Identifying Locally Turbulent Vortices within Instabilities

TL;DR

This paper introduces a novel method combining Topological Data Analysis and spectral indicators to automatically identify and characterize turbulent vortices in 2D flows, distinguishing them from laminar vortices.

Contribution

The work presents a new approach that uses TDA for vortex geometry extraction and spectral indicators for turbulence assessment, advancing vortex detection techniques.

Findings

Indicators effectively differentiate turbulent from laminar vortices.

Topological methods accurately extract vortex geometries.

Spectral analysis correlates vortex behavior with turbulence states.

Abstract

This work presents an approach for the automatic detection of locally turbulent vortices within turbulent 2D flows such as instabilites. First, given a time step of the flow, methods from Topological Data Analysis (TDA) are leveraged to extract the geometry of the vortices. Specifically, the enstrophy of the flow is simplified by topological persistence, and the vortices are extracted by collecting the basins of the simplified enstrophy's Morse complex. Next, the local kinetic energy power spectrum is computed for each vortex. We introduce a set of indicators based on the kinetic energy power spectrum to estimate the correlation between the vortex's behavior and that of an idealized turbulent vortex. Our preliminary experiments show the relevance of these indicators for distinguishing vortices which are turbulent from those which have not yet reached a turbulent state and thus known as laminar.