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Data reconstruction of rotating turbulent snapshots is investigated utilizingdata-driven tools. This problem is crucial for numerous geophysicalapplications and fundamental aspects, given the concurrent effects of directand inverse energy cascades, which lead to non-Gaussian statistics at bothlarge and small scales. Data assimilation also serves as a tool to rankphysical features within turbulence, by evaluating the performance ofreconstruction in terms of the quality and quantity of the information used.Additionally, benchmarking various reconstruction techniques is essential toassess the trade-off between quantitative supremacy, implementation complexity,and explicability. In this study, we use linear and non-linear tools based onthe Proper Orthogonal Decomposition (POD) and Generative Adversarial Network(GAN) for reconstructing rotating turbulence snapshots with spatial damages(inpainting). We focus on accurately reproducing both statistical propertiesand instantaneous velocity fields. Different gap sizes and gap geometries areinvestigated in order to assess the importance of coherency and multi-scaleproperties of the missing information. Surprisingly enough, concerningpoint-wise reconstruction, the non-linear GAN does not outperform one of thelinear POD techniques. On the other hand, supremacy of the GAN approach isshown when the statistical multi-scale properties are compared. Similarly,extreme events in the gap region are better predicted when using GAN. Thebalance between point-wise error and statistical properties is controlled bythe adversarial ratio, which determines the relative importance of thegenerator and the discriminator in the GAN training. Robustness against themeasurement noise is also discussed.

Multi-scale data reconstruction of turbulent rotating flows with Gappy POD, Extended POD and Generative Adversarial Networks