102 research outputs found
Numerical Simulation of Vortex Crystals and Merging in N-Point Vortex Systems with Circular Boundary
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 L. Onsager. 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\geq 3. In order to investigate the properties
of the phase space structure of this three-point vortex system with circular
boundary, we examine the Poincar\'e plot of this system. Then we show that
topology of the Poincar\'e 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^{-\alpha},(\alpha\approx 2.2-2.8) at the
region 10^0<k<10^1 after the merging.Comment: 30 pages, 11 figures. to be published in Journal of Physical Society
of Japan Vol.74 No.
Quasi-stationary States of Two-Dimensional Electron Plasma Trapped in Magnetic Field
We have performed numerical simulations on a pure electron plasma system
under a strong magnetic field, in order to examine quasi-stationary states that
the system eventually evolves into. We use ring states as the initial states,
changing the width, and find that the system evolves into a vortex crystal
state from a thinner-ring state while a state with a single-peaked density
distribution is obtained from a thicker-ring initial state. For those
quasi-stationary states, density distribution and macroscopic observables are
defined on the basis of a coarse-grained density field. We compare our results
with experiments and some statistical theories, which include the
Gibbs-Boltzmann statistics, Tsallis statistics, the fluid entropy theory, and
the minimum enstrophy state. From some of those initial states, we obtain the
quasi-stationary states which are close to the minimum enstrophy state, but we
also find that the quasi-stationary states depend upon initial states, even if
the initial states have the same energy and angular momentum, which means the
ergodicity does not hold.Comment: 9 pages, 7 figure
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