Classification of robust isolated vortices in two-dimensional hydrodynamics
Classification of robust isolated vortices in two-dimensional hydrodynamics
复制标题
二维流体动力学中鲁棒孤立涡的分类
DOI：
10.1017/s0022112097007933
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发表时间：
1998
影响因子：
3.7
通讯作者：
J. Sommeria
中科院分区：
文献类型：
--
作者：
P. Chavanis;J. Sommeria
我们确定解决方案的欧拉方程表示孤立的漩涡（单极，偶极子）在一个无限的域中，任意值的能量，流通，角动量和冲动。涡量和流函数之间的线性关系被假定在涡内（而流动是无旋的外部）。连续涡量场的统计力学证明了这些解在湍流中的出现。由于动力学的限制，混合到一个“最大熵泡沫”的额外限制，假设。在强混合极限下（当约束较弱时），由统计理论得到涡量与流函数的线性关系。在这个极限下，熵最大化等价于拟能最小化。新的稳定性标准进行了研究，特别是意味着，在大多数情况下，涡度必须是连续的（或略有不连续）在涡边界。然后，涡半径自动确定的积分约束，我们可以得到一个孤立的漩涡，如单极和偶极子（旋转或平移）在一个单一的控制参数的分类。本文推广了Chavanis & Sommeria（1996）在有界域上得到的分类.
We determine solutions of the Euler equation representing isolated vortices (monopoles, dipoles) in an infinite domain, for arbitrary values of energy, circulation, angular momentum and impulse. A linear relationship between vorticity and stream function is assumed inside the vortex (while the flow is irrotational outside). The emergence of these solutions in a turbulent flow is justified by the statistical mechanics of continuous vorticity fields. The additional restriction of mixing to a ‘maximum-entropy bubble’, due to kinetic constraints, is assumed. The linear relationship between vorticity and stream function is obtained from the statistical theory in the limit of strong mixing (when constraints are weak). In this limit, maximizing entropy becomes equivalent to a kind of enstrophy minimization. New stability criteria are investigated and imply in particular that, in most cases, the vorticity must be continuous (or slightly discontinuous) at the vortex boundary. Then, the vortex radius is automatically determined by the integral constraints and we can obtain a classification of isolated vortices such as monopoles and dipoles (rotating or translating) in terms of a single control parameter. This article generalizes the classification obtained in a bounded domain by Chavanis & Sommeria (1996).