Low-dimensional multiscale dynamics of intermittent reversals in turbulent Rayleigh-Benard convection

TL;DR

This paper demonstrates that multiscale interactions in turbulent Rayleigh-Benard convection can be captured by a low-dimensional model, enabling efficient prediction of complex chaotic dynamics and rare flow reversals.

Contribution

The authors introduce a multiscale latent dynamical framework that reduces high-dimensional turbulence data to a 20-dimensional model while preserving key dynamics.

Findings

Model reproduces flow structures and long-term statistics accurately.

Explicit slow-fast branch modeling improves prediction of reversals.

Reduces system dimension from 10^5 to 20 while maintaining essential dynamics.

Abstract

We investigate whether a strongly turbulent flow with intermittent large-scale reorganizations admits a compact state-space description. As a representative high-dimensional chaotic system we consider two-dimensional Rayleigh--B\'enard convection at high Rayleigh number, whose dynamics are governed by multiscale interactions and rare reversals of the large-scale circulation. We introduce a multiscale latent dynamical framework in which the temporal evolution is first decomposed into slow and fast components and each is mapped to a nonlinear low-dimensional representation that is evolved by a closed dynamical system, showing that temporal scale separation alone enables an autonomous low-dimensional description of the chaotic dynamics. This strategy reduces the system from an original state space dimension of $O(10^5)$ to a compact 20-dimensional latent space while preserving the essential multiscale dynamics. Our model reproduces the main trends of instantaneous flow structures, Reynolds stresses, energy autocorrelations, and long-time quantities such as angular momentum and wall observables, Furthermore, a waiting time analysis of flow reversals validates the statistical alignment of model prediction and DNS results. The explicit modeling of separate slow and fast branches yields significantly improved accuracy in both short-time flow structures and long-time reversal statistics, compared to single-branch alternatives. These results provide evidence that intermittent turbulent dynamics can evolve on a compact manifold when their intrinsic multiscale structure is respected, offering a route toward reduced dynamical descriptions and prediction of rare events in high-dimensional chaos.