Predicting the skin friction’s evolution in a forced turbulent channel flow

The present paper reports on the ability of neural networks (NN) and linear stochastic estimation (LSE) tools to predict the evolution of skin friction in a minimal turbulent channel ($R{e}_{\tau }=165$) after applying an actuation near the wall that is localized in space and time. Two different NN architectures are compared, namely multilayer perceptrons (MLP) and convolutional neural networks (CNN). The paper describes the effect that the predictive horizon and the type/size/number of wall-based sensors have on the performance of each estimator. The performance of MLPs and LSEs is very similar, and becomes independent of the sensor’s size when they are smaller than 60 wall units. For sufficiently small sensors, the CNN outperforms MLPs and LSEs, suggesting that CNNs are able incorporate some of the non-linearities of the near-wall cycle in their prediction of the skin friction evolution after the actuation. Indeed, the CNN is the only architecture able to achieve reasonable predictive capabilities using pressure sensors only. The predictive horizon has a strong effect on the predictive capacity of both NN and LSE, with a Pearson correlation coefficient that varies from 0.95 for short times (i.e., of the order of the actuation time) to less than 0.4 for times of the order of an eddy turn-over time. The analysis of the weights and filters in the LSE and NNs show that all estimators are targeting wall-signatures consistent with streaks, which is interpreted as the streak being the most causal feature in the near-wall cycle for the present forcing.