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Word representation of streamline topologies for structurally stable vortex flows in multiply connected domains
| Title: | Word representation of streamline topologies for structurally stable vortex flows in multiply connected domains |
| Authors: | Yokoyama, Tomoo Browse this author | | Sakajo, Takashi Browse this author →KAKEN DB |
| Keywords: | streamline topology | | vortex flows | | multiply connected domains | | Hamiltonian vector field |
| Issue Date: | 8-Feb-2013 |
| Publisher: | The Royal Society |
| Journal Title: | Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences |
| Volume: | 469 |
| Issue: | 2150 |
| Start Page: | 20120558 |
| Publisher DOI: | 10.1098/rspa.2012.0558 |
| Abstract: | Let us consider the incompressible and inviscid flows in two-dimensional domains with multiple obstacles. The instantaneous velocity field becomes a Hamiltonian vector field defined from the stream function, and it is topologically characterized by the streamline pattern that corresponds to the contour plot of the stream function. The present paper provides us with a procedure to construct structurally stable streamline patterns generated by finitely many point vortices in the presence of the uniform flow. Starting from some basic structurally stable streamline patterns in the disc of low genus, we repeat some fundamental operations that append a streamline pattern with increasing one genus to them. Thanks to the inductive procedure, one can assign a sequence of the operations as a representing word to each structurally stable streamline patterns. We also give the canonical expression for the word representation, which allows us to make a catalogue of all possible structurally stable streamline patterns in a combinatorial manner. As an example, we show all streamline patterns in the disk of genus one and two. |
| Relation: | http://rspa.royalsocietypublishing.org/ |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/51916 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 坂上 貴之
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