  We use machine learning to perform super-resolution analysis of grossly
under-resolved turbulent flow field data to reconstruct the high-resolution
flow field. Two machine-learning models are developed; namely the convolutional
neural network (CNN) and the hybrid Downsampled Skip-Connection Multi-Scale
(DSC/MS) models. These machine-learning models are applied to two-dimensional
cylinder wake as a preliminary test and show remarkable ability to reconstruct
laminar flow from low-resolution flow field data. We further assess the
performance of these models for two-dimensional homogeneous turbulence. The CNN
and DSC/MS models are found to reconstruct turbulent flows from extremely
coarse flow field images with remarkable accuracy. For the turbulent flow
problem, the machine-leaning based super-resolution analysis can greatly
enhance the spatial resolution with as little as 50 training snapshot data,
holding great potential to reveal subgrid-scale physics of complex turbulent
flows. With the growing availability of flow field data from high-fidelity
simulations and experiments, the present approach motivates the development of
effective super-resolution models for a variety of fluid flows.
