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

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--Bénard 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.

Figures (13)

• Figure 1: (a) Velocity field at a random instant for $Ra=10^8$ and $Pr=4.3$. Streamlines of the velocity field $\bf{u}$ are superposed over the color map. (b) Time evolution of angular momentum $L_z(t)/\text{max}|L_z(t)|$.
• Figure 2: A cartoon of the data-driven framework applied to the full DNS of RBC.
• Figure 3: Linear dimension reduction: (a) Spectrum of POD eigenvalues $\lambda_i$. (b) Comparison of the Reynolds stress component $\langle u_x'u_y' \rangle$ from DNS and POD reconstruction. (c) Temporal evolution of the modal amplitudes, $a_i(t)$, for the three leading POD modes. (d) Decomposition of the first three POD coefficients into slow and fast components using Gaussian filtering. Solid line represents slow components while dash line represents fast components.
• Figure 4: Non linear dimension reduction: (a) Relative reconstruction error as a function of latent dimension $d_h^{\text{slow}}$ for slow-scale autoencoder. (b) Relative reconstruction error as a function of latent dimension $d_h^{\text{fast}}$ for fast-scale autoencoder. (c) Temporal evolution of the relative reconstruction error for POD, a single-stage autoencoder with $d_h=20$, and the proposed multiscale autoencoder with total latent dimension $d_h=20$.
• Figure 5: (a) Comparison of angular momentum $L_z$ and reconstructed velocity and temperature fields at select time shown in the top panel. (b-d) Reynolds stresses of $\langle u_x'u_x' \rangle$, $\langle u_x'u_y' \rangle$ and $\langle u_y'u_y' \rangle$ among DNS, POD, and multiscale autoencoder, corresponding to panels b to d, respectively.