Identifying Locally Turbulent Vortices within Instabilities
Fabien Vivodtzev, Florent Nauleau, Jean-Philippe Braeunig, Julien Tierny
TL;DR
The paper tackles automatic identification of locally turbulent vortices in 2D flows by integrating Topological Data Analysis with spectral indicators. It builds a pipeline that simplifies enstrophy via persistence and segments vortices with the Morse-Smale complex, then analyzes per-vortex energy spectra to derive turbulence indicators, notably the slope in the inertial subrange consistent with $E(k)\sim k^{-5/3}$. The main contributions are a topology-driven vortex segmentation approach and spectral descriptors that correlate with turbulence state, demonstrated on a case study with expert labeling. This topology-spectral framework offers a path toward supervised, descriptor-based turbulence detection with potential CFD applications in high-speed flow design.
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.