Human and Environmental Studies, Kyoto University
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Yoshida Takeshi
Graduate School Of Advanced Sciences Of Matter Hiroshima University
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Sano Mitsusada
Graduate School Of Human And Environmental Studies Kyoto University
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Sano M
Kyoto Univ. Kyoto
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