论文标题
点漩涡在多重连接的多边形结构域中的运动
The Motion of a Point Vortex in Multiply Connected Polygonal Domains
论文作者
论文摘要
我们研究了单点涡流在简单而多连接的多边形结构域中的运动。如果发生乘数连接域，则多边形障碍物可以看作是3D多边形圆柱体的横截面。首先，我们利用共形映射将多边形结构域转移到圆形域。然后，我们采用Schottky-Klein Prime函数来计算圆形域中的点涡流运动的哈密顿式。我们比较在对称和不对称结构域中哈密顿的轮廓线的拓扑结构之间进行比较。特别注意点涡流轨迹与多边形障碍的相互作用。在这种情况下，我们讨论了对称破坏的影响，以及障碍物位置和形状对涡旋运动行为的影响。
We study the motion of a single point vortex in simply and multiply connected polygonal domains. In case of multiply connected domains, the polygonal obstacles can be viewed as the cross-sections of 3D polygonal cylinders. First, we utilize conformal mappings to transfer the polygonal domains onto circular domains. Then, we employ the Schottky-Klein prime function to compute the Hamiltonian governing the point vortex motion in circular domains. We compare between the topological structures of the contour lines of the Hamiltonian in symmetric and asymmetric domains. Special attention is paid to the interaction of point vortex trajectories with the polygonal obstacles. In this context, we discuss the effect of symmetry breaking, and obstacle location and shape on the behavior of vortex motion.
