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The advancement of high-performance computing has enabled the generation of large direct numerical simulation (DNS) datasets of turbulent flows, driving the need for efficient compression/decompression techniques that reduce storage demands while maintaining fidelity. Traditional methods, such as the discrete wavelet transform, cannot achieve compression ratios of 8 or higher for complex turbulent flows without introducing significant encoding/decoding errors. On the other hand, super-resolution generative adversarial networks (SR-GANs) can accurately reconstruct fine-scale features, preserving velocity gradients and structural details, even at a compression ratio of 512, thanks to the adversarial training enabled by the discriminator. Their high training time is significantly reduced with a progressive transfer learning approach and, once trained, they can be applied independently of the Reynolds number. It is demonstrated that SR-GANs can enhance dataset temporal resolution without additional simulation overhead by generating high-quality intermediate fields from compressed snapshots. The SR-GAN discriminator can reliably evaluate the quality of decoded fields, ensuring fidelity even in the absence of original DNS fields. Hence, SR-GAN-based compression/decompression methods present a highly efficient and scalable alternative for large-scale DNS storage and transfer, offering substantial advantages in terms of compression efficiency, reconstruction fidelity, and temporal resolution enhancement.