  Generative Adversarial Networks (GANs) have been widely used for generating
photo-realistic images. A variant of GANs called super-resolution GAN (SRGAN)
has already been used successfully for image super-resolution where low
resolution images can be upsampled to a $4\times$ larger image that is
perceptually more realistic. However, when such generative models are used for
data describing physical processes, there are additional known constraints that
models must satisfy including governing equations and boundary conditions. In
general, these constraints may not be obeyed by the generated data. In this
work, we develop physics-based methods for generative enrichment of turbulence.
We incorporate a physics-informed learning approach by a modification to the
loss function to minimize the residuals of the governing equations for the
generated data. We have analyzed two trained physics-informed models: a
supervised model based on convolutional neural networks (CNN) and a generative
model based on SRGAN: Turbulence Enrichment GAN (TEGAN), and show that they
both outperform simple bicubic interpolation in turbulence enrichment. We have
also shown that using the physics-informed learning can also significantly
improve the model's ability in generating data that satisfies the physical
governing equations. Finally, we compare the enriched data from TEGAN to show
that it is able to recover statistical metrics of the flow field including
energy metrics and well as inter-scale energy dynamics and flow morphology.
