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Keywords = Schottky-Klein prime function

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19 pages, 6466 KB  
Article
The Motion of a Point Vortex in Multiply-Connected Polygonal Domains
by El Mostafa Kalmoun, Mohamed M. S. Nasser and Khalifa A. Hazaa
Symmetry 2020, 12(7), 1175; https://doi.org/10.3390/sym12071175 - 16 Jul 2020
Cited by 1 | Viewed by 3122
Abstract
We study the motion of a single point vortex in simply- and multiply-connected polygonal domains. In the 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 [...] Read more.
We study the motion of a single point vortex in simply- and multiply-connected polygonal domains. In the 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. Full article
(This article belongs to the Special Issue Symmetry in Numerical Analysis and Numerical Methods)
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