Convolutional-network models to predict wall-bounded turbulence from wall quantities

TL;DR

This paper develops convolutional neural network models to predict two-dimensional velocity fluctuations in turbulent flow from wall measurements, outperforming linear methods and enabling transfer learning across different flow conditions.

Contribution

Introduces two CNN-based models, FCN and FCN-POD, for nonlinear prediction of turbulence fields from wall data, demonstrating superior performance over linear methods and exploring transfer learning capabilities.

Findings

Both models outperform extended proper orthogonal decomposition (EPOD).

FCN predicts near-wall turbulence more accurately, while FCN-POD excels at larger wall-normal distances.

Transfer learning achieves comparable performance with reduced training data.

Abstract

Two models based on convolutional neural networks are trained to predict the two-dimensional velocity-fluctuation fields at different wall-normal locations in a turbulent open channel flow, using the wall-shear-stress components and the wall pressure as inputs. The first model is a fully-convolutional neural network (FCN) which directly predicts the fluctuations, while the second one reconstructs the flow fields using a linear combination of orthonormal basis functions, obtained through proper orthogonal decomposition (POD), hence named FCN-POD. Both models are trained using data from two direct numerical simulations (DNS) at friction Reynolds numbers $Re_{\tau} = 180$ and $550$. Thanks to their ability to predict the nonlinear interactions in the flow, both models show a better prediction performance than the extended proper orthogonal decomposition (EPOD), which establishes a linear relation between input and output fields. The performance of the various models is compared based on predictions of the instantaneous fluctuation fields, turbulence statistics and power-spectral densities. The FCN exhibits the best predictions closer to the wall, whereas the FCN-POD model provides better predictions at larger wall-normal distances. We also assessed the feasibility of performing transfer learning for the FCN model, using the weights from $Re_{\tau}=180$ to initialize those of the $Re_{\tau}=550$ case. Our results indicate that it is possible to obtain a performance similar to that of the reference model up to $y^{+}=50$, with $50\%$ and $25\%$ of the original training data. These non-intrusive sensing models will play an important role in applications related to closed-loop control of wall-bounded turbulence.