  We present a new nonlinear mode decomposition method to visualize the
decomposed flow fields, named the mode decomposing convolutional neural network
autoencoder (MD-CNN-AE). The proposed method is applied to a flow around a
circular cylinder at $Re_D=100$ as a test case. The flow attributes are mapped
into two modes in the latent space and then these two modes are visualized in
the physical space. Because the MD-CNN-AEs with nonlinear activation functions
show lower reconstruction errors than the proper orthogonal decomposition
(POD), the nonlinearity contained in the activation function is considered the
key to improve the capability of the model. It is found by applying POD to each
field decomposed using the MD-CNN-AE with hyperbolic tangent activation that a
single nonlinear MD-CNN-AE mode contains multiple orthogonal bases, in contrast
to the linear methods, i.e., POD and the MD-CNN-AE with linear activation. We
further assess the proposed MD-CNN-AE by applying it to a transient process of
a circular cylinder wake in order to examine its capability for flows
containing high-order spatial modes. The present results suggest a great
potential for the nonlinear MD-CNN-AE to be used for feature extraction of flow
fields in lower dimension than POD, while retaining interpretable relationships
with the conventional POD modes.
