Geometrical and topological description of chirality-relevant flow structures

TL;DR

This paper introduces a new theoretical framework using differential forms and topology to analyze flow chirality and structures, aiming to make complex concepts accessible to a broad audience including students and researchers.

Contribution

It presents a distinctive theoretical approach combining differential geometry and topology to describe flow structures related to chirality in fluid mechanics.

Findings

Formulation of differential forms for Navier-Stokes equations

Application of topological concepts to flow chirality

Discussion of recent advances in turbulence analysis

Abstract

Issues relevant to the flow chirality and structure are focused, while the new theoretical results, including even a distinctive theory, are introduced. However, it is hope that the presentation, with a low starting point but a steep rise, is appropriate for a broader spectrum of audiences ranging from students to researchers, thus illustrations of differential forms and relevant basic topological concepts are also offered, followed by the demonstration with formulation of differential forms of the classical Navier-Stokes flow theory and the discussions of recent studies in fundamental fluid mechanics and turbulence.