Spatio-Temporal Signatures of Intermittency in Helically Rotating Turbulence through Topological Data Analysis

TL;DR

This paper applies Topological Data Analysis to identify and characterize the spatiotemporal signatures of intermittency in helically rotating turbulent flows, offering a more sensitive detection method than traditional statistics.

Contribution

The study introduces a TDA-based framework for detecting intermittency in turbulence, utilizing persistence diagrams and Wasserstein distances to analyze vorticity and length-scale fields.

Findings

TDA reveals localized, short-lived flow variations more effectively than conventional methods.

Wasserstein-distance heatmaps provide clear signatures of strong turbulent fluctuations.

The approach enhances detection of intermittency in turbulent regimes.

Abstract

A central challenge in hydrodynamic turbulence is identifying precisely when, and at which length scales, strong turbulent fluctuations (STFs) emerge and develop into intermittent events, which are often obscured by conventional statistical diagnostics. We address this problem by applying a Topological Data Analysis (TDA) framework to reveal the spatiotemporal signatures of intermittency in low-resolution ($128^3$) helically rotating turbulent flows. Vorticity magnitude and length-scale (eddy size) fields are used as scalar observables for TDA: vorticity characterizes rotational dynamics that generate multiscale flow structures, while length-scale fields encode the scales at which intermittent activity arises. Their evolving topology is quantified using persistence diagrams and Wasserstein-distance metrics. Compared with traditional statistical approaches, this framework is more sensitive to localized and short-lived flow variations, enabling clearer detection of intermittent behavior. Pronounced variations in Wasserstein-distance heatmaps provide direct signatures of STFs across space and time. Together, these results demonstrate that TDA offers an effective complementary tool for detecting STFs that lead to intermittency within turbulent regime.