Simulations of turbulent fluid flow around long cylindrical structures are computationally expensive because of the vast range of length scales, requiring simplifications such as dimensional reduction. Current dimensionality reduction techniques such as strip-theory and depth-averaged methods do not take into account the natural flow dissipation mechanism inherent in the small-scale three-dimensional (3-D) vortical structures. We propose a novel flow decomposition based on a local spanwise average of the flow, yielding the spanwise-averaged Navier–Stokes (SANS) equations. The SANS equations include closure terms accounting for the 3-D effects otherwise not considered in 2-D formulations. A supervised machine-learning (ML) model based on a deep convolutional neural network provides closure to the SANS system. A-priori results show up to 92% correlation between target and predicted closure terms; more than an order of magnitude better than the eddy viscosity model correlation. The trained ML model is also assessed for different Reynolds regimes and body shapes to the training case where, despite some discrepancies in the shear-layer region, high correlation values are still observed. The new SANS equations and ML closure model are also used for a-posteriori prediction. While we find evidence of known stability issues with long time ML predictions for dynamical systems, the closed SANS simulations are still capable of predicting wake metrics and induced forces with errors from 1-10%. This results in approximately an order of magnitude improvement over standard 2-D simulations while reducing the computational cost of 3-D simulations by 99.5%.

A machine-learning based closure is explored for the prediction of the turbulent wake of flow past a circular cylinder at a high Reynolds number. We show that classic turbulence closures based on the turbulent-viscosity hypothesis are not capable of modelling the non-linear relationship between the mean quantities and the target turbulent fields. Instead, different multiple-input multiple-output auto-encoder convolutional neural networks are explored in this work to develop a data-driven closure. A detailed hyper-parameter study is completed including network architecture, loss functions and input sets, among others. A-priori results show 80% to 90% correlation coefficients between target and predicted turbulent fields of previously unseen data. High correlation coefficients are rapidly achieved by networks with a large number of trainable parameters, whereas smaller networks require more training epochs. The integration of the model in live simulations is theoretically discussed from its stability standpoint as well as preliminary physics-based constraints ideas to provide more stable data-driven closures.

Turbulent flow evolution and energy cascades are significantly different in two-dimensional (2-D) and three-dimensional (3-D) flows. Studies have investigated these differences in obstacle-free turbulent flows, but solid boundaries have an important impact on the cross-over from 3-D to 2-D turbulence dynamics. In this work, we investigate the span effect on the turbulence nature of flow past a circular cylinder at . It is found that even for highly anisotropic geometries, 3-D small-scale structures detach from the walls. Additionally, the natural large-scale rotation of the Kármán vortices rapidly two-dimensionalise those structures if the span is 50Â % of the diameter or less. We show this is linked to the span being shorter than the Mode B instability wavelength. The conflicting 3-D small-scale structures and 2-D Kármán vortices result in 2-D and 3-D turbulence dynamics which can coexist at certain locations of the wake depending on the domain geometric anisotropy.