Predicting the Temporal Dynamics of Turbulent Channels through Deep Learning
Abstract: The interest towrds machine learning applied to turbulence has experienced a fast-paced growth in the last years. Thanks to deep-learning algorithms, flow-control stratigies have been designed, as well as tools to model and reproduce the most relevant turbulent features. In particular, the success of recurrent neural networks (RNNs) has been demonstrated in many recent studies and applications. The main objective of this project is to assess the capability of these networks to reproduce the temporal evolution of a minimal turbulent channel flow. We first obtain a data-driven model based on a modal decomposition in the Fourier domain (FFT-POD) on the time series sampled from the flow. This particular case of turbulent flow allows us to accurately simulate the most relevant coherent structures close to the wall. Long-short-term-memory (LSTM) networks and a Koopman-based framework (KNF) are trained to predict the temporal dynamics of the minimal channel flow modes. Tests with different configurations highlight the limits of the KNF method compared to the LSTM, given the complexity of the data-driven model. Long-term prediction for LSTM show excellent agreement from the statistical point of view, with errors below 2% for the best models. Furthermore, the analysis of the chaotic behaviour thorugh the use of the Lyapunov exponent and of the dynamic behaviour through Pointcaré maps emphasizes the ability of LSTM to reproduce the nature of turbulence. Alternative reduced-order models (ROMS), based on the identification of different turbulent structures, are explored and they continue to show a good potential in predicting the temporal dynamics of the minimal channel.
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