Spatio-Temporal Mode Decomposition for Unsteady Flow with Convolutional Neural Network

We develop CNN Mode Decomposition Models, to perform spatio-temporal mode decompositions of flow around a cylinder at Reynolds number, Re_D=U_∞D/ν=100, as an example of unsteady flows. The input of the model, which is a time series of flow field during one cycle of vortex shedding, are mapped into 1, 2 or 3 modes in the latent space, and then a time series of each decomposed flow field is reconstructed from each mode. The models with only 1, 2 and 3 modes can represent the flow field for one cycle of vortex shedding with high accuracy. For the model with 2 modes, both the decomposed flow fields are unsteady. The first decomposed field represents large unsteady structures similar to the Karman vortices. The second decomposed field includes similar-size and opposite-phase structures in the wake and compensates the discrepancies. For 3 modes model, 1st decomposed field shows a steady flow field, similar to the time-averaged flow field. Large unsteady structures, corresponding to the Karman vortices in the wake region, appear in 2nd decomposed field. 3rd decomposed field consists of unsteady structures of opposite phase, smaller size, and smaller magnitude in the wake.