A priori assessment of rotational invariance in multiscale convolutional neural network-based subgrid-scale model for wall-bounded turbulent flows

This study presents a novel rotationally invariant data-driven subgrid-scale (SGS) models for large-eddy simulation (LES) of wall-bounded turbulent flows. Previous studies have typically imposed invariance via scalar invariants or the canonical form (e.g. based on its eigenframe of rate-of-strain tensor), whereas this study introduces a modified deep neural network (DNN) architecture that inherently respects rotational invariance. Building upon the multiscale convolutional neural network SGS model (MSC model) developed by the authors, which outputs SGS stress tensors ( $ \tau _{ij} $ τij), the DNN architecture is modified to satisfy the principle of material objectivity by removing bias terms and batch normalisation layers while incorporating a spatial transformer network algorithm. The proposed data-driven SGS models were trained on a turbulent channel flow at $ {\rm Re}_\tau = 180 $ Reτ=180 and evaluated under both non-rotated and rotated input conditions. The models accurately predicted $ \tau _{ij} $ τij and key turbulence statistics, including SGS dissipation, backscatter, and SGS transport, for non-rotated inputs. In addition, in the case of rotated inputs, they significantly outperformed the baseline MSC model, reducing the mean absolute error (MAE) of the $ \tau _{12} $ τ12 predictions from 0.402 to below 0.047 and achieving up to two orders of magnitude lower MAE in the turbulence statistics. Moreover, the models effectively generalise to unseen rotated inputs, accurately predicting $ \tau _{ij} $ τij despite the input configurations not being encountered during the training, indicating the general applicability of the proposed model. These findings highlight that the proposed data-driven SGS models address the key limitations of common data-driven SGS approaches, particularly their sensitivity to rotated input conditions. It also marks an important advancement in data-driven SGS modelling for LES, particularly in flow configurations where rotational effects are non-negligible.