Quantifying Spatiotemporal Chaos in Rayleigh-B\'enard Convection

TL;DR

This paper uses numerical simulations to analyze high-dimensional chaos in Rayleigh-Bénard convection, focusing on Lyapunov exponents and vectors to understand pattern dynamics and system size effects.

Contribution

It introduces a detailed analysis of Lyapunov spectra and vectors in fluid convection, revealing how chaos characteristics evolve with system parameters and size.

Findings

Lyapunov exponents are positively correlated with the leading exponent during chaos.

A transition from boundary to bulk dominated dynamics occurs with increasing system size.

The fractal dimension varies with system parameters, indicating different chaotic regimes.

Abstract

Using large-scale parallel numerical simulations we explore spatiotemporal chaos in Rayleigh-B\'enard convection in a cylindrical domain with experimentally relevant boundary conditions. We use the variation of the spectrum of Lyapunov exponents and the leading order Lyapunov vector with system parameters to quantify states of high-dimensional chaos in fluid convection. We explore the relationship between the time dynamics of the spectrum of Lyapunov exponents and the pattern dynamics. For chaotic dynamics we find that all of the Lyapunov exponents are positively correlated with the leading order Lyapunov exponent and we quantify the details of their response to the dynamics of defects. The leading order Lyapunov vector is used to identify topological features of the fluid patterns that contribute significantly to the chaotic dynamics. Our results show a transition from boundary dominated dynamics to bulk dominated dynamics as the system size is increased. The spectrum of Lyapunov exponents is used to compute the variation of the fractal dimension with system parameters to quantify how the underlying high-dimensional strange attractor accommodates a range of different chaotic dynamics.