Cascade-Net for predicting cylinder wake at Reynolds numbers ranging from subcritical to supercritical regime

The application of machine learning techniques embedded with fluid mechanics has gained significant attention due to their exceptional ability to tackle intricate flow dynamics problems. In this study, an energy-cascade-conceptualized network termed Cascade-Net is proposed. This model is grounded in generative adversarial networks to predict the spatiotemporal fluctuating velocity in the near-wall wake of a circular cylinder in a physics-informed manner. A comprehensive dataset is obtained by wind tunnel testing, comprising the near-wake velocity field and wall pressure of a rough circular cylinder with Reynolds numbers from subcritical to supercritical regimes. By leveraging convolutional neural networks, the Cascade-Net utilizes the pressure data, Reynolds numbers, and a few of velocity measured in the wake field to predict the spatiotemporal fluctuating velocity. The velocity fluctuations are predicted hierarchically at different resolved scales, ensuring that the energy cascade in turbulence is accurately simulated. The results show that the Cascade-Net presents good generalization performance and is capable of accurately predicting fluctuating velocity fields and the second-order moments in both extrapolation and interpolation cases at various Reynolds numbers. The mechanism of Cascade-Net in prediction is also investigated by parametric analysis in the convolutional layer and spatial attention gate, manifesting that the Cascade-Net is heavily dependent on the velocity characteristics of the larger resolved scale adjacent to target smaller scales to prediction, which interprets the success of Cascade-Net in capturing the intricate physics of the cylinder wake.