open access

https://hdl.handle.net/2115/51916

Word representation of streamline topologies for structurally stable vortex flows in multiply connected domains

英語

Hamiltonian vector field

2013-02-08

The Royal Society

Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences

469(2150)

20120558

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.

学術雑誌論文

Accepted Manuscript

1364-5021