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We introduce a wall model for large-eddy simulation (WMLES) applicable to rough surfaces with Gaussian and non-Gaussian distributions for both the transitionally and fully rough regimes. The model is applicable to arbitrary complex geometries where roughness elements are assumed to be underresolved, i.e. subgrid-scale roughness. The wall model is implemented using a multi-hidden-layer feedforward neural network, with the mean geometric properties of the roughness topology and near-wall flow quantities serving as input. The optimal set of non-dimensional input features is identified using information theory, selecting variables that maximize information about the output while minimizing redundancy among inputs. The model also incorporates a confidence score based on Gaussian process modelling, enabling the detection of potentially low model performance for untrained rough surfaces. The model is trained using a direct numerical simulation (DNS) roughness database comprising approximately 200 cases. The roughness geometries for the database are selected from a large repository through active learning. This approach ensures that the rough surfaces incorporated into the database are the most informative, achieving higher model performance with fewer DNS cases compared with passive learning techniques. The performance of the model is evaluated bothaprioriandaposterioriin WMLES of turbulent channel flows with rough walls. Over 550 channel flow cases are considered, including untrained roughness geometries, roughness Reynolds numbers and grid resolutions for both transitionally and fully rough regimes. Our rough-wall model offers higher accuracy than existing models, generally predicting wall shear stress within an accuracy range of 1%–15 %. The performance of the model is also assessed on a high-pressure turbine blade with two different rough surfaces. We show that the new wall model predicts the skin friction and the mean velocity deficit induced by the rough surface on the blade within 1%–10 % accuracy except the region with transition or shock waves. This work extends the building-block flow wall model (BFWM) introduced by Lozano-Durán & Bae (2023.J. Fluid Mech.963, A35) for smooth walls, expanding the BFWM framework to account for rough-wall scenarios. 

Not all the information in a turbulent field is relevant for understanding particular regions or variables in the flow. Here, we present a method for decomposing a source field into its informative$$\boldsymbol {\varPhi }_{I}(\boldsymbol {x},t)$$and residual$$\boldsymbol {\varPhi }_{R}(\boldsymbol {x},t)$$components relative to another target field. The method is referred to as informative and non-informative decomposition (IND). All the necessary information for physical understanding, reduced-order modelling and control of the target variable is contained in$$\boldsymbol {\varPhi }_{I}(\boldsymbol {x},t)$$, whereas$$\boldsymbol {\varPhi }_{R}(\boldsymbol {x},t)$$offers no substantial utility in these contexts. The decomposition is formulated as an optimisation problem that seeks to maximise the time-lagged mutual information of the informative component with the target variable while minimising the mutual information with the residual component. The method is applied to extract the informative and residual components of the velocity field in a turbulent channel flow, using the wall shear stress as the target variable. We demonstrate the utility of IND in three scenarios: (i) physical insight into the effect of the velocity fluctuations on the wall shear stress; (ii) prediction of the wall shear stress using velocities far from the wall; and (iii) development of control strategies for drag reduction in a turbulent channel flow using opposition control. In case (i), IND reveals that the informative velocity related to wall shear stress consists of wall-attached high- and low-velocity streaks, collocated with regions of vertical motions and weak spanwise velocity. This informative structure is embedded within a larger-scale streak–roll structure of residual velocity, which bears no information about the wall shear stress. In case (ii), the best-performing model for predicting wall shear stress is a convolutional neural network that uses the informative component of the velocity as input, while the residual velocity component provides no predictive capabilities. Finally, in case (iii), we demonstrate that the informative component of the wall-normal velocity is closely linked to the observability of the target variable and holds the essential information needed to develop successful control strategies. 

Predicting extreme events in chaotic systems, characterized by rare but intensely fluctuating properties, is of great importance due to their impact on the performance and reliability of a wide range of systems. Some examples include weather forecasting, traffic management, power grid operations, and financial market analysis, to name a few. Methods of increasing sophistication have been developed to forecast events in these systems. However, the boundaries that define the maximum accuracy of forecasting tools are still largely unexplored from a theoretical standpoint. Here, we address the question: What is the minimum possible error in the prediction of extreme events in complex, chaotic systems? We derive the minimum probability of error in extreme event forecasting along with its information-theoretic lower and upper bounds. These bounds are universal for a given problem, in that they hold regardless of the modeling approach for extreme event prediction: from traditional linear regressions to sophisticated neural network models. The limits in predictability are obtained from the cost-sensitive Fano’s and Hellman’s inequalities using the Rényi entropy. The results are also connected to Takens’ embedding theorem using the information can’t hurt inequality. Finally, the probability of error for a forecasting model is decomposed into three sources: uncertainty in the initial conditions, hidden variables, and suboptimal modeling assumptions. The latter allows us to assess whether prediction models are operating near their maximum theoretical performance or if further improvements are possible. The bounds are applied to the prediction of extreme events in the Rössler system and the Kolmogorov flow.