Connecting Lyapunov Vectors with the Pattern Dynamics of Chaotic Rayleigh-B\'enard Convection

TL;DR

This paper investigates the chaotic behavior of Rayleigh-Bénard convection by analyzing the relationship between Lyapunov vectors and flow pattern dynamics using advanced numerical simulations and pattern diagnostics.

Contribution

It introduces a novel approach linking Lyapunov vectors with flow pattern diagnostics to better understand chaos in convection systems.

Findings

Strong correlation between Lyapunov vector magnitude and flow pattern features

Effective use of pattern diagnostics to predict regions of high chaos

Quantitative analysis of pattern dynamics using precision-recall metrics

Abstract

We explore the chaotic dynamics of Rayleigh-B\'enard convection using large-scale, parallel numerical simulations for experimentally accessible conditions. We quantify the connections between the spatiotemporal dynamics of the leading-order Lyapunov vector and different measures of the flow field pattern's topology and dynamics. We use a range of pattern diagnostics to describe the spatiotemporal features of the flow field structures which includes many of the traditional diagnostics used to describe convection as well as some diagnostics tailored to capture the dynamics of the patterns. Using precision-recall curves, we quantify the complex relationship between the pattern diagnostics and the regions where the magnitude of the leading-order Lyapunov vector is significant.