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Oceanic eddies are ubiquitous in global oceans and play a major role in ocean energy transfer and nutrients distribution, thus being significant for understanding ocean current circulation and marine climate change. They are characterized by a combination of high-speed vertical rotations and horizontal movements, leading to irregular three-dimensional spiral structures. While the ability to detect eddies automatically and remotely is crucial to monitoring important spatial-temporal dynamics, existing methods are inaccurate because eddies are highly dynamic and the underlying physical processes are not well understood. Typically, remote sensing is used to detect eddies based on physical parameters, geometrics or other handcrafted features. In this paper, we show how Deep Learning may be used to reliably extract higher-level features and then fuse multi-scale features to identify eddies, regardless of their structures and scales. We learn eddy features using two principal component analysis convolutional layers, then perform a non-linear transformation of the features through a binary hashing layer and block-wise histograms. To handle the difficult problem of spatial variability across synthetic aperture radar (SAR) images, we introduce a spatial pyramid model to allow multi-scale features fusion. Finally, a linear support vector machine classifier recognizes the eddies. Our method, dubbed DeepEddy, is benchmarked against a dataset of 20,000 SAR image samples, achieving a 97.8 +/- 1% accuracy of detection.