Data-driven forecasting of high-dimensional 3D Rayleigh-Benard turbulence using Hankel-DMD

Dynamic Mode Decomposition (DMD) with Takens’ delay-embedding (Hankel-DMD) is used to forecast the spatio-temporal evolution of the fully turbulent flow in a high-dimensional 3D Rayleigh-Benard convection system at the Rayleigh number of one million. A long dataset is produced using DNS, which is then employed to build a reduced-order model for the horizontally averaged temperature anomaly (which is a function of height z and time t) using Hankel-DMD, which is data-driven and model-free. Compared with the DNS data, the reduced model can fairly accurately predict the spatio-temporal evolution of the temperature anomaly and the leading principal components for a few hundred advective time scale before the prediction diverges from DNS and decays to zero. The impact of the length of the dataset used to build the reduced model, the embedded delay, and the reduced dimension on the prediction accuracy and prediction limit are investigated in detail to find the optimal range for these parameters and understand the capabilities and limitations of this approach.