Tomoki Uda (Toyama University): Topological Flow Data Analysis and its Applications

We introduce Topological Flow Data Analysis (TFDA), a recently developed mathematical framework for classifying the topology of streamlines in two-dimensional incompressible fluid flows from the perspective of dynamical systems. Sakajo and Yokoyama proposed this theory, which provides a systematic method for analysing the topological structure of streamline patterns. Based on this theory, a computational tool has been developed, integrating techniques from topological data analysis to extract and categorise streamline topology.

A key component of TFDA is a tree-based representation called the partially Cyclically Ordered rooted Tree (COT). This representation encodes the nested structure of vortices and the relative spatial arrangement of streamlines, allowing for the systematic characterisation of different topological states in fluid flows.

In this talk, we will present applications of TFDA in meteorology, oceanography, and two-dimensional fluid dynamics.

Zoom Information:

https://us02web.zoom.us/j/2022111100

(Meeting code: 2022111100 Password: skcm2)