NONERGODICITY OF POINT VORTICES
NONERGODICITY OF POINT VORTICES
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DOI：
10.1063/1.858014
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发表时间：
1991-05
影响因子：
4.6
通讯作者：
J. Weiss;J. McWilliams
中科院分区：
文献类型：
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作者：
J. Weiss;J. McWilliams
二维流体中N个点涡的运动是一个具有2N维相空间的哈密顿动力系统。从开放域的运动方程出发，导出了二维方形双周期域中点涡的运动方程。哈密顿量有三个已知的运动常数，因此被认为对于四个或更多的漩涡是不可积的。从包含6个总能量不同的涡的几个初始条件对轨迹进行数值积分。通过比较时间平均和集合平均涡旋对统计量，直接测试了由运动常数定义的表面上的遍历性。发现动力学不是遍历的。有证据表明，非遍历性并不是由于相空间的总体破碎，而这种破碎可能是由对称性破坏引起的。涡流对统计量也被用来检验混沌运动的随机性。结果表明，涡旋的时间平均统计量与涡旋的时间平均统计量明显不同。
The motion of N point vortices in a two‐dimensional fluid is a Hamiltonian dynamical system with a 2N‐dimensional phase space. The equations of motion for point vortices in a two‐dimensional square doubly periodic domain are derived from those for an open domain. The Hamiltonian has three known constants of the motion and is thus believed to be nonintegrable for four or more vortices. Trajectories are numerically integrated from several initial conditions containing six vortices with varying total energy. Ergodicity on the surface defined by the constants of the motion is directly tested by comparing time‐average and ensemble‐average vortex pair statistics. It is found that the dynamics is not ergodic. There is evidence that the nonergodicity is not due to a gross fragmentation of phase space as might result from a broken symmetry. Vortex pair statistics are also used to test the randomness of the chaotic motion. It is found that the time‐averaged statistics of the vortices are clearly distinct from those...