Word representation of streamline topologies for structurally stable vortex flows in multiply connected domains
Seminar Room 1, Newton Institute
The instantaneous flow field of the inviscid and incompressible fluids in two-dimensional multiply connected exterior domains is described by a Hamiltonian vector field whose Hamiltonian becomes the stream function, which is the imaginary part of the complex potential. The flow is characterized topologically by the streamline pattern, which consists of the contour lines of the stream function. The present research provides us with a new topological classification procedure of the structurally stable streamline patterns generated by many vortex points in the presence of the uniform flow. The procedure allows us to assign a word representation to each structurally stable Hamiltonian vector field in the multiply connected domains. In the present talk, I will explain how to assign the word to the structurally stable streamline patterns and show all the streamline patterns in multiply connected domains of low genus with their word representations.