A method capable of comparing and analyzing the spatio-temporal structures of unsteady flow fields has not yet been established. Temporal analyses of unsteady flow fields are often done after the data of the fields are reduced to low-dimensional quantities such as forces acting on objects. Such an approach is disadvantageous as information about the flow field is lost. There are several data-driven low-dimensional representation methods that preserve the information of spatial structure; however, their use is limited due to their linearity. In this paper, we propose a method for analyzing the time series data of unsteady flow fields. We firstly propose a data-driven nonlinear low-dimensional representation method for unsteady flow fields that preserves its spatial structure; this method uses a convolutional autoencoder, which is a deep learning technique. In our proposed method, the spatio-temporal structure can be represented as a trajectory in a low-dimensional space using the visualization technique originally proposed for dynamic networks. We applied the proposed method to unsteady flows around a two-dimensional airfoil and demonstrated that it could briefly represents the changes in the spatial structure of the unsteady flow field over time. This method was demonstrated to also be able to visualize changes in the quasi-periodic state of the flow when the angle of attack of the airfoil was changed. Furthermore, we demonstrated that this method is able to compare flow fields that are constructed using different conditions such as different Reynolds numbers and angles of attack.

We focus on the qualitative but widely used method of tuft flow visualization, and propose a method for quantifying it using information technology. By applying stereo image processing and computer vision, the three-dimensional (3D) flow direction in a real environment can be obtained quantitatively. In addition, we show that the flow can be divided temporally by performing appropriate machine learning on the data. Acquisition of flow information in real environments is important for design development, but it is generally considered difficult to apply simulations or quantitative experiments to such environments. Hence, qualitative methods including the tuft method are still in use today. Although attempts have been made previously to quantify such methods, it has not been possible to acquire 3D information. Furthermore, even if quantitative data could be acquired, analysis was often performed empirically or qualitatively. In contrast, we show that our method can acquire 3D information and analyze the measured data quantitatively.

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