Algorithms of topological flow data analysis for Hamiltonian flows with doubly periodic boundary conditions

Abstract

Abstract. Based on the classification theory of streamline topology of Hamiltonian (incompressible) flows satisfying doubly periodic boundary conditions by Kimura et al., this paper provides a practical computational algorithm for converting the topological structure of a given stream function into a partially cyclically ordered rooted tree. By implementing this algorithm in software, we apply it to numerical data of two-dimensional turbulence. We then show that coherent vortex structures, which play an important role in theoretical studies of two-dimensional turbulence, are successfully extracted from the viewpoint of topology.