In this study, a deep learning-based approach is applied with the aim of reconstructing high-resolution turbulent flow fields using minimal flow field data. A multi-scale enhanced super-resolution generative adversarial network with a physics-based loss function is introduced as a model to reconstruct the high-resolution flow fields. The model capability to reconstruct high-resolution laminar flows is examined using direct numerical simulation data of laminar flow around a square cylinder. The results reveal that the model can accurately reproduce the high-resolution flow fields even when limited spatial information is provided. The DNS data of turbulent channel flow at two friction Reynolds numbers Reτ=180 and 550 are used to assess the ability of the model to reconstruct the high-resolution wall-bounded turbulent flow fields. The instantaneous and statistical results obtained from the model agree well with the ground truth data, indicating that the model can successfully learn to map the coarse flow fields to the high-resolution ones. Furthermore, the possibility of performing transfer learning for the case of turbulent channel flow is thoroughly examined. The results indicate that the amount of the training data and the time required for training can be effectively reduced without affecting the performance of the model. The computational cost of the proposed model is also found to be effectively low. These results demonstrate that using high-fidelity training data with physics-guided generative adversarial network-based models can be practically efficient in reconstructing high-resolution turbulent flow fields from extremely coarse data.

This study proposes a newly developed deep-learning-based method to generate turbulent inflow conditions for spatially developing turbulent boundary layer (TBL) simulations. A combination of a transformer and a multiscale-enhanced super-resolution generative adversarial network is utilised to predict velocity fields of a spatially developing TBL at various planes normal to the streamwise direction. Datasets of direct numerical simulation (DNS) of flat plate flow spanning a momentum thickness-based Reynolds number, $Re_\theta = 661.5\unicode{x2013}1502.0$ , are used to train and test the model. The model shows a remarkable ability to predict the instantaneous velocity fields with detailed fluctuations and reproduce the turbulence statistics as well as spatial and temporal spectra with commendable accuracy as compared with the DNS results. The proposed model also exhibits a reasonable accuracy for predicting velocity fields at Reynolds numbers that are not used in the training process. With the aid of transfer learning, the computational cost of the proposed model is considered to be effectively low. Furthermore, applying the generated turbulent inflow conditions to an inflow–outflow simulation reveals a negligible development distance for the TBL to reach the target statistics. The results demonstrate for the first time that transformer-based models can be efficient in predicting the dynamics of turbulent flows. They also show that combining these models with generative adversarial networks-based models can be useful in tackling various turbulence-related problems, including the development of efficient synthetic-turbulent inflow generators.

Turbulence is a complex phenomenon that has a chaotic nature with multiple spatio-temporal scales, making predictions of turbulent flows a challenging topic. Nowadays, an abundance of high-fidelity databases can be generated by experimental measurements and numerical simulations, but obtaining such accurate data in full-scale applications is currently not possible. This motivates utilising deep learning on subsets of the available data to reduce the required cost of reconstructing the full flow in such full-scale applications. Here, we develop a generative-adversarial-network (GAN)-based model to reconstruct the three-dimensional velocity fields from flow data represented by a cross-plane of unpaired two-dimensional velocity observations. The model could successfully reconstruct the flow fields with accurate flow structures, statistics and spectra. The results indicate that our model can be successfully utilised for reconstructing three-dimensional flows from two-dimensional experimental measurements. Consequently, a remarkable reduction in the complexity of the experimental setup and the storage cost can be achieved.

This study presents a deep learning-based framework to recover high-resolution turbulent velocity fields from extremely low-resolution data at various Reynolds numbers by utilizing the concept of generative adversarial networks. A multiscale enhanced super-resolution generative adversarial network is applied as a model to reconstruct the high-resolution velocity fields, and direct numerical simulation data of turbulent channel flow with large longitudinal ribs at various Reynolds numbers are used to evaluate the performance of the model. The model is found to have the capacity to accurately reconstruct the high-resolution velocity fields from data at two different down-sampling factors in terms of the instantaneous velocity fields, two-point correlations, and turbulence statistics. The results further reveal that the model is able to reconstruct high-resolution velocity fields at Reynolds numbers that fall within the range of the training Reynolds numbers.

Turbulence is a complicated phenomenon because of its chaotic behavior with multiple spatio-temporal scales. Turbulence also has irregularity and diffusivity, making predicting and reconstructing turbulence more challenging. This study proposes a deep-learning approach to reconstruct three-dimensional (3D) high-resolution turbulent flows from spatially-limited data using a 3D enhanced super-resolution generative adversarial networks (3D-ESRGAN). In addition, a novel transfer-learning method based on tricubic interpolation is employed. Turbulent channel flow data at friction Reynolds numbers Reτ = 180 and Reτ = 500 were generated by direct numerical simulation (DNS) and used to estimate the performance of the deep-learning model as well as that of the tricubic interpolation-based transfer learning. The results, including instantaneous velocity fields and turbulence statistics, show that the reconstructed high-resolution data agree well with the reference DNS data. The findings also indicate that the proposed 3D-ESRGAN can reconstruct 3D high-resolution turbulent flows even with limited training data.