Ohkitani Koji, Al Sulti Fayeza
Department of Applied Mathematics, School of Mathematics and Statistics, The University of Sheffield, Sheffield S3 7RH, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Jun;81(6 Pt 2):067302. doi: 10.1103/PhysRevE.81.067302. Epub 2010 Jun 30.
A characterization of reconnection of vorticity contours is made by direct numerical simulations of the two-dimensional Navier-Stokes flow at a relatively low Reynolds number. We identify all the critical points of the vorticity field and classify them by solving an eigenvalue problem of its Hessian matrix on the basis of critical-point theory. The numbers of hyperbolic (saddles) and elliptic (minima and maxima) points are confirmed to satisfy Euler's index theorem numerically. Time evolution of these indices is studied for a simple initial condition. Generally speaking, we have found that the indices are found to decrease in number with time. This result is discussed in connection with related works on streamline topology, in particular, the relationship between stagnation points and the dissipation. Associated elementary procedures in physical space, the merging of vortices, are studied in detail for a number of snapshots. A similar analysis is also done using the stream function.
通过对二维纳维-斯托克斯流在相对较低雷诺数下进行直接数值模拟，对涡度等值线的重新连接进行了表征。我们识别了涡度场的所有临界点，并根据临界点理论通过求解其海森矩阵的特征值问题对它们进行分类。数值上证实了双曲型（鞍点）和椭圆型（极小值和极大值）点的数量满足欧拉指标定理。针对一个简单的初始条件研究了这些指标的时间演化。一般来说，我们发现这些指标的数量随时间减少。结合关于流线拓扑的相关工作，特别是驻点与耗散之间的关系，对这一结果进行了讨论。针对多个快照，详细研究了物理空间中相关的基本过程，即涡旋的合并。还使用流函数进行了类似的分析。
