Machine learning-based vorticity evolution and super-resolution of homogeneous isotropic turbulence using wavelet projection

Abstract

A wavelet-based machine learning method is proposed for predicting the time evolution of homogeneous isotropic turbulence where vortex tubes are preserved. Three-dimensional convolutional neural networks and long short-term memory are trained with a time series of direct numerical simulation (DNS) data of homogeneous isotropic turbulence at the Taylor microscale Reynolds number 92. The predicted results are assessed by using the flow visualization of vorticity and statistics, e.g., probability density functions of vorticity and enstrophy spectra. It is found that the predicted results are in good agreement with DNS results. The small-scale flow topology considering the second and the third invariants of the velocity gradient tensor likewise shows an approximate match. Furthermore, we apply the pre-trained neural networks to coarse-grained vorticity data using super-resolution. It is shown that the super-resolved flow field well agrees with the reference DNS field, and thus small-scale information and vortex tubes are well regenerated.